IV Minsk International Forum
on Heat and Mass Transfer

 

May 22-26, 2000

A.E. AKSENOVA, V.A. PERVICHKO, V.V. CHUDANOV
AN INTEGRATED APPROACH TO SIMULATION OF HEAT AND MASS EXCHANGE IN COMPLEX DOMAINS
Institute for the Problems of Safe Development of Atomic Power Engineering, Russian Academy of Sciences, Moscow, Russia

A new approach to solving the problems of computational thermal hydrodynamics of an incompressible fluid in a complex domain is presented. Main attention is given to the technology of effective design of multiblock orthogonal grids and construction of high-speed finite - volumetric schemes of solution of heat and mass transfer equations. The construction of complex domains is carried out with the help of the package of computer-aided design for PC of platforms Mechanical Desktop (version 3.0). The created domain is saved in the file of the format IGES, which then is converted in the format for the calculated program of construction of orthogonal grids. The flow patterns on grids constructed with the help of the new technology are given.

A.K. ALEKSEEV
ON THE WALL-TEMPERATURE CONTROL OF FREE CONVECTION
Energiya Rocket-Space Corporation, Korolev, Moscow Region, Russia

The problem of determining the temperature on the lower boundary of a volume of viscous liquid which ensures the prescribed distribution of temperature or velocity is considered. The flow parameters were calculated by means of finite differences using three-dimensional nonstationary Navier-Stokes equations in Boussinesq form. An adjoint problem is used for fast calculation of discrepancy gradient with the calculation time as for a forward problem. The same finite difference method is used for both forward and adjoint problems. The optimization was performed using the conjugate gradient method.

Yu.P. ARESTENKO, N.I. VASILIEV, V.V. GUGUCHKIN* , A.S. TROFIMOV
FLUCTUATIONS OF WALL TEMPERATURES ON HEAT REMOVAL BY A GAS-LIQUID FLOW
Kuban' State Technological University, Krasnodar, Russia

We present techniques and results of experimental investigation of temperature fluctuations near a heated wall in a bubble flow. We obtained amplitude-frequency characteristics for various velocities and gas contents at Reynolds numbers 0-25·10³. It is found that the presence of bubbles in a flow increases the amplitude of temperature fluctuations. An experimental relation is obtained for the effect of gas content on the relative temperature of fluctuation.
*) Deceased

A. ASSEBAN, N. FOMIN, M. LALLEMAND, E. NOGOTOV, J.-B. SAULNIER
NATURAL CONVECTION OVER A HEATED PLATE WITH FORWARD-FACING STEPS
Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer Institute," National Academy of Sciences of Belarus, Minsk, Belarus; Laboratoire d'Etudes Thermique, ENSMA, France

Natural convection of air over a heated plate with forward-facing steps is studied both numerically and experimentally. Numerical modeling of heat transfer processes is based on using the well-known codes, namely FLUENT and CONV, and allows determining and temperature maps in both laminar and turbulent regimes. After validating the data of modeling by comparison with available experimental data, the local heat flux and Nusselt number fields are calculated and averaged heat transfer coefficient is evaluated in terms of relevant dimensionless parameters. Experimentally temperature distribution in natural convective flow were obtained by using a Mach-Zehnder interferometer with direct CCD recording and advanced speckle photography technique.

V.A. BABENKO, P.YA. CHEREPANOV
THIRD- AND FOURTH-ORDER STATISTICAL MOMENTS IN A TURBULENT WAKE DOWNSTREAM OF A PLANE WING PROFILE
Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer Institute," National Academy of Sciences of Belarus, Minsk, Belarus

We investigate statistical moments of the 3rd- and 4th-order in a plane wake downstream of tugged and self-propelled body of wing type. The data obtained experimentally for the moments S_u1 = <u³₁>/<u²₁>^3/2, S_u1 , F₁ = <u⁴₁>/<u²₁>², F₂=<u⁴₂>/<u²₁>², S_t=<t³>/<t²>^3/2, S_t, F_t=<t⁴>/<t²>² <u₂t²>, <u²₂>, t,<u₁u₂t> are compared with their theoretical approximations which are based on calculated 1st- and 2nd-order moments. The behavior of experimentally measured 3rd- and 4th-order statistical moments of velocity and temperature fluctuation fields allows a conclusion that the regime of self-propulsion in a plane wake flow has a specific behavior. 

V.A. BABENKO, P.YA. CHEREPANOV
STATISTICAL 1ST- AND 2ND-ORDER MOMENTS IN A DYNAMIC AND SCALAR TURBULENT WAKE DOWNSTREAM A PLANE WING PROFILE IN THE MODE OF SELF-MOTION
Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer Institute," National Academy of Sciences of Belarus, Minsk, Belarus

We consider the results of comprehensive testing of Kolovandin's turbulence model for a thermally stratified flow downstream a plane wing profile. The data of numerical simulation are compared in detail with a laboratory experiment and conclusions of self-similar analysis. In contrast to the well-known investigations of the turbulence of a momentum-free wake, in the present work the dynamics of turbulence parameters is simulated up to the final stage of degeneration.

R.G. BARANTSEV, D.A. PASHKEVICH, A.V. SHATROV
HEAT TRANSFER IN THE BOUNDARY LAYER OF A REACTING GAS
St.Petersburg State University, St.Petersburg, Russia

We consider a laminar boundary layer in a supersonic flow of a viscous reacting gas near a heated flat plate. The problem is solved by the method of joining asymptotics by means of two-point Pade-approximants. Earlier this method was used to calculate temperatures in the hypersonic boundary layer of a viscous perfect gas. In the present work it is extended to the case of a reacting gas and is discussed from more general viewpoints.

A. BARTULIS, E. SHCHERBININ
HEAT AND MASS TRANSFER IN ROTATING FLOWS WITH CURVED BOUNDARIES
Institute of Physics at the Latvian University, Salaspils, Latvia

The axisymmetrical flow between rotating curved surfaces has been calculated using the local similarity method. Peculiarities of secondary meridional flow at increasing Reynolds number has been found out. It is shown that at a not large and rather a large Reynolds numbers calculation procedure is steady, but in intermediate region a steady solution cannot be obtained. The simulated velocity field has been used for calculating transfer of concentration on the bottom of a cavity.

I.A. BASSINA, M.KH. STRELETS, V.K. SHIKOV
NUMERICAL MODELING OF CONVECTIVE HEAT TRANSFER IN A COMPRESSIBLE TURBULENT BOUNDARY LAYER UNDER EXTREMELY HIGH COOLING
Russian Scientific Center "Applied Chemistry", St.Petersburg; Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow

A systematic comparison of numerical predictions by different turbulence models with experimental data published recently for a compressible turbulent boundary layer of a high-enthalpy air flow (T_eup to 6700 K, P_e up to 5 atm, M_e up to 3.5) is performed. It is shown that conclusions about suitability of some turbulence models previously made for moderate cooling are not justified under the conditions of very high cooling (enthalpy factor 0.01-0.1) in combination with flow compressibility and variability of gas properties.

V.U. BONDARCHUK, A.D. CHORNYI
VERTICAL HEAT AND MASS TRANSFER IN TURBULENT STABLY STRATIFIED FLOWS
Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer Institute," National Academy of Sciences of Belarus, Minsk, Belarus

On the basis of the 2nd-order statistical model numerical simulation of homogeneous shear turbulence in a stably stratified flow is carried out. It is shown that the action of buoyancy without mean shear results in wavy change of turbulent parameters. In the case of joint influence of stable stratification and mean shear directed against a vector of acceleration of gravity the turbulence is suppressed by buoyancy at large Richardson numbers (Ri > 0.3), and it reduces the vertical heat and mass transfer. At mean shear directed along a vector of acceleration of gravity for all the investigated Richardson numbers Ri = 0.04-0.36 the turbulence of flow is increased which results in intensification of vertical heat and mass transfer.

B.F. BOYARSHINOV
HEAT AND MASS TRANSFER IN A BOUNDARY LAYER IN EVAPORATION AND COMBUSTION OF ETHANOL IN A TURBULIZED AIR STREAM
Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

The influence of the dynamic properties of external flow on mass transfer in a boundary layer was investigated experimentally. The air stream turbulence was changed from 1% to 26% with the aid of lattices. The edges of height up to 15 mm were installed at the beginning of the boundary layer. The influence of viscosity was evaluated from comparison of experimental data for cases with combustion and without it. It is revealed that the extremes of mass transfer parameters exist for certain combination of the main stream turbulence level and the height of the edge. Without combustion it is a maximum of evaporation rate. With combustion - the flame breakdown main stream velocity maxima, and also it is the minimum of burning rate. In both cases the multiple changes of mass transfer intensity are noted. The reasons of their appearance are analyzed.

V. BUDARIN
A METHOD OF FINDING EQUATIONS OF MOTION OF A DISCONTINUITY FLOW
Odessa Polytechnic University, Odessa, Ukraine

The method is based on the use of equations of elasticity theory with allowance for the influence of distinctive properties of a liquid (gas) and character of its motion. An example of using the method for finding the equations of motion of a plane and hollow vortex of ideal liquid is given. As a result it is shown that the well-known equation of motion of a plane vortex is valid only in the case of a continuous cross section, and for a hollow vortex a new equation of motion is obtained. The existence of analogy between rotation of a plane solid disk and a plane vortex is shown. The way of experimental production of vortex tube is indicated. Some practical applications of such flows are described.

V.B. BUKHARKIN, G.A. DREITSER, V.M. KRAEV
RESEARCH OF TURBULENT GAS FLOW STRUCTURE UNDER HYDRODYNAMIC INSTABILITY CONDITIONS
Moscow State Aviation Institute, Moscow, Russia

The data are obtained on the structure of a turbulent circular tube gas flow in the case of hydrodynamic unstable influence of averaged velocity longitudinal and radial components fields, their pulsations and correlations. These are supplemented with the data on the influence of stationary conditions on the turbulent viscosity coefficient and heat transfer coefficient. The existence of the zone of greatest changes in the structure parameters is confirmed. It is found that the flow nonisothermicity enhances the influence of hydrodynamic instability. Under nonisothermal boundary conditions, after the removal of the effect, the return of structure characteristics to the stationary influence slow down considerably. A new dimensionless criterion of hydrodynamic instability is suggested.

V.K. BULGAKOV, S.V. SOLOV'EV
HEAT EXCHANGE AND MAGNETIC HYDRODYNAMICS OF THE CORE OF THE EARTH
Khabarovsk State Technical University, Khabarovsk, Russia

We consider natural-convective heat exchange of electrically conducting liquid in a spherical interlayer in the Boussinesq approximation. Free-fall acceleration is directed to the center of the sphere. For the ranges of magnetic interaction S and Reynolds magnetic number Re_m 1.5·10^-5<=S<=1.5·10^-2 and 1.5·10^-8<=Re_m<=1 we found the critical number (S/Re_m)~450, in passing over which the direction of meridional circulation of liquid undergoes a change in the core of the Earth.

B. CESNA
HEAT TRANSFER AND HYDRAULIC RESISTANCE IN ROD BUNDLES OF TUBES WITH COUNTER WIRE-WINDING IN A LONGITUDINAL FLOW
Lithuanian Power Engineering Institute, Kaunas, Lithuania

The paper presents the results of experimental investigation of hydraulic resistance, mixing, and heat transfer of rod bundles consisting of 85 counter wire-wound rods in an axial air flow. The rods were spaced by means of two- and four-wire counter coils. The pitch-to-diameter ratio P/d = 1.23 was used. For the bundle with oposite wire-winding 43 rods were with 4 wire-coils and 42 rods were with 2 wire-coils. The left direction of wire winding was used for 4 wire coils and the right direction for 2 wire coils. The helical-lead-to-rod-diameter ratio was T/d = 20 for rods with 4 wire-coils and T/d = 10 for rods with 2 wire coils. Experiments were performed in an air flow within the range 4.3·10³<Re<=7·10⁴.

YU.S. CHUMAKOV
EXPERIMENTAL STUDY OF THE TRANSITION AND DEVELOPED TURBULENT FLOW REGIMES IN FREE CONVECTION BOUNDARY LAYER NEAR A VERTICAL HEATED SURFACE
State Technical University, St.Petersburg, Russia

The results of an experimental study of a free-convective boundary layer formed on a vertical isothermally heated plane surface are presented. Three regimes of flow are studied: laminar, turbulent, and a laminar-turbulent transient flow, which is given a considerable amount of attention. The free-convective flow is generated by a vertical aluminum plate 90 cm in width and 4.95 m in height. The large height of the plate gave the possibility to obtain all the three flow regimes such as laminar, transient, and a developed turbulent one. The study of the boundary-layer properties is based on the measurements of the average and fluctuational temperature and velocity components. When measuring the velocity characteristics, two components of velocity vectors (streamwise and normal) are determined. Attention is specially paid to the near-wall flow region, in particular, to the measurement of the heat flux and the wall stress. New empirical dependences of these values within a wide range of the Grashof numbers are obtained, including three flow regimes: laminar, transient, and turbulent. Some features of the flow in the transient region which are appropriate only for a free-convective flow are described. Various criteria of the beginning and end of the transient region are analyzed. In the present work a fluctuational flow is analyzed in detail in a laminar-turbulent transient region. The results of the measurements of different boundary-layer characteristics (intensity of temperature and longitudinal velocity fluctuations) are presented. The results of the present study are compared in detail with the data given in other references.

G.A. DREITSER
EVALUATING THE EFFICIENCY OF HEAT TRANSFER ENHANCEMENT IN HEAT EXCHANGERS
Moscow State Aviation Institute, Technical University, Moscow, Russia

A method of evaluating the efficiency of heat transfer enhancement in channels of heat exchangers is presented. The method allows one to evaluate any technique of heat transfer enhancement without detailed calculations of heat exchangers. A method of calculating the efficiency of heat transfer enhancement for any ratio between heat tansfer coefficients on hot and cold sides of heat exchangers is given.

B.V. DZYUBENKO, G.A. DREITSER
SPECIFIC FEATURES OF CONVECTIVE HEAT AND MASS TRANSFER FOR NONUNIFORM HEAT RELEASE IN HELICAL ROD BUNDLES
Moscow State Aviation Institute (Technical University), Moscow, Russia

The results of experimental and theoretical studies of steady and unsteady convective heat and mass transfer in helical rod bundles are presented. New generalizing relations are derived to calculate effective turbulent transfer coefficients used to close a system of equations describing thermal and hydrauluc processes in such rod bundles. The physical phenomena that characterize the specific features of heat and mass transfer for different types of unsteadiness are considered. The developed empirical method for closing a system of equations is based on both the hypothesis for local similarity of transfer processes and mathematical formalism in solving the problems.

B.V. DZYUBENKO, R.I. YAKIMENKO
SUBSTANTIATION OF THE EFFICIENCY OF HEAT TRANSFER SURFACES BY MEANS OF THE METHOD OF EFFECTIVE PARAMETERS
Moscow State Aviation Institute (Technical University), Moscow, Russia

We present the results of analysis of thermohydraulic efficiency of different types of heat transfer surfaces obtained by means of the Method of Effective Parameters. It is found that for the range of Reynolds numbers typical for Heat Exchangers (HE) of Food Industry the most effective heat transfer surface is the surface formed by a bundle of twisted tubes. This is due to augmentation of heat and mass exchange as a result of flow swirling by twisted tubes. On the basis of this analysis a compact HE of twisted tubes has been developed for champagne type wine cooling. The mass of these HE are several times less than the mass of plane tubes HE designed previously for the same food product flow rate.

E.YA. EPIK, V.A. GRIGORENKO
A THERMAL BOUNDARY LAYER IN THE PRESENCE OF UPPER BYPASS TRANSITION
Institute of Technical Thermophysics, National Academy of Sciences of the Ukraine, Kiev, Ukraine

The results of experimental investigation of heat transfer are presented for the case of origin of the "upper" bypass laminar-turbulent transition. On the basis of an analysis of integral and local characteristics of hydrodynamic and thermal boundary layers a method is proposed to calculated heat transfer enhancement in terms of turbulent viscosity at the outer edge of the hydrodynamic boundary layer. The substantiations of the calculation method using coefficients of longitudinal intermittency are developed. The promise of this method for hydrodynamic intermittency and necessity of its further revision for thermal one is shown.

E.YA. EPIK
LOCAL HEAT TRANSFER DOWNSTREAM OF A TURBULENT SEPARATION OF ANY INTENSITY
Institute of Technical Thermophysics, National Academy of Sciences of the Ukraine, Kiev, Ukraine

The results of generalization of experimental data for heat transfer in relaxating boundary layer downstream of a turbulent separation of any intensity in turbulized flows are presented. On the basis of analysis of determining criteria responsible for heat transfer intensification a new criterion of separation intensity Tu is proposed. This criterion is determined by the difference of kinetic turbulence energies at the outer edge of a dynamic boundary layer and in the external flow. Using this criterion, the similarity equation for the calculation of heat transfer intensification in relaxating turbulent boundary layer is recommended.

I.V. EGOROV, A.I. EROFEEV, D.V. IVANOV, V.P. PROVOTOROV,
PECULIARITIES OF HEAT TRANSFER IN SEPARATED HYPERSONIC GAS FLOWS AT MODERATE REYNOLDS NUMBERS
N.E.Zhukovskii Central Aerodynamic Institute, Zhukovskii, Moscow Region, Russia

Separated hypersonic flows of rarefied gas over a flat plate with a vertical barrier and over a corner of compression are investigated at Reynolds numbers Re<=10⁴. A kinetic approach (solution of the Boltzmann equation) and a continuum approach (solution of the Navier-Stokes equations (NSE)) are used. It is shown that in the solution of the kinetic problem the point of separation is located more downstream, than in the NSE case. When using slipping boundary conditions for NSE the nonmonotonous change in the distribution of heat flux over the surface takes place in the preseparated region of flow; the peak value of the heat flux distribution is more obvious in the solution of the kinetic problem.

V.V. FALEEV, A.E. BLAZHKOV, S.V. FALEEV, A.I. ZHITENEV
ABOUT A TWO-COMPONENT LAMINAR BOUNDARY LAYER ON A PERMEABLE PLATE
Voronezh State Technical University, Voronezh, Russia

An approximate solution of the problem of heat and mass transfer on a permeable wall with discontinuous boundary conditions for a nongradient flow is considered. An expression is given for the function of concentration for the case of uniform continuous injection through a longitudinal permeable inset. Moreover, a particular solution is obtained for the energy equation for a laminar boundary layer on the plate with a thermally insulated starting length.

A.V. FEDOTOV, Y.S. CHUMAKOV
MULTI-EQUATION TURBULENCE MODEL FOR A FREE CONVECTION BOUNDARY LAYER
Institute for High-Performance Computing and Data Bases, St.Petersburg, Russia; State Technical University, St.Petersburg, Russia

A multi-equation turbulence model for free-convective boundary layer near a vertical flat plate is developed. Attention was specially paid to description of the mean squared temperature fluctuations and correlation of fluctuations of longitudinal velocity and temperature. An algebraic relation taking account of specific features of a free-convective flow was used to model the projection of a turbulent heat flux into a normal to a solid surface. The numerical results obtained are in good agreement with experimental data.

L.G. GENIN, V.G. ZHILIN, V.G. SVIRIDOV, YU.P. IVOCHKIN, N.G. RAZUVANOV, E.V. SVIRIDOV
HYDRODYNAMICS AND HEAT TRANSFER OF A LIQUID METAL TUBE FLOW IN TRANSVERSE MAGNETIC FIELD
Moscow Power Engineering Institute, Moscow, Russia; Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, Russia

We carried out experimental investigations of heat transfer for a liquid metal flow in a horizontal tube in a transverse magnetic field. The experimental technique made it possible to avoid the influence of contact thermal resistance on the metal-wall interface on the measurements of heat-transfer coefficients. The buoyancy effects were taken into account. An equation is suggested which approximates the obtained data on the mean Nusselt number. Comparison with earlier experimental results is made.

YU.F. GORTYSHOV, I.A. POPOV, V.V. OLIMPIEV, B.B. KOSTYLEV
ENHANCEMENT OF HEAT EXCHANGE IN VERTICAL OPEN-ENDED CHANNELS UNDER THE CONDITIONS OF NATURAL CONVECTION OF GAS
A.N.Tupolev Kazan State Technical University, Kazan, Russia; Kazan State Power Engineering Institute, Kazan, Russia

In this paper we present results of experimental study of hydrodynamics and heat exchange in vertical open-ended cylindrical empty and intensified channels with natural convection of gas (self-draught). The boundaries of the regimes of flow are revealed and the results of generalizations of heat transfer are given. The expediency of natural convection heat exchange enhancement with laminar regime of flow is shown.

S.E. GUSEV, A.A. PINDRUS
A MAP OF REGIMES FOR FREE-CONVECTIVE HEAT TRANSFER OF AN IN-LINE TUBE BANK
Kaluga State Pedagogical University, Kaluga, Russia

Various regimes of free-convective heat transfer of a bank of horizontal isothermal tubes are discussed. The data of numerical computation are generalized in the form of correlation between heat transfer and velocity of the free-convective flow. A map of regimes has been built, and correlations for average heat transfer have been found for Prandtl numbers Pr = 0.7 and 5.

S.E. GUSEV, O.S. SHOKHINA
NATURAL CONVECTION HEAT TRANSFER OF A HORIZONTAL ISOTHERMAL CYLINDER UNDER COMBINED BOUNDARY CONDITIONS
Kaluga State Pedagogical University, Kaluga, Russia

The aim of this work is to investigate heat transfer of a horizontal isothermal cylinder placed in an infinite volume of liquid. A part of its surface is under isothermal conditions and a part of its surface under adiabatic conditions. Four cases are considered. The results of numerical and semi-integral study of local and average heat transfer from the isothermal part of the cylinder surface are given. Comparisons with experimental data known from the literature are given.

V.N. GUSEV
LIMITING REGIMES OF INTERFERENCE BETWEEN A PLANE OBLIQUE SHOCK AND A BOW SHOCK
N.E.Zhukovskii Central Aerodynamic Institute, Zhukovskii, Moscow Region, Russia

The limiting regimes of type IV interference flows are studied. The similarity laws of these flows are formed and maximum values of flow parameters are determined.

S.A. ISAEV, A.I. LEONTIEV, P.A. BARANOV, A.E. USACHEV
NUMERICAL INVESTIGATION OF TORNADO ENHANCEMENT OF HEAT-AND MASS EXCHANGE PROCESSES IN FLOW PAST PROJECTIONS WITH CONCAVES
Academy of Civil Aviation, St.Petersburg, Russia; State Scientific Research Center "Central Aerohydrodynamic Institute," Moscow, Russia

Within the framework of multiblock approach, using a finite-volume algorithm based on the physical-processes splitting concept and developed for the solution of three-dimensional nonstationary Navier-Strokes equations, a numerical analysis of spatial separated flows playing a dominant role in the mechanisms of heat transfer enhancement is carried out. Special attention is given to computer identification of self-organizing jet-vortical structures. The correctness of the developed approach is checked in comparison of numerical and physical results for a turbulent flow in a channel with a lune. The structure of a vortical flow in the vicinity of the lune on a flat wall is numerically analyzed. The connection between reorganization of vortical structure in the asymmetric lune and growth of thermal output is found out.

S.A. ISAEV, A.I. LEONTIEV, V.V. NOSATOV, G.S. SADOVNIKOV
NUMERICAL SIMULATION OF THE EFFECT OF POROUS COOLING OF BODIES IN A HYPERSONIC FLOW
Academy of Civil Aviation, St.Petersburg, Russia; N.E.Bauman Moscow State Technical University, Moscow, Russia

The efficiency of the concept of porous cooling is checked in numerical simulation of aerodynamic heating of a wall as a result of interaction of a generated shock wave with a boundary layer developing along the surface as well as in hypersonic flow past a blunt body. The calculated results are fitted to the available experimental data. Numerical prediction of flow and heat exchange characteristics demonstrated a substantial decrease in heat transfer when a low-intensity blowing of gas was applied in the most thermally stressed part of the wall.

S.N. KHARLAMOV
MATHEMATICAL SIMULATION OF TURBULENT HEAT TRANSFER IN CHANNELS WITH A CHANGING CROSS SECTION
Tomsk State University, Tomsk, Russia

In the present paper the accuracy evaluation of numerical calculations of turbulent heat transfer in the channels with a conical section and abrupt expansion is carried out on the basis of the modern turbulence model RSM - fluxes with kL - base. Results of calculations are compared with existing experimental data. Explanation of specific phenomena in transfer of averaged and fluctuating quantities caused by laminarization, separation, and attachment is given.

S.N. KHARLAMOV
CHARACTERISTICS OF FLOW AND HEAT TRANSFER IN A TURBULENT SWIRLED STREAM
Tomsk State University, Tomsk, Russia

In the present paper the results of numerical investigation of turbulent flow and heat transfer of incompressible fluid swirled in a circular cylindrical tube by the rotating wall technique are given. Analysis of transfer processes is made on the basis of the low-Reynolds number version of the RSM - fluxes turbulent model kL - base. Authenticity of the results is estimated by comparison with existing experimental data.

I.I. KOVALEV
EFFECT OF VORTEX STRUCTURES ON THE BOUNDARY LAYER OF EXTERNAL FLOW AROUND BODIES
Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer Institute," National Academy of Sciences of Belarus, Minsk, Belarus

Numerical simulation of a slot-and-jet vortex generator and its effect on the wall boundary layer is considered. The existence of unsteady flow regime is shown, with initiation of unsteady vortices which separate from the jet and are carried by outer flow. When moving downstream, they deform the longitudinal velocity profile and reduce local skin friction. The considered slot-and-jet vortex generator is shown to be an effective way of overall friction reduction in its vicinity.

N.N. KOVAL'NOGOV
THE MECHANISM AND THEORETICAL FOUNDATIONS OF CONTROLLING HEAT TRANSFER INTENSITY BY MEANS OF PERIODIC INFLUENCES ON A TURBULENT BOUNDARY LAYER
Ul'yanovsk State Technical University, Ul'yanovsk, Russia

Generalization of classical model of a path of mixing to the movement and heat mass transfer of flows in a near-wall boundary layer subjected to different kinds of controlling effects is undertaken. The results of numerical investigation are presented which made it possible to explain the mechanism, reveal the effectiveness and limits of various means of controlling the intensity of exchange processes. The possibility of controlling the intensity of heat and mass transfer and friction processes by using punched surfaces with dumping cavities is analyzed.

A.P. KOZLOV, N.I. MIKHEYEV, V.M. MOLOCHNIKOV, A.K. SAIKIN
A NEW PROBE FOR COMBINED MEASUREMENTS OF THE PARAMETERS OF A TURBULENT FLOW AND HEAT EXCHANGE
Department of Power Engineering of the Kazan' Science Center, Russian Academy of Sciences; A.N.Tupolev Kazan' State Technical University, Russia

A new probe for combined measurements of an instantaneous heat flow to a wall, longitudinal component of skin friction vector, and of wall pressure is presented. The design and principle of operation of the probe are described. Results of some tests are presented. Using the estimated measuring characteristics, it is shown that the probe can be used for combined measurements of instantaneous longitudinal component of skin friction vector, pulsations of heat flow to the wall, and of the wall pressure in a turbulent flow.

A.P. KOZLOV, N.I. MIKHEYEV, V.M. MOLOCHNIKOV, I.A. DAVLETSHIN
CORRELATION BETWEEN INSTANTANEOUS HYDRODYNAMIC AND THERMAL PARAMETERS IN A TURBULENT SEPARATED FLOW
Department of Power Engineering of the Kazan' Science Center, Russian Academy of Sciences; A.N.Tupolev Kazan' State Technical University, Russia

Using combined two-point measurements of an instantaneous heat flow to a wall, the longitudinal component of skin friction and wall pressure in a turbulent separated flow, some regularities in the transfer in space of the fluctuations of the parameters were discovered. The data on space-time correlation between the measured parameters was obtained. It is shown that large scale eddies of the mixing layer have an essential influence on this correlation. The mechanism of the interaction of eddies with the wall in different parts of the separated flow is described.

D.V. KRISHNA, D.V. PRASADA RAO
NATURAL CONVECTION IN A POROUS RECTANGULAR DUCT - THE BRINKMAN MODEL
Department of Mathematics, Sri Krishnadevaraya University, ANANTAPUR, India

The study of buoyancy driven convection flow and heat transfer in a porous medium has gained importance owing to its application in the development of geothermal technology, drying technology, insulation technology and many other technological fields. Convective heat transfer in a rectangular porous duct with differentially heated sidewalls is a problem, which has received attention by many investigators. In this paper we discuss the said problem using finite element analysis. The governing nonlinear coupled equations for the momentum and temperature under the Brinkman's model are obtained in terms of the stream function and the temperature. The Galerkin method with eight node serendipity elements is used to obtain the coupled global matrices. These coupled matrices are solved using iterative procedure. The behavior of velocity, temperature and the Nusselt number is discussed computationally for different values of governing parameters, viz. the Grashof number, the Darcy parameter, and the Prandtl number. It is observed that in a two-dimensional convection flow through a sparsely packed porous medium, the resultant velocity at any position in the given duct enhances with increase in either the permeability of the medium or the thermal buoyancy acting on the fluid. In a given duct the influence of the thermal buoyancy exhibits a critical value for G. It is also interesting to know that irrespective of the aspect ratio of the duct, the values of Nusselt number exhibit invariance for all G in low permeable mediums. In all ducts with moderate permeability the Nusselt number exhibits a hysterisis behavior for G greater than a critical value.

V.A. KUDRYAVTSEV, A.I. MAIOROVA, A.A. SVIRIDENKOV
HYDRODYNAMICS AND HEAT TRANSFER OF A THREE-DIMENSIONAL FLOW IN A FILM COOLING SYSTEM
Central Institute of Aircraft Engine Manufacturing, Moscow, Russia

We carry out experimental investigation of flow and heat transfer in a film-cooling mixing unit as well as numerical calculation on the basis of a 3d equations of turbulent flow. The fact that flow structure is independent of cooler mass flow rate, i.e. Reynolds number, and is determined only by geometry is established. The turbulence and heat transfer depend on both geometry and Reynolds number.

L.I. KURLAPOV
CONVECTIVE AND CONDUCTIVE COMPONENTS OF FLOWS IN THE EQUATIONS FOR HEAT AND MASS TRANSFER IN GASES
Al-Farabi Kazakh State University, Almaty, Kazakhstan

Heat and mass transport in driven gases is described by the equations of continuity, motion, energy, and entropy, whose joint resolution gives the fields of macroparameters and flows. The flows of these substances have two components: convective and conductive, which have a different nature. Besides, a flux of entropy contains flows which couple with the flows of other substances, the account of which can explain the existence of dissipative structures. For their unambiguous separation, a formal attribute of reversibility of the speed of these components is used.

YU.V. LAPIN, S.B. NIKOL'SKAYA, YU.S.CHUMAKOV
AN ALGENRAIC MODEL OF A FREE-CONVECTIVE TURBULENT BOUNDARY LAYER ON A VERTICAL HEATED PLATE
State Technical University, St.Petersburg, Russia

An algebraic model of turbulence is developed to calculate a free-convective boundary layer being formed along a vertical heated plate. The model is based on the two-layer scheme of a boundary layer, according to which the layer is subdivided into the inner and outer regions. The inner region which occupies the space between the wall and the velocity maximum coordinate includes a viscous sublayer zone and a logarithmic zone. The outer region includes a zone of the wall law and an intermittent zone. Within the framework of this model, relations are suggested to calculate the coefficients of turbulent viscosity and thermal diffisivity. The model is tested by comparing the calculated and available experimental data on local and integral flow characteristics.

I.G. LEBO, V.V. NIKISHIN, V.B. ROZANOV, V.F. TISHKIN, A.P. FAVORSKII
DEVELOPMENT OF A TURBULENT ZONE OF MIXING NEAR A CONTACT SURFACE OF TWO MEDIA ON THE BASIS OF 3D CALCULATIONS
Institute of Mathematical Simulation, Russian Academy of Sciences, Moscow; Physical Institute, Russian Academy of Sciences, Moscow, Russia

The paper considers the problems connected with simulation of the development of hydrodynamic Richtmeier-Meshkov instability (RMI) in multiple passage of shock wave through an interface between two media and formation of a turbulent zone of mixing near the interface. The results of direct numerical simulation of the development of the turbulent zone of mixing are presented and comparison is made between the dynamics of the growth of this zone and the versions of the program "NUT" for a multiprocessor working station "PARSYTEC CC". A nonregular regime of shock wave diffraction on the interface between two media is investigated.

V.G. LUSHCHIK, A.A. PAVELIEV, A.E. YAKUBENKO
INFLUENCE OF THE WALL TEMPERATURE REGIME ON THE TRANSITION TO TURBULENCE IN THE BOUNDARY LAYER AT A LARGE LEVEL OF EXTERNAL DISTURBANCES
"Energomash' Science and Production Association M.V.Keldysh Research Center Institute of Mechanics at the Moscow State University, Moscow, Russia

The results of numerical investigation of the influence of the external turbulence level, surface-flow temperature ratio, and flow Mach number on transition to turbulence in a boundary layer are presented. It is shown that the critical Reynolds number decreases with increase of the above parameters. The obtained qualitative and quantitative picture of the transition agrees with the available experimental data.

I.YU. MAL'CHIKOVA
CONVECTIVE HEAT AND MASS EXCHANGE IN INTERSTICES-CAVITIES OF NATURAL GEOSYSTEMS
Chita Institute of Natural Resources, Siberian Branch of the Russian Academy of Sciences, Chita, Russia

Results of natural investigations of a thermomoist regime in interstices-cavities of ice caves and psephitic slope deposits (block-fields and rock glaciers) are given. Causality between functional structure of natural geosystems and mechanism of heat and moisture transfer in them has been traced. The role of the main system-forming factor - intra-intersticial ice in convective heat and mass transfer has been analyzed. Influence of the type of dominant air mass on structure of the heat fields of interstices-cavities has been considered.

O.V. MITROFANOVA
PRINCIPLES OF SIMULATION OF FLOW AND HEAT TRANSFER IN HEATED CHANNELS WITH SWIRL-FLOW DEVICES
Moscow Engineering Physics Institute, Moscow, Russia

General principles of simulation for constructing engineering computational methods applicable for comparison of heat transfer and hydraulic parameters in channels with various types of swirl-flow devices are discussed. On the basis of the methods proposed useful recommendations for increase of thermal performance and improvement of reliability of power and heat transfer equipment may be obtained. Comparison of temperature fields for heated tubes with and without twisted tape inserts under the conditions of nonuniform heat generation illustrates good agreement of experimental and computational results.

A.A. MOHAMAD, I. SEZAI
EFFECT OF LATERAL ASPECT RATIO ON THREE-DIMENSIONAL DOUBLE DIFFUSIVE CONVECTION IN FOROUS ENCLOSURES WITH OPPOSING GRADIENTS OF TEMPERATURE AND CONCENTRATION
Department of Mechanical Eng., Easterm Mediterranean University, Turkey

In a recent work performed by the above authors on the buoyant flow in a cubic porous cavity with opposing horizontal gradients of temperature and concentration, it was found that the flow structure becomes three-dimensional for certain parameter ranges. Superimposed on the main flow rotation, secondary flow is set up in the transverse planes, which 2-D models fail to capture. The rate of heat and mass transfer predicted by the 2-D models does not reflect the true values for certain parameter ranges where the flow structure is three-dimensional. The present investigation aims to study the effect of lateral aspect ratio on the flow structure and rate of heat transfer. Interestingly, it is found that as the lateral aspect ratio increases by a factor of integer numbers (i.e., 2, 3, 4 ...) the flow structure found in the cubic cavity repeats itself in lateral direction.

P.V. NIKITIN, S.M. PROROKOV
CHARACTERISTIC PROPERTIES OF HEAT EXCHANGE AND GAS DYNAMICS IN SUPERSONIC FLOW OF HETEROGENEOUS MEDIUM IN MICRONOZZLES WITH LARGE ELONGATION
Moscow State Aviation Institute (Technical University), Moscow, Russia

In the paper a technique for designing large-elongation accelerating channels for generation of two-phase flows of optimal parameters is presented. A one-dimensional model of steady-state flow of two-phase (gas-particles) mixture along a channel is considered. The mass concentration of particles in a flow was considered to be small (up to 10%). The particles were supposed to be spherical. The size of particles is small in comparison with the path length where the gas flow parameters change significantly, so that the disturbing influence of particles on gas flow can be excluded. A micro-nozzle has a small opening angle, so the motion of particles may be assumed to be rectilinear. The results of the analysis of problem solution in this statement are given.

M.I. NIZOVTSEV, V.I. TEREKHOV, A.I. GNYRYA, E.V. PETROV
EXPERIMENTAL INVESTIGATION OF THE EFFECT OF HEAT RELEASE IN AN INTER-GLASS SPACE ON THE THERMAL CHARACTERISTICS OF A GLAZED WINDOW
Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences; Tomsk State Architecture and Civil Enginreering University, Russia

Results of experimental study of the effect of heat release in the inter-sheet space of a triple-glaze window on the temperatures of the window surfaces and resistance of the structure to heat transfer are presented. The efficiencies of heat release were compared for cold and warm air layers. The joint usage of internal heat release and heat-reflecting coating gains a considerable rise in the temperature of inner glazing and decreases heat losses through this kind of windows.

L.N. PEREPECHKO
INVESTIGATION OF HEAT AND MASS TRANSFER PROCESSES IN A BOUNDARY LAYER WITH BLOWING AND EVAPORATION
Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

In this work similarity of heat and mass transfer processes, influence of Lewis number on results and influence of gas injection on turbulent characteristics are investigated. The predictions are carried out with evaporation of ethanol and water from a wall and with blowing of hydrogen in a laminar and turbulent boundary layer. Comparison with experimental data on distribution of average and turbulent characteristics in a boundary layer is made.

L.N. PEREPECHKO
HEAT AND MASS TRANSFER IN A TURBULENT BOUNDARY LAYER WITH EVAPORATION AND COMBUSTION OF ETHANOL
Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

In this work turbulent flow in a boundary layer with evaporation and combustion of ethanol is simulated. The interaction of combustion processes and turbulence is investigated. Chemical kinetics in modeling chemical transformations is used to determine the influence of the turbulence level of the main stream on concentration of nitrogen oxides.

V.I. POLEZHAEV, E.B. SOBOLEVA
SIMULATION OF NATURAL CONVECTION OF A NEAR-CRITICAL FLUID WITH SIDE HEAT INPUT
Institute for the Problems of Mechanics, Russian Academy of Sciences, Moscow, Russia

Numerical simulation of natural convection near the thermodynamic critical point in a square cavity is performed. The temperature difference on the side boundaries is uniform, equations of state of van der Waals form are used. The influence of Rayleigh number and temperature distance up to the critical point upon heat and mass transfer in steady flows is investigated.

A.A. PRIKHOD'KO, A.V. ZINCHENKO
CONTROL OF SEPARATION OF COMPRESSIBLE MULTIPHASE FLOWS
Dnepropetrovsk State University, Ukraine

The model of interpenetrating media is used to investigate compressible multiphase flows. The governing system of conservation laws is solved using the developed implicit TVD scheme based on upwind compact differencing. A numerical algorithm is implemented in an applied program package. Results are presented for numerical simulation of interaction of shock and depression waves with boundary layers upon flat, concave, and convex surfaces. The features of the control of separation for multiphase flows are considered, as well as the influence of concentration of particles and their diameter on the evolution of flow separation is determined. An analogy between the effects on single-phase and multiphase flows is demonstrated.

A.A. PRIKHOD'KO, P.I. KUDINOV
NUMERICAL SIMULATION OF STABLE AND UNSTABLE THERMOGRAVITATION CIRCULATION IN ENCLOSED VOLUMES OF ARBITRARY CROSS SECTION
Dnepropetrovsk State University, Dnepropetrovsk, Ukraine

Based on conservation laws and Boussinesq approximation, numerical simulation of stable and unstable thermogravitation circulation in enclosed volumes of arbitrary cross section is made. A solution algorithm was developed on the basis of the SIMPLER method extended to the case of a curvilinear nonorthogonal coordinate system. The third-order TVD scheme was used to increase accuracy. The structure of the flow, streamlines and isotherms were obtained for a rectangular cavity, horizontal circular channel, and a channel with V-like cross section. Results were compared with numerical and experimental data.

V.G. PROKOPOV, N.M. FIALKO, YU.V. SHERENKOVSKII, V.L. YURCHUK, D.G. BLINOV
CONJUGATED HEAT TRANSFER IN AUTONOMIC ZONES OF CHANNELS
Institute of Technical Thermophysics, National Academy of Sciences of the Ukraine, Kiev, Ukraine

The interconnected heat transfer processes in a channel wall and flowing liquid in the channel at variable heat flux feeding to its outside surface are considered. Closed analytical solution of the problem for autonomic zone, i.e., for the field placed far enough from end sections is obtained. It is shown that in this field in spite of the absence of the influence of end boundary conditions, the Nusselt complex is still variable because the heat flux is variable too.

A.D. REKIN, V.P. LUKASH, S.A. STRYAPUNIN
EXPERIMENTAL INVESTIGATION OF HEAT TRANSFER ON A PERFORATED WALL WITH INCLINED HOLES IN A TURBULENT GAS FLOW
Central Institute of Aviation Mechanical Engineering, Moscow, Russia

Results of experimental investigation of convective heat transfer between a turbulent gas flow and perforated adiabatic wall with inclined holes are obtained. On the basis of experimental results we determined adiabatic temperature of the wall and heat transfer coefficient as a function of the intensity of mass velocity of a cooling air. As a result of the experiments in the investigated range of mass velocities of cooling flow (rV_m/rU₀= 0.01-0.05) we found: 1) decrease of adiabatic wall temperature with increase in the cooling mass velocity, since the dynamic gas pressure exceeds the dynamic cooling air pressure (in this case cooling jets do not separate from the wall) and 2) increase of heat transfer coefficients with increase in the cooling mass velocity.

V.M. REPUKHOV
GENERALIZED REYNOLDS ANALOGY, HEAT-MASS-ANALOGY, AND HEAT-MASS TRANSFER CONSERVATIVENESS LAWS
Institute of Technical Thermophysics, National Academy of Sciences of the Ukraine, Kiev, Ukraine

Generalized Reynolds analogy is considered under the conditions without field heat radiation, including wall with transpired gas under protected screen and existing similarity of the integral energy conservation equation of a mixture and full mass of its components in a turbulent boundary layer. It is shown that the well-known conservativeness heat-mass transfer laws result from the Reynolds analogy considered, which with the known friction law permit one to present the solution of the above-indicated integral conservation equations and a relative law of heat and mass transfer with variable total enthalpy and concentration of components on the wall and layer boundary, when the flow is nonisothermal and compressible.

V.M. REPUKHOV, M.M. KOVETSKAYA, G.V. KUDRYAVTSEVA
THE UNSTATIONARY FLOW, HEAT AND MASS TRANSFER IN COMPLEX CANAL SYSTEM OF THE TURBINE BLADE AND PLANE WING CONVECTIVE-SCREENING PROTECTION
Institute of Technical Thermophysics, National Academy of Sciences of the Ukraine, Kiev, Ukraine

The unstationary one-dimension differential model of the heat and mass transfer in flow of multicomponent mixture media in complex canal net is proposed. The state equation of the working media is written by constant relation between specific heat by constant pressure and volume condition. The maximum validity of the boundary conditions for the system calculation is ensured by the order of canals in the complex net. Examples of unstationary processes calculations by antiice-covered system of the plane wing heating and convective-screening protection of the gas turbine blade are given.

U.A. SAMOILOVICH, V.I. TIMOSHPOL'SKY, I.A. TRUSOVA, A.P. NESENCHUK, O.G. KHOPOVA
MOLTEN METAL MOTION IN A LIQUID CORE OF CONTINUOUSLY CAST WORKPIECE IN AN INDUCTIVE ELECTROMAGNETIC FIELD
Scientific Research Institute of Ferrous Metallurgy, Ekaterinburg, Russia; Belorussian State Polytechnic Academy, Minsk, Belarus

Equations are presented which describe the behavior of molten metal in a liquid core of a continuously cast workpiece in the field of electrodynamic forces created by an electromagnetic field. Analysis of the motion of molten metal under the influence of one and two travelling field inductors is carried out.

S.Z. SAPOZHNIKOV, V.YU. MITYAKOV, A.V. MITYAKOV
FORCED CONVECTION LOCAL HEAT TRANSFER FROM A SPHERICAL CAVITY
St.Petersburg State Technical University, St.Petersburg, Russia

The results of an experimental investigation of local heat transfer on an isothermal single spherical cavity are presented. The experiments were carried out in the Reynolds number range 2.5·10⁴-6.5·10⁴ on a spherical cavity with the dimensions h/d = 0.139, surface temperature 100°C, and the flow temperature 20°C. The efficiency of a cavity in comparison with a smooth surface is shown.

N.V. SELIVANOV
INFLUENCE OF FLUCTUATIONS OF A RECTANGULAR CAVITY ABOUT THE HORIZONTAL AXIS ON HEAT TRANSFER AT A VERTICAL SURFACE
Astrakhan' State Technological University, Astrakhan, Russia

The results of theoretical and experimental study of local heat transfer at a vertical surface of a vessel under the joint action of free and forced convection, caused by fluctuations, for highly viscous liquids are given. The solutions of the equations of mixed convection have been obtained by two methods for Prandtl number from 100 to 10 . The results of calculations match each other well. The results of the experiment on local heat transfer suit the results of numerical solutions satisfactorily. The fluctuations increased heat transfer by a factor of 2-4, the process of heat transfer in the course of fluctuations may be referred to as heat transfer under mixed convection.

O.N. SHABLOVSKII
NONLINEAR HEAT PHENOMENA IN A FLAT NONSTATIONARY FLOW FROM A CIRCULAR SOURCE OF VISCOUS FLUID
P.O.Sukhoi Gomel State Technical University, Gomel', Belarus

A problem of two-dimensional flow of incompressible viscous Newtonian fluid which is initiated by a finite-size source of mass, momentum, and energy is stated. By means of the Galerkin method the problem is reduced to a system of hydrodynamic type for two principal degrees of freedom. Nonlinear properties of a volumetric source of energy have a principal significance for thermohydrodynamical stability of flow and for the origin of bifurcation regimes. The reaction of the flow on various regimes of the source is studied. Qualitative and quantitative characteristics of nonlinear oscillations are studied thoroughtly.

YU.I. SHANIN, O.I. SHANIN
HEAT EXCHANGE AND HYDRAULIC RESISTANCE IN SWIRL-FLOW COOLING SYSTEMS
State Scientific-Research Institute of the Science and Production Association "Luch", Podol'sk, Russia

Experimental results were obtained on the hydraulic resistance z, reduced heat transfer a_r, and surface heat transfer a under one-sided heat loading in channel-type cooling systems made of copper, in which, to raise the rate of heat transfer, spiral tapes were inserted with the spacing d_g/2 0.015-0.115. The data obtained for a water coolant in the Reynolds number range 200...3 10 were piecewise generalized by exponential dimensionless equations. The most essential differences in relative resistance and heat transfer from a channel-type system without any process intensifiers were observed, in the Reynolds range 300...8000, with the maximum in the difference being attained at Re = 1000; at d_g/2 = 0.115 the heat transfer rate increases by a factor of two at a 2.3-fold increase in resistance.

YU.I. SHANIN, O.I. SHANIN
HEAT TRANSFER AND HYDRAULIC RESISTANCE OF COOLING SYSTEMS WITH SPRING-INSERTS
State Scientific-Research Institute of the Science and Production Association "Luch", Podol'sk, Russia

We carried out experimental investigation of hydraulic resistance and heat transfer in a channel- and slit-type cooling systems with spring inserts. Results were obtained for the Reynolds numbers 100<=Re<=16·10³ on the hydraulic resistance coefficient z; the coefficient of reduced a_r and surface heat transfer, with one of the walls of the cooling systems being heated. The Re ranges of Re number were isolated in which the hydraulic resistance and heat transfer are represented as exponential functions. It is established that in the range 400<=Re<=16·10³ the reduced heat transfer factor in the channel system with springs was 1.5-2.5 times higher than that for the system without springs. The data on heat transfer for a flat channel with springs agree (accurate to 15-25%) with the literature data concerning smooth round pipes furnished with spring inserts.

A.N. SHCHEGLOV, A.V. MATYUSHIN
MATHEMATICAL MODELING OF HEAT AND MASS TRANSFER IN FIRE IN A TUNNEL
All-Russia Scientific-Research Institute of Fire-Fighting Problems, Balashikha, Russia

The mathematical zone model designed for predicting the behavior of hot smoke generated during fire in tunnels with smoke venting and a sprinkler system is presented. This model computes the parameters of a ceiling jet. Predictions of the model are shown to agree well with experimental results of other authors.

D.D. SHPAKOVSKII
AERODYNAMIC HEATING OF A DEAD-END CAVERN IN INCIDENT FLOW
Omsk State Technical University, Omsk, Russia

Experimental investigation of a dead-end cavern in an incident flow was conducted. The work is devoted to the study of energy exchange between the incident flow and the gas inside the dead-end cavern. Experiments were carried out in subsonic incident flow with different models of dead-end caverns. Based on the analysis of experimental data and extensive material of experimental investigation conducted by other authors, a physical model of the occurring process was constructed. Moreover, the results of visualization of the flow pattern inside the dead-end cavern are presented.

V.P. SOLNTSEV, V.N. KRYUKOV, I.A. MATVEYEV
HEAT TRANSFER IN THE ZONE OF SEPARATION DOWNSTREAM OF A PLAT STEP
Moscow State Aviation Institute (Technical University), Moscow, Russia

Flow and heat transfer in separated flow area after a step are investigated. Experiments were made with different step heights, boundary-layer thicknesses before the step, and external flow velocity. Data on pressure distribution and heat flux over the step surface have been obtained. Dependence of the separation flow area size on main characteristics is determined. Universal distributions of coefficient of heat transfer over the step surface are established which are valid for different step heights, boundary-layer thicknesses, and external flow Reynolds numbers. A method of calculating heat flux in the separated flow area, based on the experimental data obtained is suggested.

V.P. SOLNTSEV, V.N. KRYUKOV, G.V. KUZNETSOV
EFFECT OF A CO-CURRENT STREAM ON FLOW AND HEAT TRANSFER IN THE BOTTOM AREA OF A MULTIPLE ENGINE
Moscow State Aviation Institute (Technical University), Moscow, Russia

Flow and heat transfer in the bottom area of a six-nozzle engine is studied experimentally. Experimental data have been obtained for different co-current stream Mach numbers and different rates of supersonic jet nonadaptability. The influence of main characteristics on gas pressure, temperature and heat flux near the bottom area surface is established. The effect of co-current stream characteristics and jets nonadaptability on flow scheme within internozzle space is shown. Experimental data for jets issuing from nozzles with and without a co-current stream are compared.

Z.M. STEVANOVIC, M.A. SIJERCIC
TURBULENCE HEAT-FLUX MODELING OF NATURAL CONVECTION IN TWO-DIMENSIONAL THIN-ENCLOSURES
Institute for Nuclear Sciences "Vinca", Laboratory for Thermal Engineering and Energy, Belgrade, Yugoslavia

This paper deals with the thermal buoyancy-driven flow in two-dimensional thin enclosure. Results of DNS and experimental data of turbulent natural convection between two differentially heated vertical plates for Ra = 8.227·10⁵ and Ra = 5.4·10⁵ have been used to validate the algebraic turbulence heat flux model (AHF). The AHF model reproduces well the mean flow property (velocity and temperature) and major turbulence property (turbulence kinetic energy) in the considered thin-enclosure case. No gain is achieved by employing the full, computationally more inconvenient, refined algebraic expression for the turbulence heat flux, as compared with the reduced one. The reduced expression shows important advantages as compared with simple isotropic eddy-diffusivity model, because the heat-flux includes all major generation terms.

E.P. SUKHOVICH
PROGRESS IN THE DEVELOPMENT OF SECOND-ORDER MODELS OF TURBULENCE FOR HYDRODYNAMICS AND HEAT TRANSFER
Institute of Physics at the Latvian University, Salaspils, Latvia

The historical development of turbulence modeling is briefly surveyed. The models of various levels are described. The performance of K- model, and second-order models of turbulence are discussed. Particular attention is given to the development of modern models for the dissipation-rate functions. The modeling of anisotropies in the dissipation-rate of turbulence is considered based on an analysis of the exact transport equation for the dissipation rate tensor.

T.T. SUPRUN
SPECIAL FEATURES OF A THERMAL BOUNDARY LAYER IN THE PRESENCE OF BYPASS LAMINAR-TURBULENT TRANSITION
Institute of Technical Thermophysics, National Academy of Sciences of the Ukraine, Kiev, Ukraine

Experimental investigation of a thermal boundary layer in the presence of bypass laminar-turbulent transition arising on a heated plate in the case of the influence of an increased turbulence level of external flow (Tu_c= 5-3%, U_c= 5 m/sec) was carried out in the absence of longitudinal pressure gradient and separation on the leading edge of the plate. Analysis of distributions of the profiles of temperature, its fluctuations, variations of characteristic thicknesses and shape parameter of thermal boundary layer, distributions of conduction layer thicknesses, and shape parameter of thermal boundary layer, distributions of conduction layer thicknesses, changes in the position of temperature fluctuations maximum, and other methods permit one to make the diagnosis and determine the coordinates of the thermal BLTT.

M. TAMONIS, R. MINKSTIMAS, V. SIDLAUSKAS
NUMERICAL INVESTIGATION OF NONSTATIONARY FLOW AND HEAT EXCHANGE OF FLUIDS IN CLOSED AND OPEN VESSELS
Lithuanian Power Engineering Institute, Kaunas

This work analyzes hydrodynamical processes in vessels, filled with fluids, with the help of numerical models. It is shown that nonlinear terms in finite difference equations are extremely important in the estimation of pressure. Numerical estimations illustrate the process of the formation of whirling structures including clear stratification of temperature fields at different filling regimes for vessels. It is also shown that the above processes can become the reason for occurring various unstable phenomena.

V.I. TEREKHOV, N.I. YARYGINA, A.YU. DYACHENKO, A.V. SHAPORIN
THE DYNAMICS OF VORTICES AND HEAT TRANSFER IN THREE-DIMENSIONAL CROSS-SECTIONAL TRENCHES
Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Vortex flow patterns over the bottom surface of trenches are considered. They were produced by the method of oil-film visualization inside small span rectangular cavities and trenches with inclined walls. The cavities with the aspect ratios (span/width) S/L = 1; 2 and 3 were investigated. A three-dimensional cellular asymmetric structure is observed in a rectangular cavity with S/L = 3. The role of angular vortices increases in the cavities with inclined side walls; flows also appear near butt-ends. Temperature fields measured by thermovision equipment in rectangular cavities correspond to three-dimensional flow structures. The nonuniformity in the distributions of local heat transfer coefficients in the span direction amounts to 25%. The effect of the asymmetry is less appreciable.

V.I. TEREKHOV, A.I. GNYRYA, S.V. KOROBKOV
CONVECTIVE HEAT EXCHANGE FROM A CUBE INSTALLED ON A PLANE AT DIFFERENT ANGLES OF ATTACK
Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia; Tomsk State Architecture and Civil Engineering University, Tomsk, Russia

Experimental investigations of convective thermal losses from a cube installed on a plane at different angles of attack in an air stream are carried out. The Reynolds number in the tests changed in the range Re_L= 4·10⁴-1.2·10⁵, and the angle of attack j= 0-45° with an interval of 5°. Local heat transfer and heat transfer averaged over separate faces, as well as over th entire side surface of the cube were investigated. It is found that average heat transfer from the entire cube, including its upper face, depends little on the angle of rotation, but it is important to note that local heat transfer changes substantially on rotation relative to the velocity vector direction. The data obtained can be used for calculations of thermal losses from buildings of cubic form.

N.M. TSIREL'MAN, E.N. TSIREL'MAN
INTERRELATION BETWEEN A MATHEMATICAL MODEL AND DIMENSIONLESS EQUATIONS OF TRANSFER IN A FLOW
Ufa State Aviation Technical University, Ufa, Russia

We suggest a procedure to construct the integral characteristic of momentum and heat transfer in the form of corresponding dimensionless equations. The procedure is based on dimensionless representation of only the mathematical model of the process. Moreover, it also justifies allowance for the effect of the variable properties of a moving medium, which consists in the temperature dependence of its density, dynamic viscosity, specific heat, and of thermal conductivity. For this, most practically important case in thermal physics functional and corresponding numerical parameters have been obtained which refine substantially the well-known dimensionless relations. It is proved in particular, that the latter must also represent temperature dependences of the rates of variation of thermophysical properties.

P.V. TSOI, V.P. TSOI, SH.N. NURITDINOV
VARIETY OF SYNTHESIS OF NONSTATIONARY HEAT EXCHANGE IN CHANNELS AND HEAT CONDUCTION IN COMPLEX-SHAPED BODIES
Sweco International. M.S.Osimi Tadzhik Technical University, Dyushambe, Tadzhikistan

We have developed a processing algorithm for obtaining analytical solutions of the problems of nonstationary heat exchange in channels with two-dimensional convex profiles of cross sections at different time-variable functions of heat loadings. Diversity of presenting solutions in Riemannian space that depend on the body geometry and way of change of internal heat sources made it possible to find temperature fields in fuel elements in best approximations, in which at a certain in instant of time isotherms become a system of isothermal surfaces for any time. The solvable algorithm is generalized to investigate the processes which are described by telegraph and hyperbolic heat conduction equations.

CH.M. VERDIEV
THERMOACOUSTIC SELF-OSCILLATIONS IN MIXED CONVECTION AND HEAT TRANSFER OF HYDROCARBON FLUID IN ABNORMAL IMPROVED AND WORSENED REGIMES UNDER SUPERCRITICAL PRESSURES AND HEAT TRANSFER
Azerbaijan State Oil Academy, Baku, Azerbaijan

Heat transfer measurements, as well as critical and empirical equations of mixed convection are presented for the case of a hydrocarbon fluid of supercritical pressure (toluene, benzol) through vertical small-bore (d = 1.5-4.0) mm tubes under conditions of uniform heat flux (t_f<=t_m<=t_c; tⁱⁿ_f/t_m= 0.05-0.95) in laminar transient, and turbulent conditions in abnormal improved and worsened regimes. Tests were conducted for Reynolds number range 400-60.000. The oscillation frequencies measured are shown to be associated with pressure oscillations in the test section. The boundary of thermoacoustic self-oscillations in forced convection in improved regime based on the values of heat flux and temperatures of the tube walls has been found.

E.P. VOLCHKOV, V.P. LEBEDEV, V.V. LUKASHOV
EXPERIMENTAL INVESTIGATION OF INTERACTION OF A JET WITH A SWIRLED FLOW IN A VORTEX CHAMBER
Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Experimental investigations of flow in a vortex chamber by means of a laser-Doppler anemometer are conducted. The measurements show that the flow field in the vortex chamber is not axisymmetrical. Both pulsational and average characteristics of a stream are formed largely under the effect of a precession of a near-axis jet. About 30% of the intensities of velocity fluctuations are caused by low-frequency oscillations. The frequency of precession agrees well with known dependences of frequency on the total gas flow rate obtained for the case of a stream with a strong swirl in a pipe.

O.I. YAS'KO
ON THE NATURE OF THE PHENOMENON OF TURBULENCE
Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer Institute," National Academy of Sciences of Belarus, Minsk, Belarus

A model of turbulence is suggested which is based on the hypothesis of the existence of a "mass-vortex" field created by moving mass, just as a moving electric charge forms a magnetic field. The model is tested by considering the universal velocity profile of wall turbulence. The form of the profile and its parameters are derived theoretically wuthout involving any closure empirical coeffciients. The essence of physical processes which specify a change in turbulence parameters is revealed.

V. ZAKREVSKII, P. DAUNORAS, J.i. ZIUGZDA
ASSESSMENT OF THE ENERGY EFFICIENCY OF HEAT TRANSFER SURFACES ON THE BASIS OF THE INTERRELATIONSHIP BETWEEN CONVECTIVE HEAT TRANSFER AND FRICTION LOSSES
Lithuanian Power Engineering Institute, Kaunas

On the basis of the interrelationship between convective heat transfer and friction resistance, possibilities of assessing hydraulic characteristics and efficiency of surfaces are investigated. It is established that the more sophisticated correction in the equation K_Q/K_N=f(Re), which reflects the influence of structure and dynamic factors, expands the region of applicability of the semi-empirical heat transfer theory and increases the accuracy of calculations. Extended dependencies for various surfaces are given, the parameters of which are used to evaluate intermediate variants. Applications of these general relationships make it possible to calculate the heat transfer efficiency of a surface under various operating conditions and for various design version of heat exchangers.

B.P. ZHILKIN, A.A. GULAKOV, YU.M. BRODOV, V.V. TUL'PA
INTENSIFICATION OF HEAT TRANSFER IN IMPACT JETS BY CHANGING THE SHAPE OF THE NOZZLE CROSS SECTION
Ural State Technical University, Ekaterinburg, Russia

It is shown experimentally that using a nozzle without axial symmetry, one can increase considerably heat transfer between a jet and a surface. The characteristics of the field of flow pressure on the barrier are presented. The main correlations of heat transfer in impact jets of different shapes are described. Nondimensional equations of the heat transfer of jets of different shapes are given. A comparison of the efficiency of heat transfer of various impact jets is made.

V.I. ZINCHENKO, K.N. EFIMOV, A.G. KATAEV, A.S. YAKIMOV
INVESTIGATION OF THREE-DIMENSIONAL CONJUGATE HEAT AND MASS TRANSFER OF A HIGH-ENTHALPY FLOW AROUND A BODY WITH REGARD FOR BLOWING
Tomsk State University, Russia

Some new methods of control of thermal regimes caused by a simultaneous influence of gas blowing from the porous surface of blunt body and heat transfer within the material of the shell in a three-dimensional supersonic flow around the body are investigated. The solution of the conjugate problem allows one to take into account the influence of the nonisothermic wall of the shell on the characteristics of heat and mass transfer in a boundary layer. The efficiency of the use of heat conductive, materials to decrease maximum temperatures of the shell as a result of intensive heat sink to the region of porous spherical blunting is demonstrated.

SECTION NO. 2. "RADIATIVE AND COMBINED HEAT TRANSFER"

V.S.BAZDYREV, V.I.IVANOV, YU.I.USENKO, T.N.NESTERENKO, V.A.SKACHKOV, I.E.LUKOSHNIKOV, V.N.OCHINSKY, S.A.VORONTSOVA
CONVECTIVE THERMAL DIFFUSION OF CARBON IN AN ATMOSPHERE OF THERMAL FURNACES
Zaporozhye State Engineering Academy, Ukraine

Results of mathematical modeling of convective thermal diffusion of carbon from an atmosphere of a through-type furnace with radiant heaters to a heat-processed metal surface are reported. Conditions of stable non-decarbonizing thermal processing of standartized baled steel in furnaces of the given type are defined using the model developed.

A.I.BRIL, V.P.KABASHNIKOV, V.M.POPOV
RUSE OF THE OPTICALLY THIN FLUCTUATION APPROXIMATION FOR CALCULATING THE RADIATION HEAT TRANSFER IN TURBULENT MEDIA
B.I.Stepanov Institute of Physics of the National Academy of Sciences of Belarus, Minsk, Belarus

A method for radiation transfer calculation in turbulent media is proposed. The method is free of limitations on absorption coefficient fluctuation amplitudes. It is based on modeling the temperature distribution in a turbulent medium by using the generalized telegraphic process approximation. The solution was obtained by two methods: 1) analytically, using the Laplace transformation and representing the original temperature-fluctuation distribution in the form of superposition of a sufficiently large number of the Dirac delta-functions; 2) on the basis of stochastic modeling. The method developed was applied for evaluation of the accuracy of the optically thin fluctuation approximation, which is widely used in the problem of radiation heat transfer in turbulent flows.

V.A.BURAKOV, V.V.ELIZAROV, E.N.KORCHAGIN, V.P.KOZHUKHOV, A.S.TKACHENKO, I.V.SHCHERBAKOVA
RADIATIVE-CONDUCTIVE HEAT TRANSFER IN THE NONHERMETIC DEVICE COMPARTMENT OF SPACECRAFTS
Scientific Research Institute of Applied Mathematics and Mechanics at the Tomsk State University, Russia; M.F.Reshetnev Scientific Production Association of Applied Mechanics, Russia

New dynamic thermal mathematical models, computation algorithms and software product COMSTAN (v.1.0) for calculating the radiation-conductive heat transfer in a nonhermetic device compartment of communication spacecrafts with improved, as compared to the traditional hermetic compartments, characteristics are developed. Results of numerical calculations on distribution of three-dimensional nonstationary temperature fields in three-layer honeycomb panels and the other heat-transfer parameters in the useful loading module and in the module of service systems with heat-loaded on-board equipment are presented.

V.L.DRAGUN, N.I.STETYUKEVICH
IR-EMISSION CHARACTERISTICS OF CRYSTALLL\INE HYDRATES IN A MELTING AND CRYSTALLIZATION REGION
A.V.Luikov Heat and Mass Transfer Institute of the National Academy of Sciences of Belarus, Minsk, Belarus

The relation of the phase states of crystalline hydrates with the spectral and integral characteristics of IR-emission in a range of 4000-400 cm is considered. We have measured surface flux density of thermal emission of samples surface in the cooling and heating regimes. The spectral characteristics of the investigated substances in solid and liquid states are studied. The possible mechanisms of IR-radiation generation are discussed. The results obtained may be used for investigation of the phase changes by the emission methods.

N.A.DVORNIKOV
METHOD OF RADIATIVE-CONVECTIVE HEAT TRANSFER MODELING IN FURNACES
Institute of Thermal Physics of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

A selective diffusion model of radiative-convective heat transfer is proposed. According to our estimates, at the atmospheric pressure in a furnace and with hydrocarbon fuel combustion the model is applicable, if the size of the combustion space is 0.3-5 m. Using this model, a simplified calculation method was developed and calculation of glass heating was carried out. Simultaneously, we determined a temperature regime of the furnace arch, the require fuel rate or equivalent energy for glass heating-up to the prescribed temperatures.

A.V.GERASIMOV, A.P.KIRPICHNIKOV
TWO-TEMPERATURE HEAT EXCHANGE MODEL OF AN EMITTING PLASMA OF A HIGH-FREQUENCY INDUCTION DISCHARGE NEAR THE PLASMOID AXIS
Kazan State Technology University, Russia

A relatively simple method of the increased accuracy is proposed to calculate temperature fields of a nonequilibrium emitting plasma near the channel axis of a high-frequency induction (HFI)-plasmatron. The method is based on solwing of the problem on Joule heating of the HF discharge of finite length near the plasmoid axis and generalization of the known Eckert solution for the central region of the plasmoid. The formulas obtained describe well the temperature fields distribution near the plasmoid axis and may be used in solving a wide class of the nonequilibrium heat exchange problems in the sphere of low-temperature plasma physics and technology.

M.L.GERMAN, V.A.BORODULYA, E.F.NOGOTOV, G.I.PALCHONOK
ENGINEERING METHOD FOR CALCULATION OF A TEMPERATURE REGIME IN THE FURNACE OF A SHELL-TUBE BOILER WITH REVERSE FLAME
Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer Institute" of the National Academy of Sciences of Belarus, Minsk, Belarus

An effective method for calculation of energy exchange in boilers furnaces is proposed, which is based on numerical solution of the integro-differential equation of radiative transfer. In comparison with the standard method, this method gives a more exact solution of the problem and does not require empirical corrections for fuel quality, location of burners, and so on.

L.T.GREBENSHCHIKOV, M.L.GREBENSHCHIKOV, A.L.ZOLOTAREV, V.A.KUZ'MIN, A.V.OPUSHNEV
EXPERIMENTAL STUDY OF HEAT RADIATION OF HIGH-TEMPERATURE TWO-PHASE FLOWS
Vyatka State Technical University, Kirov, Russia

Experimental results of the investigations of high-temperature two-phase flows being formed upon combustion of metal-containing fuel in a low temperature plasma generator are reported. The investigations have been carried out within a lengthwave range of 0.4-3.0 mkm by means of the specially developed spectroradiometric devices. The devices were calibrated in terms of the absolute spectral and integral radiation intensities using an absolutely black body model. Particle temperatures of the polydisperse condensed phase and gas phases were determined by a linear dependence of the particle temperature on their size. The spectral and integral emissivities of two-phase combustion products were calculated.

A.M.GRISHIN, A.A.DOLGOV, V.P.ZIMA, A.N.SUBBOTIN, R.SH.TSVYK
EXPERIMENTAL AND THEORETICAL INVESTIGATION OF THE EFFECT OF RADIATION AND COMBINED HEAT EXCHANGE ON INITIATION AND SPREAD OF SURFACE FOREST FIRES
Tomsk State University; Institute of the Atmosphere Optics of the Siberian Branch of the Russian Academy of Sciences, Tomsk, Russia

The results of experimental and theoretical investigations of surface forest fire initiation and spread, carried out recently are presented. Based on the experimental data, a degree of reliability of predicting the minimum energy of the forest fuel ignition has been estimated by means of the general mathematical model of forest fires. The methods to record luminous temperature fields for determination of fire source contours and new more exact formula for the velocity of surface forest fire spread are given.

A.M.GRISHIN, V.P.ZIMA, V.T.KUZNETSOV, A.I.SKORIK, A.N.SUBBOTIN
EXPERIMENTAL AND THEORETICAL INVESTIGATION OF FOREST FUEL IGNITION BY A LIGHT FLUX
Tomsk State University, Russia

Results of the experimental and theoretical investigations of ignition of various layers of forest fuels by a light flux are given. It is established that three regimes are possible in relation to the light flux density: smoldering, gaseous inflammation and carbonization. The values of gaseous ignition time have been numerically determined to be in good agreement with the experimental data.

A.A.KOBYSHEV, YU.D.KOROCHKIN, V.A.KOBYSHEV, E.I.NEKRASOVA, A.K.NEKRASOV
MATHEMATICAL MODELING OF COMPLEX HEAT EXCHANGE IN PLANE AND CYLINDRICAL CHANNELS
Elektrostal' Branch of the Moscow State Institute of Steel and Alloys, Elektrostal', Moscow Region, Russia; Moscow State University of Engineering Ecology, Russia

A method of approximate solution of the multi-dimensional problems of complex heat exchange in channels with arbitrary thermophysical and radiative characteristics is described that allows numerical investigations of heat exchange in radiating systems to be carried out. The results of numerical modelling of heat exchange in plane and cylindrical channels in relation to the optical thickness and the radiative - convectional interaction parameter are given. The investigation results obtained are compared to those of the other authors.

O.YU.KULESHOV, V.M.SEDELKIN
ZONE-ELEMENT METHOD AS APPLIED TO THE COMPLEX TRANSFER PROBLEMS
Saratov State Technical University, Russia

A new numerical method to solve the applied problems of complex heat transfer and radiative gas dynamics is developed. It is based on simultaneous zone and finite-element (FE) approximation of the initial modeling equations. Local optical-geometric characteristics (as basic) in combination with the FE method interpolation possibilities are used for an analysis of the radiation field. This approach takes into account the incident radiation flux non-uniformity within the zone space and thus makes the zone method more effective as a whole and, in particular, for solving the radiative and complex heat transfer problems in media with high and optical density.

A.P.KURYACHII
NUMERICAL MODELING OF RADIATION TRANSFER IN SEMITRANSPARENT MEDIA
Central Aerohydrodynamic Institute, Zhukovskii, Moscow region, Russia

A numerical method for solving the boundary-value problem describing radiation transfer in a layer of the semitransparent medium is proposed. The two-flux approximation is used. Distributions of the forward and backward radiant fluxes are represented as a liner combination of an analytical fundamental solution of the two-flux equations without nonhomogeneous terms and a partial solution of the full two-flux equations. The partial solution is obtained by numerical integration of these equations from one boundary of the layer with arbitrary initial conditions. The coefficients of the liner combination mentioned are defined from the boundary conditions of the problem.

V.A.KUZ'MIN, E.I.MARATKANOVA
MATHEMATICAL MODELING OF THE PROCESS OF THERMAL RADIATION IN ENGINE PLANTS IN THE PRESENCE OF NONEQUILIBRIA
Vyatka State Technical University, Kirov, Russia

A method of mathematical modeling was used for methodical investigation of the process of thermal radiation of combustion products of rocket engines. The influence of various nonequilibria and peculiarities on the thermal radiation characteristics of combustion products for the chamber nozzle, and flame conditions was estimated.

G.V.KUZNETSOV, A.N.KOZLOBRODOV, S.F.SANDU
HEAT TRANSFER IN THE INSTRUMENT MODULES OF SPACE VEHICLES
Scientific Research Institute of Applied Mathematics and Mechanics at the Tomsk State University, Tomsk, Russia

Results of a numerical analysis of the multi-dimensional temperature fields in the nonhermetic apparatus modules of on-board instrumentation of space vehicles with thermal control systems on the basis of low-temperature heat pipes are reported. The results are obtained with the use of a model taking into account a full complex of thermal and physics processes that occur not only in panels of a particular module of the instrument compartment but also in the devices of radioelectronic instrumentation. It is shown that heat radiation inside the apparatus module results in noticeable lowering the temperatures differences between both separate devices and pannels as a whole. It is noted that an account of the actual sizes and configurations of devices allows the accuracy of calculation of temperature fields of the devices to be increased as compared to the other models.

D.LEMPERT , M.L.GERMAN, V.P.NEKRASOV, E.F.NOGOTOV
CALCULATION OF THE EFFECTIVE ABSORPTION COEFFICIENT OF A SELECTIVE MEDIUM IN THE FINITE SPECTRAL INTERVAL WITH ALLOWANCE FOR SCATTERING
Ben-Gurion University, Beer-Sheva, Israel; Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer Institute of the National Academy of Sciences of Belarus", Minsk, Belarus.

For a set of equidistant lines of the same intensity with the Lorentz profile the authors provide a calculation procedure and a table of the correction coefficients for determination of the effective absorption coefficient of a selective medium in the finite spectral interval with allowance for scattering.

V.A.LOSHKAREV
DIAGNOSTICS AND MODELING OF HEAT EXCHANGE IN HIGH-ENTHALPY GAS FLOWS WITH LOCAL HEAT SOURCES AND SINKS
Stavropol Branch of the Rostov Military Institute, Russia

Consideration is given to the use of the laser Raman scattering method for diagnostics of near-wall high enthalpy boundary layers on the surface of ablating materials aimed at detection of volume-spatial local zones of fast gas-phase chemical reactions of the exo- and endo-thermal type between the ablation vapor and gas components of an oncoming flow. Based on the experimental data a rational mathematical model is suggested that takes into account the influence of zones on a character of complex heat exchange with a simultaneous research of heat conduction and radiation.

V.A.LOSHKAREV, V.V.LOSHKAREV
RADIATION-CONVECTION HEAT EXCHANGE IN SCREEN PROBLEMS OF ELECTROMAGNETIC FIELDS BY A HIGH-ENTHALPY BOUNDARY LAYER
Stavropol Affiliate of the Rostov Military Institute, Stavropol; Moscow Aviation Institute (Technical University), Moscow, Russia

Heat and mass exchange in chemically reacting high-enthalpy boundary layers is caused not only by the dissociation reactions of ablation steams at the atomic-molecular level but also by kinetics of high-rate gas-phase exchange reactions between the ablation streams of heat protection and the components of an oncoming flow. Evaluation is made of the role of these reactions as peculiar generators of electromagnetic radiation having the frequency, the order of which coincides with the reaction rate constant value. Making a peculiar sublayer inside the boundary layer in the form of local volume zones, they prevent not only the radiation heat exchange but also schield the efficient radio signal.

V.A.LOSHKAREV, P.V.NIKITIN
ABSORPTION OF ELECTROMAGNETIC WARES UNDER HEAT AND MASS TRANSFER CONDITIONS IN NONEQUILIBRIUM MEDIA
Stavropol Affiliate of the Rostov Military Institute, Stavropol, Russia

An analysis is made of the interaction between electromagnetic waves and heat protection materials in the thermal destruction condition. Incident radiation is absorbed by inhomogeneities occurring as a result of stability loss under non-equilibrium conditions. Nonlinear effects and dissipation create solitons which participate in dispersion of electromagnetic radiation.

A.N.MAKAROV, E.I.KRIVNEV
CALCULATION OF FLAME RADIATION DISTRIBUTION OF FIRETECHNICAL PLANTS
Tver' State Technical University, Tver', Russia

Analytical studies have been made of the relation of the geometric parameters of a linear radiation source and a surface element on a plane with intersection of the linear source and the plane. A table with formulas for calculation of the angular coefficients of radiation of the linear source to surface elements on arbitrary planes is given. The expressions derived have been used for calculation of the flame radiation flow distibution in an industrial furnace.

O.G.MARTYNENKO, M.L.GERMAN, N.I.LEMESH, E.F.NOGOTOV
RADIATIVE-CONVECTIVE HEAT TRANSFER IN MULTIELEMENT SYSTEM "SOLID-GAS-SOLID"
Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer Institute" of the Academy of Sciences of Belarus, Minsk, Belarus

A multielement system consisting of a number of closed air layers demarcated by solid walls is considered. Regularities of the radiative-convective heat transfer are investigated under various temperature conditions on external surfaces of the system. A dependence of the magnitude and structure of a heat flux transferred through the system on an amount of the gas interlayers, their geometrical parameters, optical and thermophysical properties of the bounding surfaces is investigated.

YU.M.MATSEVITYI, A.P.SLESARENKO, N.A.SAFONOV
NUMERICAL AND ANALYTIC SIMULATION OF THE RADIATION-CONVECTION HEAT EXCHANGE IN COMPOSITE ELEMENTS OF CONSTRUCTIONS AND BUILDINGS
Institute of Mechanical Engineering Problems of the National Academy of Sciences of the Ukraine, Khar'kov, Ukraine

To solve the nonlinear boundary-value problems of heat emitting bodies of the noncanonical form, the regional-structural and projection methods are proposed to be used simultaneously. The indeterminate components of the regional systems are determined by iterative methods during solving the corresponding nonlinear systems of algebraic equations. The results of solutions of concrete problems are presented.

V.I.MAZHUKIN, V.V.NOSOV, I.SMUROV
MODELING OF PLASMA EXPANSION DURING SHOCK LASER PROCESSING OF MATERIALS
Institute of Mathematical Modeling of the Russian Academy of Sciences, Moscow, Russia; Ecole Nationale d'Ingenieurs de Saint-Etienne, France

Based on mathematical modeling, an investigation has been made of the specific features of expansion and transmission coefficients of an air plasma initiated by Nd-YAG laser action at either l=1.06 mm (IR action) or l=0.355 mm (UV action) in the wavelength range 1-20GW/cm and with pulse length of 25-30 nsec. The performed modeling allows one to conclude that the plasma expansion for the IR and UV action, is significantly different. For the IR action the main expansion mechanism is fast propagation of an ionization wave toward the laser source. It is just the ionization wave that absorbs the major part of the laser radiation in this case. For the UV action, the plasma expands as the light-detonation wave, and is mainly influenced by relatively slow gas-dynamic processes. The screening effect of the plasma can be characterized by its transmission coefficient. Sharp drop of transmission over 1-2 nsec is observed for the IR action, while for the UV action the decrease is notmonotonic and takes 10-20 nsec.

G.YU.MILYAUSKAS
REGULARITIES OF UNSTEADY TRANSFER PROCESSES IN THE DISPERSED PART OF A RADIATION FLOW
Kaunas Technological University, Chair of Thermal and Atomic Power Engineering, Kaunas, Lithuania

Results of a numerical study of the unsteady radiative-conductive heat transfer in evaporating water droplets in a radiating gas flow are is presented. The dynamics of combined heating and evaporation of water droplets are studied with allowance for the relationship of transfer processes in the gas and liquid phases. The results obtained are generalized by the similarity relations.

G.V.MILOSHEVSKII, G.S.ROMANOV
EVALUATION OF HEAT LOADS IN GRAPHITE DIVERTOR PLATES UNDER ACTION OF A MAGNETIZED ELECTRON FLUX
Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer Institute of the National Academy of Sciences of Belarus, Minsk, Belarus

Results on the energy contribution by magnetized electrons into graphite divertor plates and on the development of a heat conduction flux are presented. The Monte Carlo model for simulation of the energy contribution is discussed. The energy contribution profile calculated using a Monte Carlo model is taken as the initial condition for solving the heat conduction equation. The heat conduction equation is solved numerically by employing the second-order accuracy predictor corrector scheme. Simulation results allow estimation of the thermal loads occurring on the graphite divertor surface and evaluation of the erosion rate due to thermal stresses and strains that result in cracking the release graphite and of granules from its surface.

E.I.NEKRASOVA, A.A.KOBYSHEV, YU.D.KOROCHKIN, A.K.NEKRASOV
NUMERICAL STUDY OF ASSOCIATED HEAT-EXCHANGE IN MANUFACTURE OF GLASS PIPES
Elektrostal Branch of the Moscow State Institute of Steel and Alloys, Elektrostal, Moscow region, Russia; Moscow State University of Engineering Ecology, Russia

Consideration is given to a mathematical model of complicated associated heat-exchange in the system "glass pipe-technological equipment" under vertical extraction out of a melt that allows numerical modeling the heat and temperature cycle and associated structure changes in glass depending on the pipe sizes and the main operation and design parameters of industrial plants. Results of the numerical investigation of a version of bilateral radiative cooling allowing control the heat and temperature cycles of a pipe with the purpose of forming the temperature distributions with respect to the wall thickness in the galssmaking zone, which provide rational distribution of residual thermal stresses, are reported.

B.PUNTSAGDULAM, B.V.BERG, V.A.MIKULA
SOLAR-RADIATIVE HEATING OF DIFFERENT OBJECTS IN THE REGIONS WITH SEVERE CLIMATIC CONDITIONS
Urals State Technical University, Ekaterinburg, Russia; Acacemy of Sciences of Mongolia

A number of experiments have been carried out in the Middle Urals and the permafrost zones in Mongolia. Temperature regimes of a house with a solar air heater were studied. In winter the air temperature indoors was to +20°C in the daytime, while the temperarure outside was -1°C. The economy of energy resources in winter was about 10-15% and in spring and autumm was equal to 35%. The solar heating of a greenhouse gives economy of 60-80% if it is used for 9 months in a year that makes it possible to get 2 crops during one year even under the permafrost conditions. In testing the solar concentrator, a heat receiver temperature was obtained to be 340°C. A flat solar collector (S = 1...2 m) can heat 300 liters of cold (8°C) water up to the 30-60°C for 24 hours in the Middle Urals climate in the spring-summer-autumn period.

V.M.REPUKHOV
LOCAL HEAT FLOWS AND TEMPERATURE ON A WALL IN THE PRESENCE OF A PROTECTION BLANKET AND EXTERNAL RADIATION SOURCES
Institute of Engineering Thermal Physics, National Academy of Sciences of the Ukraine, Kiev

An integral method of solving the problem of radiative-convective heat-mass transfer in a closed region with radiating and attenuating media is extended to the case of semitransparent boundaries and used to an approximate (one zone in the current section) calculation of the turbulent boundary layer (BL) under conditions of distributed injection with a protection blanket on the wall and with additional external radiation sources beyond the BL boundaries, with the exception of the indistributed flow mass. Passing from the enthalpy to temperature characteristics of the blanket in the integral equation of energy conservation in the presence of the resultant radiation flow is considered. The volume spectral absorption and scattering coefficients of the blanket are related to its absorptivity, reflectivity and transmissivity.

S.V.REZNIK, D.YU.KALININ, V.YE.TYUTYUNNIK
MODELING AND OPTIMIZATION OF THE TECHNOLOGIES OF HEAT TREATMENT OF GLASS ARTICLES
Moscow StateTechnical University, Moscow, Russia; All-Russia Scientific Research Institute of Glass, Gus'-Khrustal'nu\yi, Vladimir Region, Russia

It is shown that different technologies for glass article treatment by heat radition have common characteristic and universal mathematical and algorithmical tools based on models of raditive and conductive heat transfer (RCHT) and inverse problems (IP) methodology may used for their design. The mathematical models of RCHT and IP solution algorithms for articles made from porous and nonporous glass have been developed. The software has been developed for these models and algorithms. The examples of new software applications for annealing, thermal polishing and glassceramics production are presented.

S.P.RUSIN
ON TEMPERATURE DETERMINATION BY THERMAL RADIATION IN A SYSTEM OF OPAQUE SURFACES
Scientific Research Thermal Physics Center of Pulsed Actions at the Joint Institute of High Temperatures, Russian Academy of Sciences, Moscow, Russia

Some methods of temperature determination in a system of nonisothermal solid opaque surfaces by recording thermal radiation are analyzed. The use of the fictitious emissivity and the model calculation emissivity is discussed.

S.P.RUSIN, V.E.PELETSKII
MODELING OF THE THERMAL HEMISPHERICAL RADIATION OF MACROROUGH SOLID SURFACES BY A CAVITY SYSTEM
Scientific Research Thermal Physics Center of Pulsed Actions at the Joint Institute of High Temperatures, Russian Academy of Sciences, Moscow

Relations are obtained for hemispherical spectral emittance of an optically macrorough opaque solid surface as a function of the optical properties of a material and geometric form-factors of this surface. The calculated emittance data are compared to those based on the well known cavity models and Agababov's relation. Application of the relations obtained to experimental and calculation investigations is discussed.

A.H.SHARFSHTEIN
NONCONTACT PYROMETRY DIAGNOSTICS OF NON-EQUILIBRIUM GASEOUS MEDIA
Ufa State Aviation Technical University, Russia

A method of temperature measurement of hydrocarbon flames from vibrational spectra of the combustion products is described. An analytical pyrometry expression obtained for implementation of the method has no limitations on the temperature measured and wavelength used. Recommendations are given on the pyrometry of rarefied two-dimensional flames.

I.YU.SMUROV
PYROMETRY APPLICATIONS FOR LASER, PLASMA AND ELECTRON BEAM MACHINING
Ecole Nationale d'Jngenieurs de Saint-Etienne, Saint-Etienne, France

A set of pyrometers is developed and applied for surface temperature monitoring in pulsed periodic Nd-YAG laser welding, deep penetration welding by a CO - laser, an electron beam and a plasma arc; laser assisted machining; plasma-arc steel refining, waste treatment in plasma furnace, plasma cladding, plasma spraying. A 2D pyrometer is used to study the evolution of temperature profiles and temperature gradients versus typical variation of process variables. The colour and the true temperatures are found with the help of a two-colour pyrometer, the true temperature is also reconstructed based on polychromatic measurements (10 wavelengths). It is shown that the pyrometers developed can be used for process monitoring and on-line control in a wide range of high temperatures application.

A.N.SUBBOTIN
INFLUENCE OF RADIATIVE AND COMBINED HEAT TRANSFER ON THE SURFACE FIRE SPREAD
Tomsk State University, Russia

Ignition and burning of a forest inflammable material are discussed. The ignition is initiated by a plane fire source and then the physical processes occurring as a result of propagation of a plane combustion wave are investigated. On the basis of numerical calculations the velocities of front propagation of the surface wild fire depending on the humidity and heat and mass-exchange of the falling pine-needles with the environment are found. The gas composition above the fire source is also investigated. The emission coefficients under various external conditions and humidity levels the layer of the pine-needles are also determined. Limiting conditions of the surface fire spread as a function of the humidity level of the layer and the heat transfer coefficient are obtained.

E.I.VITKIN, A.A.KIRILLOV
RADIATION TRANSFER IN MOVING VOLUMES OF NONEQUILIBRIUM MOLECULAR GASES
B.I.Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk

A numerical simulation technique of infrared radiation transfer in moving volumes of vibrationally nonequilibrium gases is proposed. Special attention is given to line contour transformation due to relative motion of gas streams. The prediction results of radiation transfer in combustion products out-flowing into rarefied space are analysed. It is shown that for the far zone of an optically thick jet the allowance for the Doppler shift of line centers due to high velocity gradients in the flow is of fundamental importance.

SECTION NO. 3. "HEAT CONDUCTION AND PROBLEMS OF HEAT TRANSFER OPTIMIZATION"

V.P.ALEKSEEV, G.V.KUZNETSOV, D.V.OZERKIN, V.P.RUDZINSKY

SIMULATION OF THERMOPHYSICAL PROCESSES WITH OPTIMUM SYNTHESIS OF NEW TECHNICAL DECISIONS

Tomsk, State University of Control and Radioelectronics Systems; Scientific Research Institute of Applied Mathematics and Mechanics at the Tomsk State University

The outcomes of system simulation of thermophysical processes with optimum synthesis of radioelectronic equipment (REE) functional units are reported. Consideration is given to the temperature field simulation problems of plane constructions with the purpose of setting the prescribed thermal condition. Some features of simulation of thermal stressed states in hybrid - film microthermostats are surveyed with the purpose of reliability prediction. A mathematical model and methodology of optimum topology synthesis by a maximum temperature stability criterion are suggested. The system methods of reaching maximum temperature stability of devices designed on the basis of the thermophysical models suggested are discussed.

O.M.ALIFANOV
INVERSE PROBLEMS AS A METHODICAL BASIS OF IDENTIFICATION OF THERMAL MATHEMATICAL MODELS
Moscow State Aviation Institute (Technical University), Russia

Consideration is given to a system approach to mathematical modeling and experimental studies of physical processes and technical systems. The approach is based on the use of solutions of the inverse problems and makes it possible to set up a correct correspondence between mathematical and experimental modeling. This methodology can be of particular value for construction of hierarchical systems of interrelated mathematical models at different stages of investigations and developments in designing and testing of technical objects. As an example of using this approach in practice, some results are reported of the combined use of mathematical modeling, experimental and full-scale tests in designing and optimization of thermal protection of a spacecraft.

O.M.ALIFANOV, A.V.NENAROKOMOV
IDENTIFICATION OF LUMPED PARAMETER SYSTEMS
Moscow State Aviation Institute, Moscow, Russia

The paper deals with development of extreme methods to solve inverse heat transfer problems for systems with lumped parameters. Such problems are the incorrectly stated problems of mathematical physics, therefore a choice of a stable solution is of particular importance. It is shown that for this purpose the specially developed algorithms based on the steepest descent and conjugate gradient methods can be successfully used. A halt of the iterative process, providing the stability of a sought solution, should be performed be means of certain matching of the criterion functional value and a total measurement error. The technique suggested has been tested in determining the integral emissivity and the absorption coefficient of the spacecraft coating surface.

M.YA.ANTIMIROV
ANALYTICAL SOLUTION OF THE PROBLEMS ON A TEMPERATURE FIELD IN THE UNIFORM FLOW AROUND POINT AND LINE HEAT SOURCES
Riga Technical University, Latvia

New analytical solutions of two stationary problems on a temperature field in a homogeneous flow around point and linear heat sources are obtained. The solutions are obtained in an exact formulation and in a boundary layer approximation that has allowed exact determination of the domain of applicability of the boundary-layer approximation in both cases.

I.F.ASTAKHOVA, I.S.MOLCHADSKII
A MATHEMATICAL MODEL OF TEMPERATURE FIELD CALCULATION OF MULTILAYER CONSTRUCTIONS WITH ALLOWANCE FOR RADIATION HEAT TRANSFER DURING FIRE INDOORS
Voronezh State University, Russia; All-Russia Scientific Research Fire Defence Institute of the Ministry of Internal Affairs, Russia

A model of the viscous incompressible fluid in the Boussinessq approximation is proposed to investigate fire characteristics, compressibility is taken into account only by the term with a buoyancy force. Radiative heat transfer between the fire center and building structures is taken into account in the IIIrd kind boundary conditions. Analysing the radiative heat transfer in a local fire, consideration is made of inhomogeneity of the temperature and the optical properties of a flame tonque as well as a character of radiant energy transfer in an object under consideration.

A.V.ATTETKOV, I.K.VOLKOV
SINGULAR INTEGRAL TRANSFORMATION AS A METHOD TO SOLVE HEAT CONDUCTION PROBLEMS IN DOUBLE LAYER DOMAINS UNDER UNSTEADY-STATE BOUNDARY CONDITIONS OF HEAT EXCHANGE WITH AN EXTERNAL MEDIUM
N.E.Buaman State Technical University, Moscow, Russia

An analytical method to solve heat conduction problems under unsteady-state boundary conditions is proposed. The method is based on kernel splitting of the singular integral transformation obtained and used with respect to a spatial variable.

A.F.BASHKATOV, G.S.BIKBULATOVA
OPTIMIZATION OF EXTERNAL HEATING OF A PRISM WITH ALLOWANCE FOR THE RESTRICTIONS ON THERMAL STRESSES AND A MAXIMUM TEMPERATURE
Bashkir State Agricultural University, Ufa, Russia

The problem of optimum control of a prism heating with allowance for the restrictions on compressive and tensile thermal stresses and a maximum temperature is investigated. The method of solution is based on representation of the solution in a Fourier series and approximation of the original problem by a finite-dimensional problem of the optimal control with constraints on the phase variables and on the control. Error estimates of the approximation with respect to the state are obtained, results of computational experiments are reported.

V.G.BASHTOVOI, A.N.VISLOVICH, A.B.SUKHOTSKY
TRANSFORMATION OF THE SPATIAL HARMONIC OF A TEMPERATURE FIELD IN A STRATIFIED MEDIUM
Belarusian State Technological University, Minsk, Belarus

The generalized theory is developed and an experimental study (using a magnetostatic model) is made of a two-dimensional stationary temperature field in a stratified medium. It is proposed to set up expressions describing this field in a medium with an arbitrary number of strata by introducing a system of transformation parameters for Fourier components of the temperature field at the boundary of media with different thermal conductivities.

S.B.BEALE, R.DJEBBAR, M.L.POST, S.V.ZHUBRIN, B.DELESALLE
NUMERICAL ANALYSIS OF HEAT TRANSFER IN MICROHOTPLATE STRUCTURES
National Research Council, Ottawa, Ontario, K1A 0R6, Canada; Concentration Heat and Momentum Ltd., London, SW 19 5UA, United Kindom; Institut Catholique d'Arts Metiers, 59046, France

This paper describes a research programme directed towards modeling the thermomechanical behaviour of silicon microstructures. A three-dimensional numerical scheme was used to compute heat transfer and distribution of an electric potential in the layers of two microhotplate designs. Detailed information was obtained on the local temperarure distribution in the design and a surrounding substrate. Variable properties of the different layers in the microstructures were accounted for. Calculations have revealed that the overall heat transfer coefficients obtained from these studies agree with the values derived from experimental emission data within 6%.

D.G.BLINOV, V.G.PROKOPOV, YU.V.SHERENKOVSKII, N.M.FIALKO, V.L.YURCHUCK
APPLICATION OF NONCLASSICAL VARIATIONAL PRINCIPLES OF AN UNSTEADY HEAT TRANSFER PROCESS FOR SOLVING OPTIMIZATION PROBLEMS
National Technical University of the Ukraine "Kiev Polytechnic Institute"; Institute of Engineering Thermal Physics of the National Academy of Sciences of the Ukraine, Kiev

Extreme direct and dual variational formulations of unsteady-state heat conduction problems are proposed. Their application for solving the optimization, control and identification problems is shown to be efficient.

V.T.BORUKHOV, A.I.SHNIP
TO THE THERMODYNAMIC THEORY OF RELAXING SYSTEMS
Academic Scientific Complex "A.V. Luikov Heat and Mass Transfer Institute of the National Academy of Sciences of Belarus", Minsk, Belarus.

A theory of the generalized thermodynamic systems with internal variables of state is developed. Based on the entropy-free formulation of the second onset for semilinear systems of this type the necessary and sufficient conditions for its fulfilment are found and a procedure of construction of nonequilibrium thermodynamic potentials is developed. It is established that for the majority of systems a compact family of such potentials exists, among which there are the maximum and minimum potentials. Using concrete physical examples it is shown that this family contains the classical potentials. For the class of relaxation systems a formal criterion is found that sets off the classical potential from this family. The general expression for this potential is obtained.

V.A.BURAKOV, V.N.BERTSUN, O.L.KRITSKII
COMPARATIVE ANALYSIS OF NUMERICAL METHODS AS APPLIED FOR SOLVING AN ANISOTROPIC TIME-DEPENDENT HEAT CONDUCTION PROBLEM
Tomsk State University, Russia

The B.N.Chetvertushkin iterative method, modified to solve an anisotropic time-dependent heat transfer problem, is considered. A rate of the method convergence is investigated, its application for a family of essentially anisotropic time-dependent heat-conduction problems is discussed. A comparative analysis with the methods of matrix running and fractional steps is carried out.

YU.V.CHOVNYUK, S.A.MAKAROV
METHODS AND MODELS USED IN AN ANALYSIS OF MATERIAL HEATING BY MICROWAVE RADIATION
"Azhio-College" Higher School of Economics and Management, Kiev, Ukraine; Kiev National University of Civil Engineering and Architecture, Ukraine

The physical and mathematical methods and the models used an analysis of material heating by microwave radiation are discussed. The nonlinear approach to the problem and its solution are proposed.

YU.V.CHOVNYUK, S.A.MAKAROV
SPACE-TIME EVOLUTION OF THERMOELASTIC IMPULSES IN ISOTROPIC BODIES: NEW (NONHARMONIC) SOLUTIONS OF INITIAL BOUNDARY-VALUE PROBLEMS OF THERMAL DIFFUSIVITY AND HEAT CONDUCTIVITY
"Azhio-College" Hhgher School of Economics and Management, Kiev, Ukraine; Kiev National Institute of Civil Engineering and Architecture, Ukraine

The space-time evolution of thermoelastic impulses in isotropic bodies is discussed. New nonharmonic solutions of initial-boundary-value problems of thermal diffusivity and heat condictivity are proposed.

YU.V.CHOVNYUK, B.F.RUD'KO, T.N.OVSYANNIKOVA
ANALYSIS OF THE HYPERBOLIC HEAT CONDUCTION EQUATION PROPERTIES IN BIOPHYSICAL MODELS OF ALIVE TISSUE FUNCTIONING
"Vidguk" Scientific Research Center of Quantum Medicine of the Ministry of Public Health of Ukraine, Kiev

The properties of the hyperbolic heat conductivity equation in biophysical models of alive tissue functioning are discussed. The models of acoustic, electromagnetic and thermoelastic interactions in the alive tissues are proposed.

N.V.DILIGENSKII, A.P.EFIMOV, M.YU.LIVSHITS
APPLICATION OF THE PERTURBATION METHOD FOR SOLVING THE STEPHAN PROBLEM IN THE PROCESSES OF INDUSTRIAL THERMAL PHYSICS
Samara State Technical University, Russia

The method is proposed to determine the boundaries of two phases in a one-dimensional body under heat action of the sufficiently general type on the surfaces bounding the body. The method is based on reducting the Stephan problem formulated to individual linear heat conduction problems in each of the coexisting phases. In this case, a problem of position determination of the phases boundary position is reduced to a nonlinear integro-differential equation, which is solved by methods of the perturbation theory.

G.N.DUL'NEV, YU.V.LEVOCHKIN, A.N.LISITSIN, B.A.VORONENKO, D.S.VOROBIEV, A.N.PIRKO
THERMAL CONDUCTIVITY OF GROUND OIL-MEAL AS THE DETERMINING PARAMETER OF A MATHEMATICAL MODEL OF HEAT-MASS TRANSFER IN EXTRACTED OIL-CAKE FILLING
All-Russia Scientific Research Institute of Fats, St-Petersburg, Russia

The problem on mathematical modeling of heat and mass transfer through a moist granular material layer is considered. An analytical solution of the nonstationary one-dimensional problem is obtained. Solid particles in the filling are assumed to be spherical.

T.ELPERIN, G.RUDIN
TEMPERATURE AND THERMAL STRESS DISTRIBUTION IN FUNCTIONALLY GRADED MATERIALS CAUSED BY A LASER THERMAL SHOCK
Department of Mecahnical Engineering, Pearlstone Center for Aeronautical Engineering Studies Ben-Gurion University of the Negev, POB 653, Beer-Sheva, Israel

The paper presents the theoretical principles underlying the method of a laser thermal shock used for thermal testing of the assembly composed of a substrate and a functionally graded thin coating. The two-dimensional temperature and thermal stresses distributions in the assembly heated by a pump laser beam are obtained from a solution of the thermal elasticity problem. The mathematical procedure developed is based on the expansion of Laplace and Hankel transforms of the temperature and displacement distributions in the FGM in Taylor series of a coating thickness. These distributions are used to determine operating parameters of the thermal shock method, e.g., laser power, duration of heating, laser beam radius. It is found that the coating composition and the laser beam radius strongly influence the thermal stress at the coating - substrate interface.

V.N.EMEL'YANOV, V.V.LOBACHEV, M.A.SIZOV
SIMULATION OF CONJUGATE HEAT TRANSFER IN THE COOLING SYSTEM OF ACTIVE ELEMENTS OF A SOLID-STATE LASER
"Voenmekh" Baltic State Technical University, Russia

The process of unsteady heat transfer in the cooling system of a solid-state laser is discussed. A system of mathetical modeling is proposed. Distributions of temperature, heat fields are obtained both in the cooling part and in the active element of the solid-state laser.

R.SH.ENALEEV, V.A.KACHALKIN, I.A.ABDULLIN, M.R.KHALITOV
A MODEL OF HEAT-PROTECTION PROPERTIES OF TEXTILE FABRICS UNDER EXTREME SITUATIONS
Kazan State Technological University, Russia

A mathematical model of the high-intensity heat and mass transfer process in textile fabrics is presented. Internal energy sources of physical and chemical origin, i.e., volume absorption of radiation, moisture evaporation and condensation, thermal decomposition of a cellulose material are taken into account in the model equations. The worked out calculation algorithm of numerical solution of the mathematical model allows identification of the source functions and testing of different hypotheses about the heat and mass transfer mechanism.

YU.A.GLADYSHEV
GENERALIZED METHODS OF THE THEORY OF FUNCTIONS OF A COMPLEX VARIABLE AND BOUNDARY-VALUE HEAT COMDUCTION PROBLEMS
Kaluga State Pedagogical University, Russia

Effectiveness of using the methods of complex function theory in solving boundary-value problems of two-dimensional stationary heat conduction processes, especially with the compilcated geometry of regions, is well known. However, the use of the methods is strictly limited by the problem two-dimensionality, medium homogeneity, and the stationary character of the process. A review is made of the main generalizations of the complex function theory and applications of the methods for solution of the boundary-value problems of heat conduction in anisotropic and inhomogeneous media of the nonstationary problems and heat conduction problems in thin curvilinear shells.

K.B.ISAYEV
DESIGNS OF A HEAT RECEIVER FOR DETERMINATION OF ONE-DIMENSIONAL TEMPERATURE FIELDS IN COMPACT AND POWDER MATERIALS 
Institute for Problems in Material Science, National Academy of Sciences of the Ukraine, Kiev

Various designs of a heat receiver, i.e., a sample with thermocouples, both for compact and for powder materials are proposed. It allows determination of one-dimensional temperature fields in samples of these materials under one-sided heating (various high-temperature jets, concentrated solar radiation, liquid metals, etc.). On development of heat receiver designs it is taken into account that both the compact and the powder materials under heating can undergo various physical and chemical transformations.

V.V.IVANOV, L.V.KARASEVA, N.N.STANKOVA
DYNAMICS OF HEAT TRANSFER IN MULTILAYER BUILDING STRUCTURE
Rostov State University of Civil Engineering, Russia

The process of multilayer building structure heating by convection and solar radiation is mathematically described. A numerical scheme for calculation of nonstationary temperatures is suggested.

V.V.IVANOV, S.V.CHERNYSH
TRANSFER PROCESSES IN UNDERGROUND HEAT PIPELINES
Rostov State University of Civil Engineering, Russia

A mathematical model of heat transfer processes is given which allows calculation of a temperature field of the ground and evaluation of heat losses in the underground channel and channel-free heat pipelines is presented.

A.R.KACIMOV, YU.V.OBNOSOV
CONVECTION AND CONDUCTION TRANSFER IN A MEDIUM WITH INCLUSIONS (ANALYTIC SOLUTIONS)
Sultan Qaboos University, Oman, United Arab Emirates; Institute of Mathematics and Mechanics at the Kazan University, Russia

Steady heat transfer in a two-dimensional system including a circular isothermic or a parabolic inclusion, the conductivity of which differs from the ambient one is studied. For the cavity, the conduction is accompanied by convection (constant velocity) and the Helmholtz equation solution is analyzed in terms of the Concer-Philip expansions. Three regimes are distinguished when the cavity acts as a source or a dipole. For the inclusion, the Laplace equation holds in two zones of contrasting conductivity, i.e., convection is ignored. The refractive condition is imposed along the interface (the continuity of temperature and the normal flux component). Two fluxes are found in the explicit form and the impedance, angle of rotation of the incident field, and dissipation are calculated.

E.M.KARTASHOV
PRESENT-DAY ANALYTICAL METHODS TO SOLVE BOUNDARY-VALUE UNSTEADY HEAT CONDUCTION PROBLEMS IN A REGION WITH MOVING BOUNDARIES
M.V.Lomonosov State Academy of Fine Chemical Technology, Moscow, Russia

A brief survey of methods for solving the boundary-value heat conduction problems in a region with moving boundaries is presented. The methods described are the Green function method, the method of integral equations, the method of generalized series, the function transformation method, the method of differential series, the method of contour integration. The brief characteristic of the methods and the sphere of their application are given.

O.N.KHATUNTSEVA
DESCRIPTION OF HEAT TRANSFER PROCESSES IN FRACTAL STRUCTURES
"Energy" Russian Space Complex, Korolev of the Moscow Region, Russia

Consideration is given to a method used to describe physical processes occurring in the spaces with fractional dimensionality (fractal structures) by using the differential equations written for the spaces with the Euclidean geometry and by performing renormalization of a time variable.

Z.Z.KHODZHIMURATOVA, A.KH.YAKUBOV, SH.M.GULYAMOV, SH.NURITDINOV
COMPUTER-AIDED ANALYSIS OF THE CONDUCTION EQUATION AIMED AT PARAMETRIC IDENTIFICATION
Tashkent State Technological University, Uzbekistan

Consideration is given to the analytical relationship of the integral characteristics of kinetics of transient heat- (or mass) conduction processes through solids in the form of an infinite plate, sphere and an infinite cylinder at the third-kind boundary conditions.

S.KHOKHULIN, V.BULATNIKOVA
MODELING OF A THERMAL REGIME OF THE INTEGRATES STRUCTURES OF SMALL-SIZE SPACE VEHICLES
Moscow State Aviation Institute (Technical University)

A combinatory mathematical model of a thermal regime of structure under consideration is developed. The thermal models of the structural elements are described, in relation to their spatial dimensionality, by the heat balance equations or heat conduction equations of the appropriate dimension. With use of elements of the graph theory a system of graphic maping of the thermal model and the ways of model modification and updating are developed. Algorithms to solve the present problem are also developed. The algorithms employ the conventional methods of the finite-difference solution of the parabolic inhomogeneous nonstationary equations of mathematical physics, the earlier developed methods for solving the one-dimensional systems and the method of "skeleton" structures.

E.S.KISELYOV, V.N.KOVAL'NOGOV
MODELING OF A THERMAL CONDITION OF THE CONTACTING OBJECTS UNDER MATCHED GRINDING BY LIBRICANT-COOLANTS
Ul'yanovsk State Technical University, Russia

A mathematical model and a method to calculate a thermal condition of a workpiece and a grinding wheel under matched grinding by lubricant-coolants are proposed. Results of numerical and experimental research of thermal processes under matched grinding are given. The expediency of applying ultrasonic-feeding of lubricant-coolants for matched grinding of workpieces is shown. 

L.A.KOZDOBA
OPTIMAL CONTROL OF HEAT AND MASS TRANSFER PROCESSES
Institute of Technical Thermal Physics of the National Academy of Sciences of the Ukraine, Kiev

It is shown that heat and heat and mass transfer processes under certain conditions represent heat systems (HS). The heat systems have integrative system properties which are determined in solutions of primal direct problems. Optimal control problems (OCP) are the problems with allowance for thermoaerohydrodynamic processes as well as complex problems with regard for economic, ecological, biosphere and other simultaneously occurring processes. The power economy problem can be solved only by HS synthesis and by solving the OCP of heat and mass transfer. Heat and fuel economy is the target of the complex OCP in which an HS is an important but not the main subsystem from the standpoint of heat economy.

L.A.KOZDOBA
SYSTEM PROPERTIES OF HEAT SYSTEMS AND OPTIMIZATION METHODS
Institute of Technical Thermal Physics of the National Academy of Sciences of the Ukraine, Kiev

System integrative properties (IP) of systems (S) are the properties of a whole S but not of its separate parts, qualities, peculiarities, characteristics - subsystems (SS). The principle of S singularity and the plurality principle of models of the initial physical S models are described. It is shown that both the simulation and S models hierarhy principles permit one to find IP. The problems of heat systems (HS) analysis are the primal problems, the problems of HS synthesis are the optimal control (OCP) of heat and mass transfer processes. Power economy problems can be solved by synthesis of complex S, HS being included as SS. Any methods of OCP solution, including special methods of analysis and synthesis, are applied for HS optimization. Examples of IP determination of heat and heat economy S are given.

P.G.KRUKOVSKY, A.S.POLUBINSKY, M.E.KOPILENKO, S.V.NOVAK
THE STATE-OF-THE ART OF THE PROBLEM OF SIMULATION OF FIRE INDOORS
Ukrainian Scientific Research Fire Defence Institute of the Ministry of Internal Affairs of the Ukraine, Kiev; Institute of Technical Thermal Physics of the National Academy of Sciences of Ukraine, Kiev

An analysis is made of the existing models and methods of calculation of heat and mass transfer processes under fire and fire resistance conditions of building and enclosing constructions of premises of different type. Some features of different fire models, namely, zone models and computational fluid dynamics models are considered and analyzed. Special emphasis is placed on a review and analysis of capabilities of the existing and developed software: finite element packages (FEM), CFD-packages, zone models software. The results obtained by the authors on modeling of typical dwelling premises and an NPP turbine rooms for determination of the fire resistance of building constructions under real fire conditions are reported.

P.G.KRUKOVSKY, Y.M.SHWARTS
HEAT ANALYSIS OF ERRORS IN TEMPERATURE MEASUREMENT BY SILICON SENSORS WITHIN A RANGE OF 4.2-500 K
Institute of Technical Thermal Physics of the National Academy of Sciences of Ukraine, Kiev; Institute of Semiconductor Physics of the National Academy of Sciences of Ukraine

A calculation analysis is made of the errors in temperature measurement by a semiconductor silicon sensor under different conditions of heat transfer between an ambient medium and an object in contact as well as a level of current running through the sensor. The finite element method is employment to study a thermal condition of the sensor in the three-dimensional nonstationary statement with allowance for the heat conduction process in all sensor elements. The relationship of superheat of the p-n transition for the medium with a temperature measured errors for a current of 100 A, a temperature range of 4.2-500 K, heat transfer coefficient of 3-3000 W/(m·K) are presented.

V.I.KRYLOVICH, G.N.BYL', E.V.IVAKIN, A.S.RUBANOV
ON EXPERIMENTAL DETERMINATION OF A HEAT VELOCITY
Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer Institute" of the National Academy of Sciences of Belarus, Minsk

A theoretical analysis of the conditions and the requirements on the measuring equipment, at which the effect determined by the finaleat velocity can be experimentally recorded, are provided. On the basis of solutions of the hyperbolic and parabolic heat conduction equations and their numerical comparison it is shown that these effects and a heat velocity in different media can be investigated and measured by the method of thermal dynamic gratings.

V.A.KUDINOV, B.V.AVERIN, A.B.REMEZENTSEV, R.ZH.GABDUSHEV, V.A.OBUKHOV
NEW TRENDS IN OBTAINING ANALYTICAL SOLUTIONS OF BOUNDARY-MULTILAYER CONSTRUCTIONS
Samara State Technical University, Russia

Results of development of two trends in obtaining analytical solutions of heat conduction, heat and mass transfer and thermoelasticity problems for multilayer constructions are obtained. The first trend is based on exact and approximate analytical methods. The second trend is based on using the generalized functions asymmetrical unit function and the Dirac delta function.

V.A.KUDINOV, V.V.DIKOP, S.K.SERGEEV, D.K.NAZARENKO
ANALYTICAL SOLUTIONS OF PROBLEMS OF INTERRELATED HEAT AND MASS TRANSFER FOR MULTILAYER CONSTRUCTIONS
Samara State Technical University, Russia

We have obtained an analytical solution of a boundary-value problem of heat and mass transfer for a two-layer infinitely extended plate with allowance for a gradient of total pressure. Systems of coordinate functions are built which exactly satisfy the boundary conditions and conjugation conditions of the problem.

E.M.KUDRYAVTSEV, V.I.EMEL'YANOV, M.OUMRIK
UNSTEADY ENERGY TRANSFER IN A SOLID BY SOLITON-LIKE WAVES EXCITED BY A LASER PULSE
Institute of Physics of the Russian Academy of Sciences; Moscow State University, Moscow; Marsel University, France

Experimental and theoretical studies have been made of the solitonic nature of laser induced nonequilibrium wave processes of energy transfer in solids after laser pulse action. The new phonomenon is discovered, i.e., a wave of changing the optical reflection and electrical conduction, observed in the study of different types of solids. The study of this phenomenon pertains to the fundamental problems of solid-state physics and thermophysics related with nonequilibrium transfer of energy absorbed in solids upon pulse interaction of powerful electromagnetic, heat or corpuscular flows. The work was supported by RFBR, project 97-02-17954-a.

YU.I.KUKLEV, A.M.TOLSTONOZHENKO, V.V.POLITOV
ALLOWANCE FOR THE EFFECT OF AN ADDITIONAL EXOTHERMAL SOURCE IN THE NONLINEAR THEORY OF MELTING AND ABLATION OF MATERIALS
K.E.Tsiolkovskii Russian State Aviation Technological Institute, Russia

A non-linear theory of melting and ablation is considered with allowance for a supplementary exothermal source during laser destruction of element-organic compounds. The approach is based on the Rykalin-Uglov-Smurov method with use of transformation of the nonstationary heat conduction problem to a mathematical analysis of the Lanrange equations in classical mechanics (the Biot method).

G.V.KUZNETSOV, E.S.NESTEROVA, A.I.TKACHEV
HEAT TRANSFER IN INERTIA PRECIPITATION OF PARTICLES FROM HIGH TEMPERATURE GAS FLOWS
Scientific Research Institute of Mathematics and Mechanics at the Tomsk State University, Russia

A numerical solution is obtained for the temperature of a metal particle deposited from a high temperature gas. The problem is solved in a two-dimensional statement with allowance for the process of melt crystallization on a substrate without obvious phase interface separation. A time-temperature relation in the "liquid particle-solid base" zone of contact for various combinations of the thermal properties of the particle and base materials and different sizes of the particles deposited is investigated. For the purpose of temperature prediction in the particle-substrate zone of contact with a high accuracy the results obtained allow a conclusion to be made about the necessity of using the multidimensional heat conduction equations and accounting for the melt crystallization on the substrate.

YU.M.MATSEVITY
PARAMETRICAL IDENTIFICATION OF THERMOPHYSICAL PROCESSES
A.N.Podgornyi Institute for Mechanical Engineering Problems of the National Academy of Sciences of the Ukraine, Khar'kov

Classification of inverse heat conduction problems, their formulations and solution methods are under consideration. Regularization techniques for the solutions are analyzed. A review of the solved applied problems in the field of mechanical engineering, on identification of heat processes in objects of mechanical engineering, in technological processes and radioelectronic equipment is given.

YU.M.MATSEVITY, A.P.SLESARENKO, V.V.GANCHIN
REGIONAL-ANALYTICAL MODELING AND IDENTIFICATION OF THERMAL PROCESSES IN A COMBUSTION ENGINE ELEMENT
A.N.Podgornyi Institute for Mechanical Engineering Problems of the National Academy of Sciences of the Ukraine, Khar'kov

Algorithms of the regional-analytical modeling and identification of thermal processes in the combustion engine elements using the data of a thermophysical experiment are proposed. The algorithms are based on the combined use of the regional-analytical method and minimization of the mean-square functional of a difference of the sought temperatures obtained from the data of the thermophysical experiment. Numerical results of calculating the heat transfer coefficient and the heat flow over some regions of the heat ring surface are given.

S.YU.MESNYANKIN
CONTACT HEAT CONDUCTION AND THE WAYS OF ITS INCREASE
Moscow State Aviation Institute (Technical University), Russia

The influence of various factors on the contact heat conduction is analysed and the theoretical prerequisities are experimentally confirmed. Quantitative evaluation of the effect of increasing the contact heat conduction is made in the presence of coatings in flat and cylindrical connections, theoretical substantiation of the results and recommendations for practical use of the methods proposed are given.

N.D.MOROZKIN, I.I.GOLICHEV, A.V.DUL'TSEV
ITERATIVE METHOD OF SOLVING THE PROBLEM OF NONLINEAR HEATING WITH PHASE RESTRICTIONS
Bashkir State University, Ufa, Russia

The problem of the highest-speed external heating of an unbounded plate with allowance for limitations on thermal stresses and surface temperature is investigated. A nonlinear temperature dependence of the thermal conductivity and strength charactersitics (for brittle and plastic materials) is taken into account. Computing experiments have shown the high efficiency of the approach suggested.

V.P.MOTULEVICH, V.I.GUDKOV
THE METHOD OF RELATIVE CORRESPONDENCE AS APPLIED TO HEAT AND MASS TRANSFER PROBLEMS
Moscow Power Engineering Institute (Technical University), Russia

Consideration is given to the method of approximate calculations and analysis of physical phenomena based on the fact that in determination of relative values characterizing the process use can be made of less precise models than in the case of determining the absolute values. The preferable variants of correlations of the single-valued model and precise functions of one real variable as well as the ranges of changing the characteristic relative values are proposed. The examples of solving the following problems are given: heat transfer of bodies with a liquid flow in the range of the front critical point with suction and injection of a substance, the influence of surface holes on the heat transfer and friction, combustion of fuel particles in the flow enriched with oxygen. The possibilities of using the method in measurements are discussed.

G.A.NESENENKO
INVESTIGATION OF CONDENSED MATTER IGNITION IN THE PRESENCE OF A PHASE TRANSITION BY THE "GEOMETRICAL-OPTICAL" ASYMPTOTIC METHOD
N.E.Bauman Moscow State Technical University, Moscow, Russia

A new approach to the problem of condensed matter ignition accompanied by a phase transition is represented. A mathematical description of the ignition process (in terms of the dimensionless Franck-Kramenetskii variables) is based on the one-phase singularly perturbed Stefan problem with one unknown moving boundary and a nonlinear Arrhenius-type source. A solution of the problem is given in the form of asymptotic expansions in the Poincare sense in terms of the inverse powers of the Franck-Kamenetskii criterion Fk and the powers of the corresponding boundary variables. Using such expansions and taking into account the presence of the phase transition, we study the process by the analytical parametric method.

N.I.NIKITENKO
FUNDAMENTAL PRINCIPLES OF THE RADIATION THEORY OF HEAT AND MASS TRANSFER
Institute of Technical Thermal Physics of the National Academy of Sciences of the Ukraine, Kiev

The mechanism and fundamental principles of the radiation theory of heat and mass transfer in solid and liquid bodies are described which are based on energy transfer by photons emitted and absorbed by substance particles. The author has obtained the heat and mass transfer equations that take into consideration the final velocity of heat propagation and in the limit reduce to the phenomenological equations; the functions of atoms energy distributions and their degrees of freedom in diffusion processes; the formulas for specific heat diffusion and thermodiffusion coefficients of body components which agree with the experimental data.

N.I.NIKITENKO, YU.N.KOL'CHIK
A REFINED METHOD OF CANONICAL ELEMENTS FOR SIMULATION OF HEAT CONDUCTION, DIFFUSION AND DEFORMATION PROCESSES IN THE REGIONS OF ARBITRARY CONFIGURATION WITH CURVILINEAR BOUNDARIES
Institute of Engineering Thermal Physics of the National Academy of Sciences of the Ukraine, Kiev; Kiev National University of Civil Engineering and Architecture, Ukraine

A method to calculate heat and mass transfer and a stressed state of multiply connected bodies with variable thermophysical and mechanical characteristics under arbitrary boundary conditions has been developed. The method is based on the general method of canonical elements proposed earlier by the present authors and possesses certain advantages as compared to the other numerical methods of solution of such a problem. A comparison of the results of numerical experiments to some exact solutions of the problems of thermal stressed state of bodies with curvilinear boundaries testifies to the high accuracy and effectiveness of the method.

S.V.NOVAK, I.A.KHARCHENKO, P.G.KRUKOVSKII, M.E.KOPILENKO
A CALCULATING-EXPERIMENTAL APPROACH TO PARAMETER OPTIMIZATION OF FIRE-RESISTANT CONSTRUCTIONS
Scientific Research Fire Defence Institute of the Ministry of Internal Affairs of Ukraine; Institute of Engineering Thermal Physics of the National Academy of Sciences of Ukraine, Kiev.

The authors provide the statement and a calculating - experimental method to solve the problems of parameter optimization of fire-resistant constructions by using the thermometry data obtained in testing the constructions for fire-resistance.

A.S.OKHOTIN, L.I.ZHMAKIN
A SOLUTION OF THE HEAT CONDUCTION EQUATION WITH ALLOWANCE FOR THE NONLINEAR EFFECTS IN HEAT TRANSFER
A.N.Kosygin State Textile University, Moscow, Russia

An approach to thermal conductivity calculation of a substance is discussed which is based on the conception of mobility of heat carriers (electrons, phonons, etc.). An equation suggested for the mobility allows an analysis of the mechanism of heat transfer by conduction. Temperature dependences of the mobilities of heat carriers in different substances are obtained in the form of power functions.

M.A.OSHIVALOV, T.A.ULRIH, G.L.KOLMOGOROV
THERMAL BEHAVIOR OF MACHINING ATTACHMENTS IN CONTACT WELDING
Perm' State Technical University, Russia

A mathematical model of contact spot welding is suggested based on a solution of the connected system of differential electric and heat conduction equations and a system of the thermoelastoplasticity equations allowing for technological factors and nonlinear material properties. The results of an analysis of a thermal condition of electrodes under different operation conditions are discussed.

N.V.PASHATSKY, A.V.PROKHOROV
PROCESSING OF MATERIALS BY A HIGH-INTENSITY HEAT SOURCE
Ozyorsk Technological Institute at the Moscow Engineering Physics Institute, Chelyabinsk Region, Russia

A model of heating of a thick plate by a high-intensity heat source taking into account heat exchange with environment and finite sizes of a workpiece is suggested. The model is based on action of internal heat sources. Using the Fourie method an expression is obtained to calculate a temperature at any point of the plate; a calculation is carried out for various heat-transfer conditions on heating of a concrete plate by a plasmatron torch.

V.A.PINSKER
DISTRIBUTION OF TEMPERATURE AND QUASISTATIC THERMOELASTIC FIELDS IN THE SPACE CONTAINING AN INFINITE CIRCULAR CYLINDRICAL CAVITY WITH A RING-TYPE HEAT SOURCE ON ITS PERIMETER
"Drilling Equipment" Public Joint-Stock Company at the Scientific Research Institute of Drilling Equipment, Moscow, Russia

An exact analytical solution of the stated unsteady problem is obtained in the closed integral form. The important particular cases are examined in which formulas for a temperature and stresses are more simple. Asymptotics of the found solutions obtained both for small and large values of nondimensional time in the vicinity and at a distance from the cylindrical cavity are investigated. The isotherms and isobars are studied. The possibility of mechanical failure both on the cavity surface and in its vicinity is investigated.

S.B.PONOMAREV, S.V.GRIGORYEVA, A.N.DRYAZGOV, S.KHANYNI
A MATHEMATICAL MODEL AND A COMPUTER PROGRAM TO CALCULATE THE TEMPERATURE FIELD OF AN AXISYMMETRICAL CYLINDRICAL DEVICE WITH A LAMINAR LIQUID FLOW IN IT
Tambov State Technical University, Russia

A mathematical model and a computer program for temperature field calculation in an axisymmetric cylindrical device with an internal laminar liquid flow are developed. The mathematical model allows both the direct and inverse heat conduction boundary-value problems to be solved for a measuring device, used to measure thermophysical properties of the liquid by a laminar flow method. The solution of the inverse boundary-value problem is based on a numerical solution of the direct boundary-value heat conduction problem. A peculiar feature of the model investigation of heat transfer both in the liquid and in the other parts of a measuring device.

YU.S.POSTOL'NIK
HIGH-SPEED HEATING OF THERMOSENSITIVE MATERIALS WITH LIMITATIONS ON CONTROL CONDITIONS AND THE OTHER PROCESS CHARACTERISTICS
Dneprodzerzhinsk State Technical University, Ukraine

The statement and result of an approximate solution of some nonlinear problems of control of thermal processes of high-speed heating of flat, cylindrical and spherical bodies are given.

S.V.PUZACH, V.G.PUZACH, R.V. PROZOROV
MODELING OF HEAT AND MASS TRANSFER DURING FIRE INDOORS
Moscow Fire Defence Institute of the Ministry of Internal Affairs of Russia; Institute of High Temperatures of the Russian Academy of Sciences, Moscow, Russia

A three-dimensional mathematical model for calculation of heat and mass transfer during fire indoors is proposed. A comparison is made of the results obtained by the proposed model with an analytical solution and an integrated mathematical model at different mutual locations of a burning material relative to an open hole and a different level of the open hole relatively the floor. A field of the correct use of the integrated model for calculation of characteristics of the initial stage of fire is revealed. An influence of the basic characteristics of the problem on the time of release of the gases through the open hole is investigated. Characteristic temperature and velocity fields are obtained. Three-dimensional effects of the thermodynamic flow pattern are discovered.

E.YA.RAPOPORT, M.YU.LIVSHITS, YU.E.PLESHIVTSEVA
AN ALTERNANCE METHOD IN OPTIMIZATION OF THE TECHNOLOGICAL THERMAL PHYSICS PROCESSES: FUNDAMENTAL THEORETICAL PRINCIPLES, COMPUTATION ALGORITHMS, EXPERIENCE OF APPLICATION
Samara State Technical University, Russia

Parametrized problems of the optimum control of the processes of technological thermal physics are reduced to non-smooth mathematical programming problems (NPMP) with an infinite number of constraints. A computational algorithm (an alternance method) is developed to solve the NPMP. This algorithm is based on special (alternance) properties of the resultant spatial distributions of controlled fields. The indicated properties are a consequence of the general theory of the necessary extremum conditions in the NPMP under consideration. Practical results obtained are given. Examples demonstrating the possibilities of the alternance method in the parametric optimization problems of nonstationary heat and mass transfer processes.

A.F.RED'KO, V.A.MALYARENKO, YU.I.CHAIKA
HEAT- AND MASS TRANSFER PROCESSES IN MULTILAYER PROTECTING CONSTRUCTIONS
Khar'kov State Technical University of Civil Engineering and Architecture, Ukraine; Khar'kov State Academy of Municipal Management, Ukraine

The work is devoted to improvement of the technique of modeling the heat-mass transfer in multilayer protecting constructions of buildings with the purpose of perfecting the methods of their designing. The general algorithm of a solution of the problem is described. The results of solutions of the primal problems are given: measures for warmth-keeping of existing buildings; construction of buildings with multilayer external protecting constructions with resistance to heat transfer in conformity with the European standards.

A.G.RUBIN
THERMOELASTIC STRESSES IN A MASSIVE SOLID WITH A MOVING BOUNDARY UNDER TEMPERATURE HEATING WITH A FINAL VELOCITY
M.V.Lomonosov Moscow State Academy of Fine Chemical Technology, Russia

Consideration is given to the first-kind boundary-value problem of the dynamic thermoelasticity equation for a half-space with a uniform moving boundary when the temperature of the boundary surface at first linearly increases and then remains unchanged (a temperature heating with a finial velocity). For the mentioned statement of the problem exact analytical solutions of the dynamic thermoelasticity equation were obtained and on their basis an influence of the heating time, the moving boundary velocity, the depth of the considered section in the half-space on the mode of changing the thermal stresses were investigated separately and in all possible combinations.

A.A.SAMARSKII, V.I.MAZHUKIN
SOLUTION OF HEAT-MASS TRANSFER PROBLEMS BY THE DYNAMIC ADAPTATION METHOD
Institute of Mathematical Modeling of the Russian Academy of Sciences, Moscow, Russia

The problem of construction of computational grids with optimal node distribution is especially important in the evolution-type problems characterized by solution singularities that can appear and move through the entire domain. The paper is devoted to all-round demonstration of the dynamic adaptation capabilities on the example of two important and well-known heat-mass transfer problems: the combustion of matter and phase transformations in a metal. In the combustion problem the main computational peculiarity is initiation and propagation of large-gradient zones, while in the phase transformation problem it is the presence of two interacting two-dimensional phase fronts melting and evaporation.

A.A.SAMARSKII, P.N.VABISHCHEVICH
DIFFERENCE SCHEMES TO SOLVE THE HEAT AND MASS TRANSFER PROBLEMS USING IRREGULAR GRIDS
Institute of Mathematical Modeling of the Russian Academy of Sciences, Moscow, Russia

The possibilities of solving the problems of mathematical physics using irregular grids are discussed. The emphasis is laid on approximation of the convection-diffusion equations as the most important ones for applications. The main attention is given to constructing the difference schemes on triangular grids (as the most general unstructured grids). Approximations on the Delaunay grids (triangulations) which possess the optimum properties are highlighted as those possessing the most optimum properties.

YU.A.SELYANINOV
TECHNOLOGY OF SOLVING THE HEAT CONDUCTION PROBLEMS
Perm' State Technical University, Russia

A series of the problems concerned with heat transfer in solid bodies is investigated. Different statements of the heat conduction problem are considered, their analytical and numerical solutions are obtained. Comparative evaluation is made of effectiveness of the method of heat balance meshes of a coordinate grid and a numerical solution of the boundary-valueconduction problem is given. The problems of obtaining the results of a prescribed accuracy are investigated. Accumulation of errors in solving a set of equations by a sweep method is evaluated. The object-oriented technique of constructing new difference schemes is formulated. The difference schemes ensuring an increased accuracy of solutions of the nonstationary heat conduction problems on rough grids are proposed. 

O.V.SEMENOVICH, A.V.UDOT
ON NUMERICAL INVESTIGATION OF TEMPERATURE FIELDS IN SUPERLARGE INTEGRAL MICROCIRCUITS
Institute of Power Engineering Problems, National Academy of Sciences of Belarus, Minsk, Belarus

A mathematical model of heat transfer in superlarge integral microcircuits is presented. The computation technique developed is based on the method of finite elements. The results of computation experiments aimed at investigation of the effect of different factors on temperature parameters of a microcircuit are presented.

A.P.SLESARENKO
INTEGRAL TRANSFORMATIONS, REGIONAL-ANALYTICAL AND VIBRATIONAL-DIFFERENCE METHODS IN MULTIDIMENSIONAL HEAT CONDUCTION PROBLEMS FOR INHOMOGENEOUS MEDIA
A.N.Podgorny Institute for Mechanical Engineering Problems of the National Academy of Sciences of the Ukraine, Khar'kov

A combined application of integral transformations, Duamel's integral, the regional-analytical method, methods of final differences and least squares is proposed for solving the multidimensional nonstationary heat conduction problems for inhomogeneous media. The variational-difference method is proposed for solving the given problems using a three-layer differential scheme or one of the coordinates with fictitious heat fluxes and solving the obtained problems for each layer by the variational methods with the use of the regional-analytical basic functions. Numerical results of solutions of particular problems are given.

A.P.SLESARENKO, D.A.KOTULSKY
REGIONAL-ANALYTICAL AND VIBRATIONAL METHODS IN SOLVING THE CONJUGATE CONVECTION HEAT TRANSFER PROBLEMS
A.N.Podgorny Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Khar'kov, Ukraine

The combined use of region-analytical and vibrational methods is proposed to solve conjugate convection heat transfer problems with an exact account of thermal contact for homogeneous media without allowance for the thermal initial region. In the second variant of the proposed approach with allowance for the thermal initial region and introducting an uncertain heat flux on the surface of contact of the homogeneous media, the combined use is made of integral transformations, region-analytical and variational methods as well as the Duhamel integral. Numerical results of solving the particular problems are given.

K.STEPHAN, J.SOLDNER
HEAT CONDUCTION IN A PHOTOACOUSTIC CELL
University of Stuttgart, Institut fur Technische Thermodynamik und Thermische Verfahrenstechnik, Germany

Although the photoacoustic effect was discovered already more than 100 years ago by Alexander Graham Bell, who planned to use it for telecommunication, the effect fell entirely into oblivion until it experienced a renaissance around 1970 with the inversion of tuneable laser sources. We used the effect to determine thermal diffusivities of gases. The paper presents the underlying theory which is based on transient heat conduction caused by the unsteady heat absorption of a modulated infrared laser beam. The periodically modulated laser beam provokes a small temperature rise of a few millikelvins in the test gas and a pressure rise of about 1 Pa recorded by a microphone. The temperature rise follows from a solution of the energy balance under the assumptions to the fulfilled in the experiment, namely, a constant gas density in the measuring cell, a large length-to-diameter ratio and rotational symmetry of the laser beam penetrating into the gas. It is also shown how the temperature field is converted into an acoustic signal. An uncertainty of the method used to determine thermal diffisivities is discussed and experimental results are presented.

S.V.TIKHONOV, V.V.VERKHOVSKY
HEAT TRANSFER IN MIRRORS OF LOWER-WEIGHT COSTRUCTION
St.Petersburg State Institute of Precision Mechanics and Optics (Technical University), Russia; St.Petersburg State Academy of Cold and Foodstuff Technologies, Russia

A method to calculate the effective thermal conductivity of large-scale mirrors of lower-weight construction is discussed which is used for an analysis of the thermoelastic state. Heat transfer problems with allowance for heat transfer by conduction over mirror's framework and by radiation in cavities are formulated. Based on a numerical solution, the effective thermal conductivities are investigated for typical materials and mirror constructions. It is shown that for mirrors made of materials with low thermal conductivity (quartz, for example) of their framework a contribution of radiation can make up to 40%. For the mirrors with high thermal conductivity only heat transfer along the framework can be taken into account.

V.I.TIMOSHPOL'SKY, I.A.TRUSOVA, V.B.KOVALEVSKY, A.P.NESENCHUK, R.B.VAIS
OPTIMAL HEATING CONTROL PROBLEM IN TERMS OF ENGINEERING SPECIFICATIONS
Belarusian State Polytechnical Academy, Minsk, Belarus

Solutions of the problems of optimal control of media heating in furnaces of the Belarusian Metallurgical Plant and Integrated Iron-and-Steel Works in Dnepropetrovsk in accordance with functional specifications such as minimum scale formation and thermal strength are given. The solutions obtained are based on the method of asymptotic route optimization.

N.M.TSIREL'MAN
DETERMINATION OF MULTIDIMENSIONAL NONSTATIONARY TEMPERATURE FIELDS IN NONCYLINDRICAL REGIONS
Ufa State Aviation Technical University, Ufa, Russia

A definition of nonstationary temperature fields in a multidimensional region with a movable boundary with variable properties of the medium is given. The method is based on a variational description with a convolution functional and representation of the sought solution according to L.V.Kantorovich.

O.N.SHABLOVSKY
SPATIAL INHOMOGENEITY AND EVOLUTION OF THE DISCONTINUOUS RELAXING HEAT FIELDS IN NONLINEAR MEDIA
P.O.Sukhoi Gomel State Technical University, Belarus

A constructive analytical method of solving the two-dimensional equations of relaxation heat transfer is presented. The method is based on construction of a heat analogue of the so-called hydrodynamic surface. An essentially nonlinear effect of appearance of the parabola line separating the regions with elliptic and hyperbolic types of the transfer equations is discovered. The structure of two-dimensional inhomogeneity of such fields in studied both analytically and numerically. The properties of a temperature gradient and of a heat flux on the parabola line and over the front of a heat shock wave are discussed.

V.V.SHEVELEV
METHOD OF INTEGRAL TRANSFORMATIONS IN SOLVING THE BOUNDARY-VALUE PROBLEMS OF HEAT AND MASS TRANSFER IN REGIONS WITH MOVING BOUNDARIES
M.V.Lomonosov Moscow State Academy of Fine Chemical Technology, Russia

An approach to solving the Stefan problems is developed which allows formulation of equations for deviation of a law of boundary motion.

V.B.VESELOVSKII
CALCULATION OF TEMPERATURE FIELDS AND OPTIMIZATION OF THE SYSTEMS OF MAINTENANCE OF THERMAL REGIMES OF SPACE VEHICLES
Institute of Technical Mechanics of the National Academy of Sciences of the Ukraine, Dnepropetrovsk, Ukraine

Algorithms are proposed for calculation of temperature fields and optimization of the passive, active and combined systems of maintenance of thermal regimes of space vehicles.

V.B.VESELOVSKII, A.V.OSTROVSKAYA, V.I.LYASHENKO, N.I.BELYI, V.A.STOLBCHENKO
CONTACT THERMAL RESISTANCE IN CONSTRUCTION COMPONENTS
Institute of Transportation Systems and Technologies of the National Academy of Sciences of the Ukraine; "Delfin" Predneprovie Scientific-Production Center, Ukraine

Results of theoretical and experimental studies of contact heat transfer in constructions of power engineering plants and in technological processes are reported.

YU.V.VIDIN
CALCULATION OF THERMAL CONDUCTIVITIES OF SOLIDS AT VARIABLE HEAT TRANSFER COEFFICIENTS
Krasnoyarsk State Technical University, Russia

A method of successive approximations for calculations of a nonstationary temperature field of solids heated by a convective heat flux is described. The heat transfer coefficient depends arbitrarily on time. The method developed is based on a mathematical operation of transfer of a nonstationary component of the heat transfer coefficient to the temperature of a heating medium. Owing to such transformation the problem reduces to the linear one, a solution of which is either known or can be comparatively easily obtained.

V.S.VIKHRENKO, G.S.BOKUN, YA.G.GRODA
STATISTICAL-MECHANICAL DESCRIPTION OF THERMAL CONDUCTIVITY AND THERMAL DIFFUSION OF LATTICE GASES
Belarusian State Technological University, Minsk, Belarus

Based on the method of the D.Zubarev nonequilibrium statistical ensambles, the equations for evolution of numerical density of particles and energy are derived. General expressions for diffusion, thermal diffusion and thermal conductivity are obtained. These coefficients are analyzed for a lattice system of noninteracting particles for a system with interaction of the nearest neighbors.

M.S.ZHELUDKEVICH, M.L.GERMAN, A.N.OZNOBISHIN
CONTROLLED COOLING. THEORY AND EXPERIENCE OF APPLICATION
Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer Institute" of the National Academy of Sciences of Belarus, Minsk

A mathematical model and a numerical method are proposed for calculation of pulsed hardening processes and determination of controlled cooling regimes. Based on the method, a controlled hardening technology is described. The use of this technology at the Minsk Automobile Plant for hardening of hammer inserts with mass up to 8000 kg has shown the high efficiency and gives more profit in comparison with traditional hardening technologies. The main advantages of the technology are discussed.

V.I.ZINCHENKO, A.YA.KUZIN
INVESTIGATION OF THE THERMAL STATE OF A SPHERE-BLUNT CONE IN A HYPERSONIC SPATIAL FLOW BY THE METHODS OF SOLVING THE PRIMAL AND INVERSE HEAT- AND MASS TRANSFER PROBLEMS
Tomsk State University, Russia

A regularized numerical method for solving the three-dimensional boundary-value inverse heat- and mass transfer problem on determination of a heat flux and temperature on the surface of a sphere-blunt cone in a hypersonic spatial flow is developed. As a result of solving the primal and inverse problems, the efficiency of using the high-conductivity materials and blowing of a gas-cooler from the blunt sphere surface for decreasing the maximum heat fluxes and surface temperatures is shown. The limits of applicability of the one-dimensional approaches and the thin-wall method for regeneration of a heat flux to a streamlined body in a whole time range of the process are determined.

SECTION NO. 4. "HEAT AND MASS TRANSFER IN CHEMICALLY REACTING SYSTEMS"

I.A.ABDULLIN, R.SH.ENALEEV, R.R.DIMUKHAMETOV
HEAT AND MASS TRANSFER PROCESSES IN COMBUSTION OF SMALL GAS-CONTENT COMPOSITIONS

Kazan State Technological University, Tatarstan

The results of energy transfer processes in the system "small gas-content composition - steel substrate" are given. The method and technology of an automatic experiment for determination of energy parameters of the SGCC combustion are suggested. The evaluation of energy transfer components by different mechanisms is carried out.

O.V.ACHASOV, S.A.LABUDA, O.G.PENYAZ'KOV
GASDYNAMIC STIMULATION OF COMBUSTION PROCESSES
Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer Institute of the National Academy of Sciences of Belarus", Minsk, Belarus

Results of the investigation of some gasdynamics methods of control both the initiation and the propagation of deflagration and detonation types of combustion in gaseous fuel-oxidizer mixtures are presented. A comparative analysis of the regimes of deflagration combustion front propagation under different gasdynamic conditions is carried out in an undisturbed medium, with circular gas swirl in a combustion chamber as well as for large vortex fluxes being formed in the combustible mixture due to pulse injection of combusting gas jets into the chamber. Different regimes of detonation combustion initiation and propagation under gasdynamic focusing are considered.

N.E.AFONINA, V.G.GROMOV, V.L.KOVALEV
ANALYSIS OF HEAT TRANSFER ON THE CATALYTIC SURFACES OF HEAT SHIELDING COATINGS OF SPACE VEHICLES ENTERING IN THE MARTIAN ATMOSPHERE
M.V.Lomonosov Moscow State University, Russia

A model of heterogeneous catalysis of a dissociated mixture of carbon dioxide and nitrogen on a high-temperature heat shielding material surface with allowance for non-equilibrium adsorption-desorption reactions of oxygen and nitrogen atoms, carbon dioxide molecules and their recombination in the Eley-Rideal reactions is proposed. From a comparison of heat fluxes measured on a VGU-4 IPM RAS plasmatron and those calculated under the same conditions the parameters of the catalysis model are chosen on three oxidation-resistant coatings of present-day heat shielding materials. For each coating the convective heat fluxes in the critical point neighborhood of a space vehicle along the entry trajectory in the Martian atmosphere are calculated.

Zh.S.AKYLBAEV, S.G.KARITSKAYA, G.I.KOBZEV
HEAT AND MASS TRANSFER OF A LUMINESCENT PHOTOPRODUCT IN OXYGEN-SATURATED SOLUTIONS
Karaganda State University, Karaganda, Kazakhstan

In anthraquinone the events of mass transfer in the form of concentration redistribution of a luminescent photoproduct in the reaction zone are investigated. The effect found is a result of occurrence of luminescent spatial - temporary structures (STS) in the course of photochemical processes initiated by UV radiation. It is revealed that local convection, arising during photoreactions, promotes formation of "slow" and "oscillatory" stages in STS development. The various concentration ratios of the anthraquinone and the dissolved oxygen, and their influence on the occurrence and development of the STS are investigated. It is shown that the kinetic system of the differential equations and the set of chemical reactions must be supplemented with the energy transfer reaction for the solvent.

A.ANOSHKO, V.S.ERMACHENKO, R.V.MERINOV, L.F.SANDRIGAILO
DETERMINATION OF THE ELECTRON TEMPERATURE IN PLASMA FLOWS OF THE COAXIAL HALL ACCELERATOR BY USING A HALF-CORONA MODEL
Academic Scientific Complex "A.V.Luikov Heat and Mass transfer Institute of the National Academy of Sciences of Belarus", Minsk, Belarus

Results of determination of the electrons temperature in the plasma of the coaxial Hall accelerator (CHA) by using the half-corona equilibrium model are reported. A method is suggested to determine the temperature by simultaneous measurement of the intensities of a large number of spectral lines of two subsequent stages of one element-ionization which allows measurements to be made under nonequilibrium plasma conditions of the CHA.

O.S.ANTONOV, R.S.TYUL'PANOV
DETERMINATION OF THE INNER HEAT AND MASS TRANSFER CHARACTERISTICS IN DIFFUSION FLAME
St.Petersburg State Technological University of Phytopolymers, Russia

The application of the schlieren method with different optical filters and chemical species (He, Na, Cs) added to turbulent diffusion flame is considered. It is found that the character of correlation functions for optical density changes so that it can be explained by different molecular-turbulent transfer coefficients for different substances and heat in the flame microzones.

A.S.ASKAROVA, S.A.BOLEGENOVA, I.V.LOKTIONOVA
COMBUSTION EFFECT ON THE SURFACE FRICTION AND CONVECTIVE HEAT TRANSFER COEFFICIENTS IN A CHANNEL
Al'-Farabi Kazakh State National University, Kazakhstan

The outcomes of numerical research of a fuel jet combustion a in current flow of air propagating in a rectangular channel are reported. The mathematical model is based on the equations of a turbulent responding boundary layer with closing on the level-k-e -T'² of the turbulence models with algebraic relations for Reynolds stresses. The influence of the initial concentration of fuel on the surface friction and convective heat transfer coefficients is investigated. The exponential dependence of a Nusselt number on the local Reynold number in the restricted flow area is obtained.

A.F.BUBLIEVSKY, E.I.YURINOK, O.I.YAS'KO
PHYSICAL MODELING OF CURRENT-VOLTAGE CHARACTERISTICS OF AN AIR-BLOWN D.C. ARC IN A PLASMATRON WITH TUBE ELECTRODES
Academic Scientific Complex "A.V.Luikov Heat & Mass Transfer Institute" of the National Academy of Sciences of Belarus, Minsk, Belarus

An analysis of the current-voltage characteristics (I-V) for an air-blown d.c. arc in a plasmatron with two tube electrodes is carried out by the multiple linear regression methods. The main effect on I-V is manifested by different heat transfer processes with convection dominating among them. Gasdynamic factors demonstrate a rather weak influence. Changing the discharge chamber geometry does not exert a strong influence on I-V, however it impedes the formation of a common I-V characteristic.

A.F.BUBLIEVSKY, E.I.YURINOK, O.I.YAS'KO
INFLUENCE OF THE TYPE OF A HEATED GAS IN A PLSMATRON WITH TUBE ELECTRODES ON THE D.C. ARC CURRENT-VOLTAGE CHARACTERISTIC 
Academic Scientific Complex "A.V.Luikov Heat & Mass Transfer Institute" of the National Academy of Sciences of Belarus, Minsk, Belarus

The influence of different processes on formation of current-voltage characteristics (I-V) in a d.c. plasmatron with two tube electrodes in analyzed by the multiple linear regression methods. Air, nitrogen, hydrogen, helium, and argon have been used as the working gases. It is shown that heat transfer processes play the main role in I-V formation in all the gases, whereas the gasdynamic factors are not so substantial. However, the role of individual mechanisms is different for various gases that makes it difficult to obtain a I-V characteristic common for several gases with good accuracy.

V.A.BURAKOV, I.S.TIMASHEVA, I.V.SHCHERBAKOVA
MATHEMATICAL MODEL OF DYNAMICS OF HEAT AND MASS TRANSFER PROCESSES WITH QUARTZ CERAMICS ABLATION IN A HIGH-TEMPERATURE FLOW OF SOLID FUEL COMBUSTION PRODUCTS
Scientific Research Institute of Applied Mathematics at the Tomsk State University, Russia

A new mathematical model, an algorithm and a computer program are developed for calculation of dynamics of the heat and mass transfer processes with nonstationary quartz ceramic ablation of channel walls in a high temperature flow of the plasma-forming magnesium-containing combination fuel combustion products. The numerical investigations have revealed an essential influence of the thermochemical mass removal, mechanical erosion and "wave" roughness of the liquid film on the dynamics of heat and mass transfer processes with nonstationary ablation of the quartz ceramic channel walls in the supersonic flow of combustion products of the plasma-forming magnesium-containing fuel 0.7 Mg+0.3 KNO₃ + air.

I.F.BYUAKOV, V.A.BORODIN, A.P.CHERNUKHO, A.P.SOLNTSEV, A.YU.KUZMITSKII, S.A.ZHDANOK, N.A.ZARUTSKAY
PROCESSES OF CH -TO- H O MIXTURE CONVERSION IN A HIGH-VOLTAGE ATMOSPHERIC PRESSURE DISCHARGE PLASMA
Academic Scientific Complex "A.V. Luikov Heat and Mass Transfer Institute of the National Academy of Sciences of Belarus", Minsk, Belarus

The CH -to- H O mixture conversion process in a high voltage atmospheric discharge plasma has been studied. The results of a thermodynamic analysis and experimental results on hydrogen yield and energetic parameters of the process are reported.

A.D.CHORNYI, V.A.SOSINOVICH
SYSTEM OF THE EQUATIONS FOR THE ONE-POINT DENSITY OF SCALAR FLUCTUATION PROBABILITY DISTRIBUTION IN HOMOGENEOUS TURBULENCE
Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer Institute of the National Academy of Sciences of Belarus", Minsk, Belarus

A closed system of the equations for the one-point density of scalar fluctuation probability distribution in homogeneous turbulence is presented. The problem pertains to ill-posed because of the negative term describing transfer in the phase space of scalar fluctuations. This causes the instability of the known numerical procedures on searching for a solution of the equation for the density of probability distribution. In the work, use is made of the method of construction of stable difference schemes for the ill-posed evolution problems from the viewpoint of the theory of regularization of difference schemes and their uniform stability with respect to the initial data.

V.I.DROBYSHEVICH, V.A.KIRILLOV, N.A.KUZIN, K.E.PAUKSHTIS
EXPERIMENTAL AND NUMERICAL STUDIES OF -METHYLSTYRENE HYDROGENATION
Institute of Computing Mathematics and Mathematical Geophysics, Institute of Catalysis of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

The goal of this work is to create mathematical and computing models of a vapor-gas-liquid catalytic reactor with a fixed catalyst bed. The mathematical model is based on the equations of conservation for mass and heat. Construction is based on the model hydrogenation reaction of -methylstyrene to kumol. As result, we obtained a computing model and created a special algorithm to solve it. For implementation of this algorithm a computer program was written. Results of computing experiments are in good agreement the with experimental and literature data.

YU.P.FINAT'EV, A.V.VLASOV
CONTROL OF THE RECOMBINATION PROCESSES IN A GAS MEDIUM TO IMPROVE THE CHARACTERISTICS OF ALPHA-IONIZATION PRESSURE TRANSDUCERS
Moscow Power Engineering Institute, Moscow, Russia

The possibility of control of the recombination processes in a gas medium to improve the characteristics of an alpha-ionization pressure transducer is discussed. A new method to increase the upper bound of the working range of the alpha-ionization pressure transducer is suggested based on metered input of an oxidizer to the transducer's ionization chamber, thus changing a composition of the recombining particles.

K.B.GALITSEISKII
MODELING OF RADIATION-CONVECTIVE HEAT-MASS TRANSFER IN CHEMICALLY REACTING JET FLOWS
Moscow Aviation Institute (Technical University), Russia

The problem of radiation-convective heat transfer in chemically reacting supersonic turbulent gas jets is considered. The methods of calculation of electromagnetic radiation due to ionization of high-temperature jets, the problem of radiant energy transfer in a chemically reacting flow, and the methods of calculation of the coefficient absorption and a degree of refraction in ionized flows are analyzed. The algorithm of numerical simulation of the radiation-convective heat transfer in a turbulent chemically reacting jet flow it presented. The results of numerical calculations of the spectral intensity of ionized supersonic turbulent jet emission are discussed.

V.V.GAVRILYUK, YU.M.DMITRENKO, S.A.ZHDANOK, G.V.MINKINA, S.I.SHABUNYA, N.L.YADREVSKAYA, A.D.YAKIMOVICH
METHANE-TO-HYDROGEN CONVERSION IN A SINGLE FILTRATION COMBUSTION WAVE
Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer Institute of the National Academy of Sciences of Belarus", Minsk, Belarus

The results of experimental and numerical studies of the hydrogen production process based on noncatalytic air-methane mixture-to-hydrogen conversion in a single filtration combustion wave are presented. The maximum reaction temperature in the reaction zone increases with the flow rate and reaches its constant value that weakly depends on the material and particles of the porous filling.

V.V.KALINCHAK, S.G.ORLOVSKAYA, N.N.KOPYT
RADIATION EFFECT ON STABLE AND CRITICAL REGIMES OF HIGH-TEMPERATURE OXYDATION OF METALS
I.I.Mechnikov Odessa State University, Ukraine

Stable and critical regimes of high-temperature metal oxydation with account allowance for radiation heat transfer between a metal and reactor walls are investigated. The mechanism of a spontaneous transition from the high-temperature to low-temperature oxidation regime, with the oxide film reaching its critical thickness, is studied. An influence of a particle diameter on the critical oxide film thicknesses corresponding to particle ignition and extinction is analyzed.

A.K.KOPEIKA, V.V.GOLOVKO, A.N.ZOLOTKO
INFLUENCE OF A NON-CHEMICAL HEAT SOURCE IN THE CONDENSED PHASE ON COMBUSTION STABILITY OF LIQUID EXPLOSIVES
Institute of Combustion and Nontraditional Technologies; I.I.Mechnikov Odessa State University, Ukraine

Combustion of the liquid explosives (LE) in heat-conductive shells is investigated. The possibility of disturbing the LE stationary combustion is shown using the Zeidovich's hypothesis about the decisive role of the ratio between the velocity of an LE heating wave and the combustion rate. The consideration of the additional contribution to the velocity of LE heating wave leads to the essentially different qualitative picture as compared to the known one. Exactly, in that case, the disturbance of LE combustion stability must be observed with a decrease, not an increase, in the external pressure. The good agreement of the calculated and experimental data allows us to make the assumption about the existence of such instability in relation to another volatile LE.

B.L.KOPELIOVICH
NUMERICAL INVESTIGATION OF GAS-FREE MIXTURE SPIN COMBUSTION
Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer Institute of the National Academy of Sciences of Belarus", Minsk, Belarus

A numerical investigation of gas-free mixture combustion in a narrow cylindrical channel has showed that due to intense heat removal cyclic changes in the reaction front take place which lead to formation of sites. When rigorous periodicity in emergence of the sites on the discontinuity discrete line sets up, a chaotic multisite regime gives way to spin combustion.

L.I.KRASOVSKAYA, M.A.BRICH
THREE-DIMENSIONAL MODELING OF HEAT AND MASS TRANSFER FOR PLASMA JET MIXING IN ELECTRIC ARC REACTORS
Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer Institute of the National Academy of Sciences of Belarus", Minsk, Belarus

A three-dimensional model of plasma jet mixing is developed. A theoretical study of heat and mass transfer, flow and temperature fields in mixing chambers with three electric arc plasmatrons is carried out.

G.V.KUZNETSOV, G.YA.MAMONTOV
MATHEMATICAL MODELING OF HEAT AND MASS TRANSFER DURING HIGH-TEMPERATURE DESTRUCTION OF EPOXY GLASS
Scientific Research Institute of Applied Mathematics and Mechanics at the Tomsk State University; Tomsk State University, Russia

A mathematical model of high-temperature destruction of epoxy glass under intensive heat and gasdynamic action has been formulated. Results of the numerical reseach agree well with the known experimental data. Scales of the thermomechanical processes accompaning epoxy glass destruction are estabilisheed.

Y.V.KUZNETSOV, V.P.RUDZINSKII
HIGH-TEMPERATURE HEAT AND MASS TRANSFER IN A COKE LAYER OF THERMOPROTECTIVE MATERIALS
Scientific Research Institute of Applied Mathematics and Mechanics at the Tomsk State University, Russia

High-temperature heat and mass transfer in a coke layer of thermoprotective materials has been investigated using a model taking into account the structural inhomogeneity of coke of the typical "carbonizing" thermoprotective material (TMP). Scales of the gas and coke temperature nonequilibrium at high temperatures (2000 K) of an external medium are established. Expediency of using the models allowing for gas and coke temperature nonequilibrium in solving the thermal protection problems is demonstrated.

D.S.MIKHATILIN, YU.V.POLEZHAEV
PHYSICOCHEMICAL PROCESSES IN A SURFACE LAYER UNDER THERMOCHEMICAL AND THERMOEROSIONAL DESTRUCTION OF MATERIALS
Institute of High Temperatures of the Russian Academy of Sciences, Moscow, Russia

A comparative analysis is made of the influence of changing the thermophysical characteristics of a glass-fiber plastic material under thermochemical and thermoerosional distribution with supersonic gas and dust-laden gas flows past the material. The positions of the region of phenolformaldehyde resin decomposition and of the regions implemented in heating rate tests are analysed.

D.S.MIKHATULIN, Yu.V.POLEZHAEV, D.L.REVIZNIKOV
INVESTIGATION OF HEAT EROSION RESISTANCE OF GLASS-FIBER PLASTIC STRUCTURES IN A FLIGHT IN THE ATMOSPHERE
Joint Institute of High Temperatures of the Russian Academy of Sciences, Moscow Aviation Institute, Moscow, Russia

Results of a numerical study of heat erosion-caused destruction of the external glass-fiber plastic heat shield at the frontal point of a hypersonic vehicle during a flight at a height of 10-30 km with a speed of M = 3-7 are reported.

A.P.NEFEDOV, B.V.ROGOV, V.A.SINEL'SHCHIKOV, M.A.KHOMKIN
SPECIAL FEATURES OF THE DISTRIBUTION OF COMPONENTS IN A NONISOTHERMAL BOUNDARY LAYER OF COMBUSTION PRODUCTS
Scientific-Research Center of Thermophysics and Pulse Effects, Russian Academy of Sciences, Moscow

We present results of experimental and numerical investigation of a laminar boundary layer being formed on the surface of a plate immersed in a high-temperature flow of combustion products. Velocity, temperature, and concentration profiles are measured for a number of components, including OH radicals, CO molecules, and atoms of the alkali metals Li and Cs. The role of volumetric and surface processes in the formation of spatial distribution of components is analyzed. The comparison of experimental data with the results of numerical simulation at different compositions of combustion products and conditions on the surface of the plate made it possible to establish the reliability of the proposed model of chemical kinetics.

I.SH.NORMATOV, Z.KH.GAIBULLAEVA, N.SHERMATOV, R.O.AZIZOV, M.T.IDIEV
EFFICIENCY OF USING THE THERMAL AND RECOMBINATION ENERGY OF HYDROGEN ATOMS IN IMPLEMENTING THE SOLID-STATE REACTIONS AND STRIPPING OF DANBURITE
V.I.Nikitin Institute of Chemistry, Dushanbe, Tadjikistan, Russia

The role of hydrogen and aluminum hydride atoms in the solid-state reaction of indium antimonide formation and in transferring the boron-containing mineral, i.e., danburite, to its labile form is established. By X-ray investigations it has been detected that formation of indium antimonides powders under continuous bombardment of the mechanical mixture of Sb₂S₃ and indium by hydrogen atoms occurs by formation and mutual transformations of some intermediate compounds. The essential influence of the a luminum hydride content and CO pressure on increasing the degree of passing B₂O₃ to the solution is found.

S.G.ORLOVSKAYA, V.V.KALINCHAK, V.I.SADKOVSKII, T.A.KUROCHKINA
HIGH-TEMPERATURE HEAT AND MASS TRANSFER OF A POROUS PARTICLE WITH AN ACCOUNT OF THE STEFAN FLOW ON ITS SURFACE
I.I.Mechnikov Odessa State University, Ukraine

The regularities of high-temperature heat and mass transfer and of kinetics of two concurrent chemical reactions on a particle surface are studied with allowance for the internal reaction and the Stefan flow. The role of the internal reaction at different stages of the high-temperature heat and mass transfer of a carbon particle heated by laser radiation is established. The effect of the internal reaction on the induction period, the combustion time and temperature, critical particle diameters characterizing its ignition and extinction is analyzed.

V.P.PATSKOV
NUMERICAL ANALYSIS OF THE PROCESS OF THERMAL DECOMPOSITION OF SOLE PARTICLES OF HIGH-ASH BITUMINOUS COAL UNDER PRESSURE
Scientific-Technical Center of Coal Energy Technologies of the National Academy of Sciences and the Ministry of Power Engineering, Kiev, Ukraine

The mathematical model, algorithm and some results of a numerical analysis of the process of thermal decomposition of sole particles of high-ash bituminous coal of grade GSSh under conditions of functioning of the technological plants with PCFB were examined. The effective diffusion, heat condition, filtration, phase and chemical transfer of the products of pyrolis were taken into consideration. The substantial influence of the intermediate condensed phase of the process was noted.

N.PEDISIUS, R.SLEZAS
EXPERIMENTAL STUDY OF NITROGEN OXIDE FORMATION UNDER STAGED COMBUSTION OF GASES
Lithuanian Institute of Power Engineering, Kaunas, Lithuania

Experiments were carried out to study NO formation in staged combustion of natural gases. The measurements were made in cylindrical combustors. The gas-air mixture was supplied through a premixing nozzle into a combustion chamber and the secondary air or the gas air mixture was injected at different heights of the chamber. The results have shown that for the near-stochiometric value of the primary zone equivalence ratio, the NO formation is determined by the inhomogeneity of the fuel/air mixture in the secondary injection stage. For the primary fuel-rich mixture, the NO formation is mainly determined by the amount of unburnt hydrocarbons in the primary zone which undergo the NO->HCN->N2 reactions and yield NO. The third air injection may have some effect on the NO formation if the combustion is incomplete during injection.

O.G.PENYAZ'KOV
STRUCTURE AND STATISTICAL PROPERTIES OF THE DETONATION WAVE FRONT
Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer Institute of the National Academy of Sciences of Belarus", Minsk, Belarus

The evolution of a cellular structure has been studied during long-time gas detonation wave propagation in a round tube. Acetylene-containing combustible gas mixtures with different degrees of regularity have been used. Together with the smoke-foil technique the contact-free self-emission method has been developed to measure current and average values of a detonation cell size. Propagation regimes, hereianfter referred to as detonation modes, in the round tube are found when the rate of chemical energy release is strongly synchronized with the boundary conditions and the gasdynamic flow structure inside the detonation wave, and the shape of cellular structure is found to have the best symmetry. It is shown that the single-mode propagation is hardly probable and a general time-dependent state of the local energy release in the detonation wave front can be presented as superposition of periodic functions corresponding to the states of different detonation modes. On the basis of a smoke-foil analysis, a spatial structure of the detonation wave front has been investigated for different states.

O.S.RABINOVICH
CONDITIONS OF PASSING A COUNTERWAVE OF CONDENSED SYSTEM FILTRATION COMBUSTION THROUGH AN INERT INTERLAYER
Academic Scientific Complex "A.V. Luikov Heat and Mass Transfer Institute of the National Academy of Sciences of Belarus", Minsk, Belarus

The method of numerical simulation has been employed to investigate the dependences of the critical width of an inert interlayer on the governing parameters of a combustion wave, i.e., the concentration of a gaseous reagent and the filtration rate of a gas. Consideration is given to systems with different exponents of the power function of reaction retardation by the combustion product. It is shown that the critical width of the inert interlayer decreases with an increase in the filtration rate and in the degree of conversion of the condensed reagent and vanishes at the boundary of the region of counterwave stability.

M.N.ROLIN, S.I.SHABUNYA
SIMULATION OF CHEMICAL REACTIONS IN A SPATIALLY NON-UNIFORM BARRIER DISCHARGE
ACADEMIC SCIENTIFIC COMPLEX "A.V.LUIKOV HEAT AND MASS TRANSFER INSTITUTE OF THE NATIONAL ACADEMY OF SCIENCES OF BELARUS", MINSK, BELARUS

A numerical model is proposed to describe barrier discharge occupying a part of the discharge slot because of the limited capacity of power supply. A system of the governing equations is formulated that describes the following stages of discharge evolution: avalanche, sreamer and plasma degradation. The scheme of chemical reactions for the discharge in nitrogen is given. The dependencies of the power and the degree of the discharge uniformity on the power supply characteristics are obtained to illustrate the ability of the computer code.

V.SAMOILIKOV, A.L.KABLUKOV
HEAT AND MASS TRANSFER IN THE REACTORS FOR RAPID THERMAL PROCESSING OF SILICON WAFERS
Moscow State Institute of Electronic Technology, Russia

The change of a waffer diameter up to 300 mm with reducing the time of exposure is the push to research of physics of the processes in RTP reactors. The main targets of the research are visualization of a gas flow in the reaction area, development of a mathematical model of the process, testing the mathematical model and confirmation of its adequacy.

A.M.SAFONOVA, N.K.LUNEVA, N.I.REKASHOVA, S.V.BATURA, O.A.SHCHUREVICH, I.A.LYUDCHIK, A.V.VINOGRADOV, A.V.KRAUKLIS
SYNTHESIS OF A CARBON ADSORBENT BY THERMAL PROCESSING OF IMPREGNATED WOODD
Institute of General and Inorganic Chemistry of the National Academy of Sciences of Belarus; Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer Institute of the National Academy of Sciences of Belarus", Minsk, Belarus

Results of an investigation of the process of thermal decomposition of impregnated wood under conditions of filtering combustion of the propane - butane gaseous mixture are reported. The method of obtaining of the fine-porous active carbon with a volume of adsorbative pores of up to 0.54 cm³·g^-1, adsorbtive activity for iodine to 70.4 wt.% and ion exchange capacity to 2 mmol·g^-1 has been developed.

B.S.SEPLYARSKII
IGNITION OF POROUS SUBSTANCES UNDER CONDITIONS OF COUNTER UNSTEADY-STATE GAS FILTRATION
Institute of Structural Macrokinetics of the Russian Academy of Sciences, Chernogolovka, Moscow region, Russia

With the aid of the wave theory of ignition (WTI) determination is made for the first time of the dependence of duration of the ignition stages of a porous substance heated by a body under conditions of counter unsteady-state gas filtration on the basic parameters of the problem, namely, the dimensionless temperature drop , the Re criterion being the width ratio of the filtration zone to the heating zone, and the dimensionless heat capacity c equal to the ratio of the volume heat capacities of the gas and condensed phases. The investigation performed has made it possible to obtain simple expressions which allow calculation of time characteristics of ignition from the main parameters of the process without using a computer.

B.S.SEPLYARSKII, N.I.VAGANOVA
CONVECTIVE COMBUSTION OF "GAS-FREE" SYSTEMS
Institute of Structural Macrokinetics of the Russian Academy of Sciences, Chernogolovka, Moscow region, Russia

To explain an abnormally high combustion rate revealed in incineration of "gas-free" titanium carbon black and titanium - carbon black - polystyrene systems under conditions of one-dimensional filtration of impurity gases, a convective combustion mechanism is suggested. An analysis of the available experimental and theoretical works has shown that under conditions of impurity gas release the convective combustion mechanism can be provided by motion of a melt layer of one of the reagents due to pressure drop of the impurity gases. Physical and mathematical models of convective combustion of the "gas-free" systems are formulated. It is established that for implementation of the combustion regime at a speeding-up rate it is necessary to have a free volume not occupied with the mixture. It is shown that in the initial combustion stage and with the free volume exceeding the sample volume, the front velocity and the gas pressure increase according to the exponential law. Analytical expressions are obtained to calculate the mean rate of convective combustion. Investigations of the model formulated in the work have allowed explanation of the experimentally observed differences in regularities of combustion of the "gas-free" system under conditions of counter, countercurrent, bilateral filtration of impurity gases.

A.SHARIFOV
COMBINED HYDROCARBON CONVERSION METHOD IN A TUBULAR REACTOR WITH CATALIZING BOX
Tadjik Technical University, Dushanbe, Tadjikistan

A combined method of hydrocarbon convesrion in a tubular reactor with a catalizing box is proposed which allows efficient use of the reaction heat and saving of hydrocarbons burnt for heating in the tradiational conversion methods. A mathematical model of the method is constructed that takes into consideration not only the processes of heat exchange but also the mass exchange processes, which occur simultaneously and result in chemical conversions of hydrocarbons with the formation of hydrogen and the other products of the conversion.

A.N.SUBBOTIN
REGULARITIES IN THE UNDEGROUND FIRE PROPAGATION UNDER VARIOUS CONDITIONS OF HEAT AND MASS EXCHANGE WITH AN EXTERNAL MEDIUM
Tomsk State University, Russia

Initiation and propagation of peat fire caused by a fire spot are considered. A peat layer is modeled by a multiphase multicomponent reacting porous medium. Numerical calculations are provided that show the mechanism of the fire spot formation and the regularities in its spread over the peat layer depending on the heat exchange conditions.

E.N.TARAN, G.T.TSYGANKOV
ON STABILITY, STRUCTURE AND PROPERTIES OF AN INFLEXIBLE LAMINAR FLAME
Institute of Geotechnical Mechanics of the National Academy of Sciences of Ukraine, Dnepropetrovsk, the Ukraine

A study is made of the conditions of stable combustion and the structure of an unflexible laminar flame formed upon fuel mixture outflow at a velocity up to 95 m/sec, Renolds numbers Re_out>Re_cr and hydrodynamic pressure on the axis up to 5,000 Pa. It is established that on initiation of combustion of the fuel-rich mixture near the nozzle orifice the flow in the channel of the inflexible laminar flame with almost a constant velocity retains at a distance of several tens of the nozzle diameters. The reason for an abnormally long jet section behind the nozzle with a constant velocity is an abrupt increase in the gas velocity in the combustion zone of a diffusional flame formed around a jet of the fuel mixture outflowing into the atmosphere. The influence of formation of ash clusters in the diffusional flame on the gas viscosity, occurrence of turbulence in the central jet of the fuel mixture is discussed.

V.I.TIMOSHENKO, V.P.GALINSKII, I.S.BELOTSERKOVETS, V.M.KISEL, YU.I.EVDOKIMENKO, V.KH. KADYROV
ON MATHEMATICAL MODELING AND EXPERIMENTAL IMPROVEMENT OF GAS DYNAMIC AND HEAT MASS EXCHANGE PROCESSES IN BURNERS FOR HIGH-SPEED GAS FLAME SPRAYING
Institute of Technical Mechanics of the National Academy of Sciences of the Ukraine, Dnepropetrovsk, Ukraine; Institute for Problems of Material Science of the National Academy of Sciences of the Ukraine, Kiev, Ukraine

Consideration is given to some problems of the methodology of theoretical and experimental modeling of gas dynamic paths of burners, providing more full use of the chemical energy fuel for heating and acceleration of particles of the material sprayed which is based on the principle of control of a two-phase gas stream by the mass flow rate effect. The strategy of calculated-experimental improvement of the processes in a gas dynamic path of the burner is formulated. The estimates of maximum allowable volume-averaged values of parameters of a two-phase stream in the combustion chamber of the burner and at the site of input are given. For alumina particles of various fraction the influence of the relative mass flow rate on the gas dynamic and thermophysical parameters of the two-phase stream in the burner channel with a supersonic accelerating site is evaluated.

B.A.TROSHEN'KIN, V.B.TROSHEN'KIN
HEAT TRANSFER IN LIBERATION OF HYDROGEN IN THE REACTION OF ACTIVATED ALUMINUM WITH WATER
Institute for Problems in Mechanical Emgineering of National Academy of Sciences of the Ukraine, Kharkov, Ukraine

An investigation is made of heat transfer between the aluminum-activated sample and water under chemical reaction conditions. The profile of temperatures over section of the sample is studied. The heat transfer coefficients are generalised in the form of a criterional equation. A substantial influence of the Reynold number of the fluid of a lift flow is revealed. The regularities established allow us to state that a rate of entropy production in the chemical system caused by decreasing the Gibbs potential follows the rate of entropy production in the dissipative structure.

V.I.TRUSHLYAKOV, V.V.SHALAI, V.V.TASHLANOV, V.S.SALNIKOV
SIMULATION OF UNSTEADY HEAT AND MASS TRANSFER PROCESSES IN A HETEROGENEOUS CATALYTIC REACTOR WITH COMBINED HEAT EXCHANGE
Omsk State Technical University, Russia

A diffusion two-phase two-dimensional mathematical model of unsteady heat and mass transfer processes in a heterogeneous catalytic multisectional reactor with the regenerative - recuperative type of heat exchange is presented. Results of the mathematical simulation are in good agreement with experimental data. Dynamics of temperature fields and degrees of conversion of the oxidized component in the reactor with neutralization of gas waste of the toxic propellant component is investigated numerically. The existence of negative and positive feedbacks for a heat flux in the reactor and their inversion are established. The criterion reflecting the time of occurrence of positive recuperative effect in the reactor is introduced.

P.P.VOLOSEVICH, E.I.LEVANOV
DYNAMICS AND HEATING OF A HIGH TEMPERATURE PLASMA IN THE PRESENCE OF A MAGNETIC FIELD
Institute for Mathematical Modeling of the Russian Academy of Sciences, Moscow, Russia

A review of the results, obtained with the aid of self-similar solutions and numerical experiments, for the phenomena associated with propagation of thermal, gas dynamical and magnetohydrodynamical waves in a high temperature plasma is given.

M.V.ZAKE
ELECTRIC FIELD EFFECT ON THE PROCESSES OF HEAT AND MASS TRANSFER AND FUEL COMBUSTION IN FLAME CHANNEL FLOWS
Institute of Physics of the Latvian University, Salaspils, Latvia

Results of experimental investigations of the radial electric field-effect on the processes of heat and mass-transfer in a channel flow of the propane flow are reported. It is shown that at a positive potential of the central electrode the radial electric field initiates the transfer of positive hydrocarbon ions from the central part of the reaction hot zone to the water-cooled channel walls. The field-induced changes in the flame composition profiles entail the local changes in the reaction rates, heat release and temperature distribution in the flame flow. The changes in the temperature distribution are followed by changes in heat transfer to the channel walls. Tbe laboratory and industrial investigations of the electric field effects on the flame channel flows demonstrate that these effects can be used to control a rate of NO formation and levels of degrading emissions from the district heating loiler houses.

U.K.ZHAPBASBAEV, E.P.MAKASHEV, E.K.AKTAEV
GAS DYNAMICS OF COMBUSTION OF A SYSTEM OF FLAT SUPERSONIC HYDROGEN JETS IN A COCURRENT SUPERSONIC AIR FLOW
Al'-Farbi Kazakh State National University, Alma-Ata, Kazakhstan

Results of calculations and theoretical studies of burning of a system of flat supersonic hydrogen jets in a cocurrent supersonic air flow are reported based on the parabolized Navier-Stokes equations with use of the multi-stage hydrogen oxidation mechanism and a one-parameter (k-lw) turbulence model. The calculated data show regularities of gas-dynamical, chemical, thermal conditions of hydrogen ignition in relation to a degree of uncalculatedness, the coccurrent-state parameter and the other regime parameters. In particular, occurrence of large-scale structures in pressure and velocity distributions and their influence on mixing and burning of hydrogen supersonic jets in the cocurrent supersonic flow are shown.

S.A.ZHDANOK, V.A.BORODIN , A.P.CHERNUKHO, I.F.BUYAKOV, A.P.SOLNTSEV, A.KUZMITSKII, N.A.ZARUTSKAYA
STUDY OF THE PROCESS OF CH₄- H₂O MIXTURE CONVERSION IN A HIGH VOLTAGE ATMOSPHERIC PRESSURE DISCHARGE PLASMA
Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer Institute of the Belarusian Academy of Sciences", Minsk, Belarus

The CH₄-H₂O mixture convesrion process in a high voltage atmospheric discharge plasma has been studied. The results of thermodynamic analysis and the experimental results on hydrogen yield and energetic parameters of the process are given.

S.A.ZHDANOK, A.P.CHERNUKHO, I.F.BUYAKOV, A.P.SOLNTSEV, A.S.SOLNTSEV, N.A.ZARUTSKAYA
EXPERIMENTAL STUDY OF THE REVERSE REACTIONS FLOW IN THE METHANE PARTIAL OXIDATION PROCESS ON PLATINUM CATALYST
Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer of the National Academy of Sciences of Belarus", Minsk, Belarus

Results of the experimental study of two reverse reactions of the endothermic stage of the methane partial oxidation process on a platinum catalyst are given. The approach to simulation of this process is discussed.

SECTION NO. 5. "HEAT AND MASS TRANSFER IN TWO-PHASE SYSTEMS (INCLUDING PHASE CHANGES)"

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D.V. ALEXANDROV
ON THE THEORY OF INCIPIENCE OF A MUSHY REGION IN BINARY MELT SOLIDIFICATION
A.M.Gorky Ural State University, Ekaterinburg, Russia

The well-known problem of incipience of a mushy zone for binary melt solidification processes is solved with the aid of Laplace transform in a laboratory coordinate system. Integral relations for the rate of solidification and the time of incipience of a mushy zone are derived when crystallization proceeds near a cooling wall. The last assumption is confirmed by numerical calculations and by the relations obtained. In other words, a mush appears ahead of solidification front in the initial stage of crystallization (when the front moves towards the binary melt near the cooling wall). Thus, the time when the classical description of crystallization by means of the Stefan thermodiffusion model becomes incorrect and when the mushy region appears due to the concentrational (constitutional) supercooling is found.

V.V. ANTONIK, A.I. PETRUCHIK, A.D. SOLODUKHIN, N.N. STOLOVICH, S.P. FISENKO
HEAT AND MASS TRANSFER IN EVAPORATIVE COOLING OF WATER FILMS ON TWO VERTICAL PLATES
BELENERGO Belarusian State Power Engineering Concern, Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer Institute," National Academy of Sciences of Belarus, Minsk, Belarus

A mathematical model of evaporative cooling of water film on vertical plates is developed which is a boundary-value problem for a system of four ordinary nonlinear differential equations. Using the model, calculations were carried out and their comparison with the data obtained on a commercial cooling tower was made. It is established that at small and average density of irrigation the model allows one to describe well the parameters of vapor-air mixture above plates and temperature of the water cooled. The comparison of experimental and calculated data also shows that at a nominal hydraulic load the contribution of film currents is not less than 50% in a cooling tower.

A.N. ANTONOV, N.K. AKSENOV, A.V. GORYACHEV, N.E. GORYACHEVA
CALCULATION AND EXPERIMENTAL INVESTIGATION OF HEAT-AND MASS TRANSFER PROCESSES IN ICING CONDITIONS
Central Institute of Aviation Engine Manufacturing, Moscow, Russia

A method and code for calculating heat- and mass transfer processes in icing conditions were developed. A method and code for calculating transformation of artificial cloud parameters in test rig conditions were developed. The basic components of icing process investigation technology such as artificial cloud modeling, monitoring of parameters of mix of airflow and water drop in a test rig channel; ice accretion growth monitoring by video; computer analysis of video images and stroboscope application were developed.

A.A. ANTUKH, P.V. BOKHAN, A.G. KULAKOV, V.K. KULIKOVSKII, M.I. RABETSKII
HEATING AND SORPTION PANELS FOR VACUUM DRYING OF TIMBER
Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer Institute," National Academy of Sciences of Belarus, Minsk, Belarus

Some new heat pipe panels were suggested and manufactured for timber drying vacuum chambers. These panels are based on loop and vapor-dynamic thermosyphons. They have an isothermal surface temperature which is maintained automatically. Solid sorption panels were tested to improve the drying technology of the vacuum chamber. Different adsorbents were tested experimentally for such panels.

N.N. AVAKIMYAN, N.I. VASIL'EV, V.V. GUGUCHKIN , I.V. TERESHCHENKO, A.S. TROFIMOV
WAVES ON THE SURFACE OF METAL MELT IN A MELT-WATER SYSTEM
Kuban' State Technological University, Krasnodar, Russia

Results of experimental investigations are presented for the processes of interaction of melted metal with evaporating liquid. A series of successive photographs (in 10^-4 sec) of the process of development of perturbation on the melt surface are presented. The scale and velocity of motion of a wave on the melt surface are evaluated. A model of the growth of the amplitude of a wave is suggested represented as a consequence of instability of the melt surface in the vapor layer that separates liquid from the melt.

N.N. AVAKIMYAN, N.I. VASIL'EV, V.V. GUGUCHKIN , I.V. TERESHCHENKO, A.S. TROFIMOV
GROWTH OF SECONDARY VAPOR BUBBLES ON THE WALL OF A PRIMARY BUBBLE IN SUPERHEATED LIQUID
Kuban' State Technological University, Krasnodar, Russia

We present the results of analysis of a high-speed filming of the process of growth of vapor bubbles in superheated liquid. We show that on the surface of a primary bubble secondary bubbles appear and grow, so that the primary bubble turns out to be surrounded by secondary ones. A model is suggested for the process of growth of secondary bubbles; in this model the surface of the primary bubble is broken by local pressure of vapor output.

B.P. AVKSENTYUK, V.V. OVCHINNIKOV
A PREMATURE BURNOUT
S.S.Kutateladze Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

A unified mechanism for the occurrence of a premature burnout in forced convection boiling and in pool boiling is suggested. A region of the regime parameters, at which a premature burnout in subcooled forced convection boiling may occur, is determined. The equation for the computation of the lower limit of a premature burnout is suggested.

V.A. BERSHADSKII, G.A. DREITSER, V.P. FIRSOV, I.V. ANTYUKHOV
LENGTH OF CONDENSATION ZONE IN TUBES WITH SUPPLY OF A GAS WAKE JET IN A NITROGEN AND HYDROGEN FLOW
Moscow Aviation Institute (Technical University), Moscow, Russia

The size of a nonequilibrium condensation region in a flow of cryogenic liquids (nitrogen, hydrogen) in tubes in subcooled conditions with axial supply of a gas jet in the direction of flow is investigated. Experiments were conducted in visual test sections of the diameter of 95 and 140 mm which were made from a quartz glass and were located in a low-pressure chamber. The axial input of gas flow was made through a jet injector of diameter 6 and 8 mm. The generalizations of experiments on the condensation zone length with the use of representations about the predominance of turbulent splitting and condensation of steam bubbles were made. Generalizing relations for calculation of dimensionless lengths of the condensation zone in the flow of liquid hydrogen and nitrogen are obtained for wake input of gas into flow.

E.A. BOLTENKO
EFFICIENCY OF VAPOR GENERATING FACILITIES BASED ON THE USE OF TWISTED AND TRANSIT FLOWS
Elektrogorsk Scientific Research Center on Safety of Atomic Electrostations, Elektrogorsk, Russia

The report presents the assessment of the efficiency of the augmentation method which consists in simultaneous use of twisted and transit flows moving along the gap formed by concave and convex surfaces of the annulus and along the convex heat transfer surface, respectively. It has been shown that as compared with a smooth channel or a twisted flow channel, the simultaneous use of twisted and transit flows allows heat removal rate and critical heat flux to be significantly increased on both heat transfer surfaces.

A.V. BORISHANSKAYA, V.V. KYUCHKIN, A.N. LISITSYN, A.V. FEDOROV, V.S. BELYAEV, O.A. DANILYUK
DEVELOPMENT OF THE THEORY OF THE BOILING OF SOLUTIONS WITH A NONVOLATILE COMPONENT
All-Russian Scientific-Research Institute of Fats, St.Petersburg, Russia

The results of investigation are presented that do not contradict the general methodology of modeling the nucleate boiling process of solution. The development of boiling model based on experimental results is given and the earlier hypothesis of the mechanism of nucleate boiling heat transfer is confirmed. The experimental results explained the peculiarities of the heat transfer of solutions with a nonvolatile component at high temperature difference.

F.N. BOROVIK, G.S. ROMANOV
WIDE-RANGE EQUATION OF STATE OF MATTER WITH ACCOUNT OF EVAPORATION, DISSOCIATION, AND IONIZATION
Academic Scientific Complex "A.V.Luikov Heat and Mass Transfer Institute," National Academy of Sciences of Belarus, Minsk, Belarus

Semiempirical wide-range equation of state of granite and water based on decomposition of pressure and energy into a cold component and thermal nuclear and electronic components is presented. The thermal electronic components of energy and pressure are calculated with the Thomas-Fermi model which allows one to take into account both thermal and pressure ionization. The description of the cold isotherm is based on experimental data. Evaporation and dissociation are taken into account with corresponding addends in the free energy. Condensed state is described in the frame of Debye's approximation. The coexistence curve of condensed and gas phases are calculated. Isoenergetic curves in the plane of density - temperature and of density - pressure are considered.

G.N. BOYARKIN, I.N. PERGUN, S.P. SHAMETS, A.G. YANISHEVSKAYA
THERMAL PROCESSES IN ELECTROSLAG CASTING OF ALLOYED STEELS
Omsk State Technical University, Omsk, Russia

The method of production of blanks by means of centrifugal electroslag casting is described. Thermal-physical processes are considered which occur inside a casting volume in melting of electrode and cristallization of metal and slag inside a form. The results of computer simulation of processes by means of the ANSYS program are also given.

A.M. BRENER, L.A. KIM
THE RELAXATIONAL TRANSFER KERNELS METHOD IN NONLOCAL AND NONLINEAR EQUATIONS OF HEAT AND MASS TRANSFER
State University of South Kazakhstan, Shimkent, Kazakhstan

New equations for relaxational transfer kernels evolution with allowance for the cross effects and low nonlinearity have been proposed, and new nonlocal heat and mass transfer equations on the basis of this model have been derived. Some special features of these equations solutions behavior were obtained by analysis and numerical experiments. It was concluded that allowance for the cross effects leads to appearance in the transfer equations terms responsible for the wave dispersion and the nonlinearity terms responsible for the peculiar interference of fluctuations appearing in different moments.

N.V. BULANOV
INFLUENCE OF THE DISPERSE COMPOSITION OF EMULSION ON HEAT-EXCHANGE CHARACTERISTICS
Institute of Thermophysics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia

The paper gives the results of theoretical study of heat transfer to emulsions whose dispersed phase is low boiling as compared with a dispersion medium. It has been found that the density of a heat flux q to emulsion from a cooled surface depends substationally on both the average size of droplets and their volume distribution. At small temperature stresses the observed density q is the greater, the larger are the average and maximum volume of droplets of the emulsion dispersed phase.

O.G. BURDO, S.I. MILINCHUK, E.A. KOVALENKO
CONJUGATE HEAT AND MASS TRANSFER IN CRYSTALLIZATION FROM FOOD SOLUTIONS
Odessa State Academy of Foodstuff Technologies, Odessa, Ukraine

The paper considers the prospects of development of modern methods used in dehydration of foodstuff. The main tendencies of development of low-temperature techniques of separation of solutions are formulated. The advantages of the technique of block freezing and ways of its further perfection are shown. Simulation of the processes of low-temperature crystallization from solutions is carried out and the necessity of creation of model of a conjugate heat- and mass transfer is justified. The outcomes of experimental researches of processes of freezing of fruit juices and lactic whey are presented. It is shown that the model developed adequately features the process of crystallization from food solutions with an error not exceeding 10%.

V.D. CHAIKA
CALCULATION OF STEAM CONTENT OF TWO-PHASE FLOW IN WATER BOILING ON HORIZONTAL TUBES (SINGLE AND BUNDLES)
Far-Eastern State Technical Fish Farming University, Vladivostok, Russia

Calculation of steam content of two-phase flow is made for water boiling on horizontal single copper tubes 10, 16, 24, 34, and 70 mm in diameter and also on five-row-bundle copper tube 34 mm in diameter at a pressure of 26<p<=200 kPa and specific heat flux of q -onset of nucleation and up to 200 kW/m². With the help of high-speed filming boiling process characteristics simultaneously in two directions are presented and formulas are obtained. Empirical nondimensional correlations are based on various experimental results. The formulas also take account of the effect of side tubes and tube pitch.

A.V.CHICHINDAEV
HEAT- AND MASS TRANSFER IN AIR-STEAM COOLING OF A THERMALLY STRESSED COMPACT HEAT EXCHANGER
Novosibirsk State Technical University, Novosibirsk, Russia

A model of calculation of local heat transfer in a cross-flow compact heat exchanger with allowance for heat- and mass transfer of a humid air in a cold channel is explained in the case of air-steam cooling of thermally stressed heat exchanger. The outcomes of numerical research of fields of temperatures and thermal stresses, arising in the exchanger are presented depending on the reference temperature, water-quantity of cold air for various constructions of heat exchangers. The features of complex optimization (technological, thermal, anti-thermally stressed) of heat exchangers of the given type permitting the increase of their resource of operation are described.

D.A. DANILOV, P.K. GALENKO
HYPERBOLIC HEAT TRANSFER IN RAPID SOLIDIFICATION OF SUPERCOOLED LIQUIDS
Udmurtiya State University, Izhevsk, Russia; Laboratory of the Physics of Condensed Media, Physical Faculty, Udmurtiya State University, Izhevsk, Russia

A model of rapid solidification in supercooled pure metallic liquid is developed that includes local nonequilibrium heat transfer and kinetics of liquid-solid interface motion. Taking into account the finiteness of the speed V of heat transport, a general solution of the problem about local nonequilibrium heat transfer with the moving heat source at the planar solidification front is obtained. We analyze the solution both in steady-state and nonsteady-state regimes of solidification. On the basis of conjoint solution of heat and kinetic equations we find the self-consistent regimes of rapid solidification front motion.

N.A. DIKII, V.I. SHKLYAR, V.V. DUBROVSKAYA
INVESTIGATION OF HEAT AND MASS TRANSFER IN STEAM CONDENSATION IN CONTACT APPARATUS WITH NETTING PACKING IN THE PRESENCE OF CONSIDERABLE AMOUNT OF NONCONDENSING GAS
National Technical University of the Ukraine, Kiev Polytechnic Institute, Kiev, Ukraine

Results of experimental investigation of heat and mass transfer in contact apparatus with netting packing in gas-steam mixture condensation are presented. The dependencies of heat transfer coefficient on gas-steam mixture velocity, spray density, packing length, and noncondensing gases amount have been established. Generalizing correlations are proposed to determine heat transfer coefficients and apparatus flooding rates.

N.A. DIKII, V.E. TUZ, YA.E. TROKOZ, I.M. KUZ'MENKO
HEAT AND MASS EXCHANGE IN EVAPORATION OF LIQUID IN CHANNELS WITH POROUS WALLS
National Technical University of the Ukraine, Kiev Polytechnic Institute, Kiev, Ukraine

A technique of calculating contact heat and mass exchange apparatus with porous surface is suggested on the basis of results of mathematical simulation and experimental investigations of the processes of heat and mass transfer in channels with porous walls.

A.A. DOLINSKII, B.I. BASOK
HEAT AND MASS EXCHANGE AND FRAGMENTATION OF THE INCLUSIONS OF PARTICLES IN ADIABATICALLY EFFERVERSING DISPERSED MEDIA FLOWS
Institute of Technical Thermophysics, National Academy of Sciences of the Ukraine, Kiev, Ukraine

The theoretical and experimental results of hydrodynamics and heat and mass exchange in superheated (metastable) liquid flow under adiabatic transport to a low pressure region are prescribed. The results of hydrodynamic fragmentation of dispersed inclusions of particles are also given.

L.A. DOMBROVSKII, L.I. ZAICHIK
ALLOWANCE FOR THE DYNAMICS OF A VAPOR BUBBLE IN CALCULATION OF THERMAL INTERACTION OF A HOT SPHERICAL PARTICLE WITH SURROUNDING WATER
Institute of High Temperatures, Russian Academy of Sciences, Moscow, Russia

A nonstationary problem of thermal interaction of a hot spherical particle and surrounding water is being solved for conditions of heavy accident at a nuclear reactor. In calculation of heat transfer through a vapor gap thermal radiation of particle is taken into account. For the initial stage of interaction an analytical solution is obtained in isobaric approximation; comparison with a full numerical solution has shown that oscillations of vapor pressure and vapor gap thickness do not influence mean parameters of heat transfer from a particle to water. Results on the damping effect of thermal radiation of particle on oscillations of particle vapor envelope are obtained. Possible destruction of a melt drop under the influence of pressure fluctuations in the vapor gap is evaluated, and the size of a drop is determined at which its further destruction is impossible.

G.A. DREITSER, V.P. FIRSOV, I.V. ANTYUKHOV
FEATURES OF HEAT TRANSFER IN FILM BOILING DISPERSED REGIME OF LIQUID NITROGEN IN TUBES
Moscow Aviation Institute (Technical University), Moscow, Russia

The results of experimental and theoretical research of heat transfer and hydrodynamics in dispersed flow film boiling of liquid nitrogen in tubes are presented. The results of experiments and their generalization are considered for flow of saturated liquids in steady and unsteady cooling regimes in vertical channels. Generalizations of experimental data on size distribution of drops, heat transfer and friction on the interphase surface are obtained. The dependence for calculation of hear transfer in interaction of drops and vapor with the channel wall with allowance for the turbulence of the lifting phase is obtained.

G.A. DREITSER, V.P. FIRSOV, I.V. ANTYUKHOV, A.A. KURILENKO
FILM BOILING HEAT TRANSFER OF LIQUID NITROGEN AND HYDROGEN IN TUBES AT LARGE LIQUID SUBCOOLINGS
Moscow Aviation Institute (Technical University), Moscow, Russia

The results of experimental investigation of film boiling of liquid nitrogen in vertical tubes of diameter 9.7 mm and 20 mm and liquid hydrogen in tubes of diameter 70 mm are presented. The experiments were carried out in conditions of unsteady cooling of the test section in the range of mass flow velocity change from 500 to 15,000 kg/m²sec, pressure from 5 to 20 bars, dimensionless liquid subcooling from 0.05 to 0.6, wall temperature from 200 to 900 K. It is shown that in conditions of large subcoolings of liquids the slug annular vapor-liquid flow regime is realized and the existence of two basic regimes of heat transfer is possible: similar and nonsimilar with respect to the temperature of a heat generating surface. The generalizing dependences on heat transfer in slug similar annular film boiling regime of liquid nitrogen and hydrogen are obtained.

YU.V. DYACHENKO, A.V. CHICHINDAEV
FEATURES OF HEAT- AND MASS TRANSFER IN COMPACT HEAT EXCHANGERS
Novosibirsk State Technical University, Novosibirsk, Russia

The outcomes of experimental investigation of a heat exchanger-condenser of a system of air conditioning onto dry and humid air are presented. The model of calculation of local heat transfer in a cross-flow compact heat exchanger with allowance for heat- and mass transfer of a humid air in cold and hot channels is explained at positive and negative temperatures. The outcomes of numerical investigation are given, the features of complex optimization (technological, thermal, anti-icing) heat exchangers of given type are described.

G.V. ERMAKOV, S.A. PERMINOV, E.V. LIPNYAGOV
FORMATION OF VAPOR NUCLEI IN A SUPERHEATED LIQUID ON GAS INCLUSIONS
Institute of Thermophysics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia

The possibility of existence of a steadily equilibrious vapor-gas nucleus in a highly superheated liquid is shown. A phenomenological and a kinetic models of its fluctuation-diffusion growth are proposed. The results of calculation are in good agreement with experiment.

A.S. GAVRISH
WATER STEAM DROPWISE CONDENSATION - PECULIARITIES OF HEAT EXCHANGE AND PROCESS MECHANISM
"Kiev Polytechnic Institute" National Technical University of the Ukraine, Kiev, Ukraine

In this paper the results of experimental investigation of water steam dropwise condensation are presented. Covering of heat, exchange surface with fluorine-containing disulphide simulator promotes dropwise condensation for long-time period. Also condensate modes space-development characteristics were determined. Steam flow velocity affects the process mechanism, especially the departure drop diameter values. The dependence of average heat removal coefficients on vapor pressure was determined. All experimental data were generalized by means of either dimensional values or dimensionless complex numbers. At necessary preconditions the mathematical model solution can be based on standard mathematical functions, such as Green ones and Fourier numbers.

A.A. GORBUNOV, I.M. DERGUNOV, A.P. KRYUKOV
GROWTH OF VAPOR FILM ON A HEATER IMMERSED INTO HIGHLY CONDUCTING LIQUID
Institute of the Problems of Mechanics, Russian Academy of Sciences; Moscow Power Engineering Institute, Moscow, Russia

Results of numerical investigation of vapor film evolution in sodium film boiling under microgravity conditions are presented. The gas molecular-kinetic theory with combination of continuum mechanics are used for system description. Two different heat transfer models are considered. The peculiarities of vapor cavity evolution connected with interphase resistance and liquid thermal resistance are obtained. The influence of temperature and pressure in the vessel on the vapor film growth-collapse is investigated.

L.A. GORYAINOV
MATHEMATICAL SIMULATION OF HEAT AND MASS TRANSFER PROCESSES OF THE GENERALIZED CYCLE OF GROWTH OF SINGLE CRYSTALS FROM MELT BY UNIAXIAL CRYSTALLIZATION
Moscow State University of Railways, Moscow, Russia

For obtaining monocrystals (sapphire, ruby, IAG) we use methods of uniaxial crystallization (horizontal and vertical uniaxial crystallizations, Chohralsky method, Stockbarger method, etc.). For analyzing heat and mass transfer processes for all of the above-mentioned methods we introduced a concept of universal cycle. Heat and mass transfer models will be different for the cycle periods. Mathematical models were formulated for the method of vertical uniaxial crystallization.

N.I. GRIGORIEVA, V.E. NAKORYAKOV
SIMULATION OF ABSORPTION HEAT AND MASS TRANSFER PROCESSES IN BINARY TWO-PHASE SYSTEMS
Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

We present the results on simulation of related heat and mass transfer processes in absorption of vapor by a solution flowing down a tube stack. The use of self-similar solutions over the initial thermal section and precise analytical solutions in sections with a linear temperature profile is substantiated. An example of calculation for a multipass absorber is given. The change in all local heat and mass transfer characteristics is analyzed over the depth of the tube stack.

A.K. ILYIN, V.D. CHAIKA
NEW DATA ON HEAT EXCHANGE IN WATER BOILING ON HORIZONTAL PIPE PACKAGES
Astrakhan' State Technical University; Far East State Technical Fish Farming University, Vladivostok, Russia

On the basis of experimental results the data for calculating heat exchange in water boiling on horizontal pipe packages are described. Other characteristics of pipe packages are also determined.

G.K. IVANITSKII
COMPUTATIONAL SIMULATION OF STATIONARY AND NONSTATIONARY DISCHARGE OF ADIABATICALLY BOILING LIQUIDS FROM SHORT TUBES
Institute of Technical Thermophysics, National Academy of Sciences of the Ukraine, Kiev, Ukraine

On the basis of a previously developed model of the dynamics of a vapor bubble ensemble a qualitatively new approach to modeling is proposed to analyze both stationary and nonstationary flashing flows in short channels and ducts. The distinguishing feature of the model is the consideration of pressure and temperature differences between vapor and liquid phases of the flow with due account of thermodynamic nonequilibrium. The model in view is capable of determining the basic parameters of two-phase flows in an arbitrary cross section of the channel at any instant. This approach to modeling is shown to be useful in predicting the transition to the critical flow regime and clarifying the mechanism of a loss-of-flow accident. Calculated data on discharge of saturated water through a tube over a wide range of temperatures in comparison with corresponding experimental results are presented.

V.I. KOLESNICHENKO, A.I. TSAPLIN
CONVECTIVE HEAT AND MASS TRANSFER DURING CRYSTALLIZATION UNDER ELEVATED PRESSURE
Perm' State Technical University, Perm', Russia

A comparison of processes of free laminar convection of water during crystallization in a rectangular cell heated from one side at atmospheric and elevated (p = 50 MPa) external pressures is made. Thermodynamic properties of water at high pressures have been calculated using the empirical Taight's equation of state and thermodynamic relationships.

S.V. KONEV, N.S. KONEVA
SPECIAL FEATURES OF HEAT AND MASS EXCHANGE IN CRYOGENIC HEAT ACCUMULATORS
Academic Scientific Complex "A.V.Lukov Heat and Mass Transfer Institute," National Academy of Sciences of Belarus, Minsk, Belarus

We analyze the operation of cryogenic heat accumulators with melting-crystallization phase changes. Numerical investigations are carried out for Ethane, T_mel= 90 K; Isopentane, T_mel= 110 K; and Heptane, T_mel= 190 K. We have developed designs of accumulators the charging and discharging of which is carried out with the aid of a heat pipe, i.e., thermal diode. Experimental investigations of the constructions developed made it possible to optimize the capillary structure with accumulating matter. The advantages of conical capillaries are shown.

E.A. KOSOLAPOV, A.V. MALAKHOV, S.N. ZELENOV
MATHEMATICAL SIMULATION OF THE PROCESSES OF HEAT AND MASS TRANSFER FOR TWO-PHASE FLOWS IN COMPRESSORS
Nizhnii-Novgorod State Technical University, Nizhnii-Novgorod, Russia

The paper is concerned with mathematical simulation of flows of gas with drops of water in a compressor. This model represents two continuos media. The boundary conditions for a system of equations are presented. The description of the numerical technique is given.

A.P. KRYUKOV, I.N. SHISHKOVA, A.K. YASTREBOV
STUDY OF UNSTEADY EVAPORATION-CONDENSATION PROCESSES ON THE SURFACE BY THE METHODS OF MOLECULAR-KINETIC THEORY
Moscow Power Engineering Institute, Moscow, Russia

The process of unsteady evaporation has been studied by dried numerical solution of the kinetic Boltzmann equation. Calculation results for vapor flows are illustrated by dependences of density on coordinate at different time moments. It has been shown that a system of waves appears in a vapor phase. The first wave moves with supersonic velocity and can be described by the Rankine-Hugoniot correlation. Calculations have been made for initial data of Onishi and Tsuji paper (1994) in which unsteady evaporation-condensation process has been studied by solving the model BGK-type equation. Also Furukawa and Murakami experimental investigation (1999) of unsteady superfluid helium evaporation has been modeled. The solution presented agree with the results of these papers.

A.P. KRYUKOV, P.V. KHURTIN
DESCRIPTION OF HEAT AND MASS TRANSFER IN FILM BOILING OF SUPERFLUID HELIUM IN MICROGRAVITY WITHIN A CAPILLARY-POROUS BODY
Moscow Power Engineering Institute, Moscow, Russia

In this paper a possible method is presented to calculate some parameters of experimental installation for investigation of superfluid helium (He II) film boiling in microgravity. The stationary process of He II film boiling on a cylindrical heater within the cavity inside a capillary-porous body is studied. The molecular-kinetic approach is applied to describe the transport phenomena on the He II-vapor interface. Some calculating results are given which illustrate the presented approach. The investigation lead to the conclusion that during the operation of experimental installation the superfluid helium mass flow rate can be of the order of gramme per minute.

YU.A. KUZMA-KICHTA, A.S. KOMENDANTOV, G. BARTSCH
IMPROVING OF THE CHARACTERISTICS OF VAPOR GENERATING TECHNIQUES BY HEAT TRANSFER ENHANCEMENT
Moscow Power Engineering Institute, Moscow, Russia; Technical University, Berlin, Germany

The effect of porous coating on boiling heat transfer in channel, critical heat flux, heat transfer characteristics in transition and post- and dryout regions is investigated. The calculated dependences are presented. The efficiency of applying porous coating for heat transfer enhancement in vapor generating techniques is analyzed. It is shown that applying porous coating in two zones of evaporator of boiling type permits one to increase its heat transfer coefficient by 30%.

S.I. LEZHNIN, N.A. PRIBATURIN, S.B. SAMOILENKO, V.A. FEDOROV
COMBINED REGIMES OF SELF-EXCITED OSCILLATIONS DURING CONDENSATION WITHIN PIPES
Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

A model of the dynamics of vapor bubbles collapse in a channel is developed which takes into account the hydraulic damping in a condensate flow. Numerical results are compared with experimental data. In the conditions of high condensation rate the numerical experiments show that the auto-oscillations with a high frequency, such as the so-called "chugging"-oscillations, could be obtained. Moreover, the possible combinations of different types of auto-oscillations, that take place in condensation inside pipes, are considered.

O.A. LONSHCHAKOV, V.G. D'YAKONOV
CONDENSATION HEAT TRANSFER OF ETHYLACETATE AND WATER VAPORS IN A VERTICAL TUBE
Kazan State Technological University, Kazan, Russia

The results of experimental studies of the influence of mass fraction on the intensity of condensation heat transfer of ethylacetate-water vapor mixtures in a vertical tube are presented. Experimental data are compared with theoretical dependences obtained for pure liquids. The results demonstrate that application of this calculation formulas for mixtures gives a 40-50% overestimate. The results ontained are correlated as Nu = f(Pe, We, Ku).

M.O. LUTSET
INVESTIGATION OF THE VICINITY OF THE FRONT OF CHANGE IN BOILING REGIMES
S.S.Kutateladze Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

The results of experimental investigation of heat transfer processes in the vicinity of border between areas of nucleate and film boiling are given. The experiment is carried out in liquid nitrogen on a sapphire plate with sprayed platinum gauges of temperature. The distributions of temperature and heat fluxes in a liquid along a heater axis are obtained during the process of propagation of the film boiling site. The front site instability is found. The instability is a consequence of Taylor instability of film boiling. The heat fluxes into a liquid realized in a transient area turned out to be much larger than the critical heat flux.

D.YE. MARTSINYUK, A.P. SOROKIN
DETERMINATION OF TWO-PHASE LIQUID METAL FLOW REGIME BOUNDARIES IN THE LOOP WITH NATURAL CIRCULATION
Academician A.I. Leipunskii Physics and Power Engineering Institute. Obninsk, Russia

The experimental pattern of liquid metal boiling under atmospheric pressures is carried out and analyzed. The description of experimental loop and experimental investigations on boiling of sodium-potassium coolant in the model of a fast reactor fuel subassembly under conditions of natural circulation is presented.

V.I. MAZHUKIN, M.M. CHUIKO
2D STEFAN PROBLEM WITH EXPLICIT PHASE FRONT TRACKING
Institute of Mathematical Simulation, Russian Academy of Sciences, Moscow, Russia; Institute of Mathematics, National Academy of Sciences of Belarus, Minsk, Belarus

In the paper a numerical method is considered for solving a two-dimensional Stefan problem with explicit tracking of two phase fronts. The method is based on the dynamic adaptation approach and utilizes time-dependent solution-driven co-ordinate transformation. The presentation of the method is performed on example of the problem typical for laser material treatment. Main computational complexity of this problem is due to the presence of two phase fronts, and great difference between typical sizes of solid and liquid phase domains.

V.I. MAZHUKIN, V.V. NOSOV, U. SEMMLER
MODELING OF THE INFLUENCE OF TEMPORAL LASER PULSE SHAPE ON THE PROCESSES OF METAL TREATMENT
Institute of Mathematical Simulation, Russian Academy of Sciences, Moscow, Russia; Society of Scientific-Technical Development, Kemnitz, Germany

The paper presents results of mathematical simulation dealing with unsteady effects induced by variation of temporal energy distribution in laser pulse, for the so-called engineering range of intensity 10⁴-10⁷ W/cm and duration 10^-6-10^-2 sec. It is established that passing from rectangle to Gaussian shape of laser pulse, dynamics of a number of the process parameters, particularly, the melting front velocity and the melt layer thickness change significantly. The maximum melt thickness for Gaussian pulses is reached after the laser pulse termination and exceeds the value of steady-state estimation by 1-2 orders of magnitude. However, this approximation appears to be quite accurate to predict thickness of the layer evaporated.

O.O. MIL'MAN, S.I. MUNYUNIN
ENHANCEMENT OF HEAT TRANSFER IN AN AIR-COOLING CONDENSER OF NUCLEAR POWER PLANT COOLING SYSTEMS IN THE CASE OF HYDRODYNAMIC VAPOR AND CONDENSATE FLOW CRISIS
Kaluga Turbine Works Public Company, Kaluga, Russia; Kaluga State Pedagogical University, Kaluga, Russia

The hydrodynamic and heat transfer in condensation of vapor inside tubes in the case of counter-current flow of vapor and condensate in vertical and inclined tubes are considered. The methods of flow stabilization with the exception of liquid blocking are proposed. The possibility of heat exchanger stable work with a simultaneous 1.2-1.34-fold increase in the heat transfer coefficient is shown.

A.I. NAKORCHEVSKII
DYNAMICS AND HEAT/MASS TRANSFER IN OSCILLATING HETEROGENEOUS SYSTEMS
Institute of Technical Thermophysics, National Academy of Sciences of the Ukraine, Kiev, Ukraine

In heterogeneous systems with an easily deformable interphase surface low-frequency oscillations of the carrying phase velocity increase the interphase heat- and mass transfer. The devices that initiate asymmetric (modulated) oscillations of carrying phase are the most efficient. Among the methods of mathematical simulation we give preference to the method in which the velocity, temperature, and concentration nonequilibrium states of interacting phases are taken into account. It is possible to change essentially the dynamics parameters of working medium processing in the pulsation apparatus with flexible division membrane by varying the working medium physics properties.

V.A. NEMTSEV, A.M. CHERKASHIN
HEAT AND MASS TRANSFER OF A BUBBLE IN THE VOLUME OF CHEMICALLY REACTING AND INERT SOLUTIONS
Institute of the Problems of Energetics, National Academy of Sciences of Belarus, Minsk, Belarus; Institute of Radiative Physicochemical Problems, National Academy of Sciences of Belarus, Minsk, Belarus

A mathematical model for dynamics of a vapor bubble in chemically reacting solution has been formulated and numerically realized on a computer with due account of the kinetics of chemical reactions and phase transitions for the cases of a stationary bubble in the liquid volume and floating up under the effect of lifting forces. The model describes the bubble dynamics in chemically inert liquids and solutions under limited transitions. The results of numerical investigations on growth and collapse of vapor bubbles in the volume of chemically reacting and inert liquids are presented. The comparison of the mathematical model with the available experimental data has also been carried out, which shows a good agreement of the theory and experiment.

V.A. NEMTSEV
HEAT TRANSFER IN HORIZONTAL VAPOR GENERATING CHANNELS
Institute of the Problems of Energetics, National Academy of Sciences of Belarus, Minsk, Belarus

The model of calculation of heat transfer in the region of the separated regime of two-phase flow is presented. The model showed a satisfactory agreement with experimental data on temperature regimes of vapor generating tubes with various carriers.

E.I. NESIS, YU.N. SKIBIN, A.G. ZVYAGINTSEV, S.E. NESIS, L.M. KUL'GINA
ABOUT REMOTE CONTROL OF THE INTENSITY OF HEAT EXCHANGE IN BOILING AND CONVECTION
Stavropol State University, Stavropol, Russia

As a result of multiple experiments it was established that the radius R being formed in the active center of the surface changes during the process of boiling according to the formula: R = const*t , where the value of n depends on the regime and conditions of phase conversion of liquid into steam. The intensivity of heat transfer from the heater to the surrounding liquid depends also on these conditions. The accompanying processes of sound spouting, oscillations of the active center temperature are the functional results of the law of steam bubbles growth. An experimental setup has been devised. It allows one to determine automatically the n-index of the growth of a spherical nucleus from the acoustic pressure P_ac of the sound wave produced by the bubble. It will enable one to fulfil the remote control of the regime and boiling conditions and the accompanying process of heat transfer.

A.V. OVSYANNIK
SOME CHARACTERISTIC PROPERTIES OF BOILING OF A LIQUID IN HORIZONTAL RING CHANNELS
P.O.Sukhoi Gomel State Technical University, Gomel, Belarus

The results of experimental study of the process of boiling of liquids on smooth and longitudinally ribbed surfaces in a horizontal ring channel are presented. Investigations have shown the effect of a pressurized vapor-liquid mixture on the intensity of the boiling process resulting in an increase of mixture turbulence and heat transfer coefficient value and decrease in temperature head.

I.M. PADERIN, L.A. MIKHALEVICH, G.V. ERMAKOV
"RUNNING-IN" OF SURFACES IN BOILING-UP OF WEAKLY AND STRONGLY SUPERHEATED LIQUIDS
Institute of Thermophysics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia

Investigation of the process of the "running-in" of various metal surfaces during the boiling-up of a superheated liquid on them is presented. Its nonstationarity with an appreciable aftereffect has been revealed. As a result of the surface "running-in" the character of a statistical distribution changes from experimental to that with a maximum. The results obtained can be described with the aid of the Erlang distribution of the k-th order, the distribution order increasing with the duration of the "running-in". The similarity of the process of "running-in" of metal surfaces at different degrees of liquid superheating on them has been revealed.

I.S. PAL'CHIKOV, A.P. BASKAKOV, N.F. FILIPPOVSKII, V.A. MUNTZ
HEAT AND MASS TRANSFER DURING MOIST GAS COOLING WITH PARTIAL MOISTURE CONDENSATION
Ural State Technical University, Ekaterinburg, Russia

Rise in the price of energy resources makes it profitable to cool combustion products more deeply after power-producing and hot water boilers. In the process of deep cooling the water steam contained in the flue gas condenses on cooling surface, increasing heat transfer to the surface and decreasing flue gas dew point. Heat transfer between products of natural gas combustion, leaving a steam boiler and individual water cooled tube, situated across the gas flow, was investigated. Experimental results coincide well with the result of calculation based on the heat and mass transfer analogy. The heat transfer coefficient increases with decrease of the tube temperature below the temperature of the dew point because of heat release in the process of steam condensation. A heat exchanger for deep cooling of combustion products leaving a steam boiler was constructed on the basis of data obtained and is now in operation from December 1998.

A.N. PAVLENKO, I.P. STARODUBTSEVA
TRANSIENT REGIMES OF BOILING
Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Numerical simulation of the dynamics of development of 1D and 2D sites of film boiling is being performed. While analyzing boundary conditions at the front of the change of boiling regimes, we introduce the dimensionless parameter , which characterizes the ratio of the temperature gradient at the front to the linear scale of capillary force action. Here we show the effect of the nonstationary heat transfer coefficient in various zones of the front on the values of equilibrium density of the heat flux and propagation velocity of the film boiling boundary.

P.A. PAVLOV
HEAT AND MASS EXCHANGE IN CONDITIONS OF RAPID HEATING UP
Institute of Thermophysics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia

In superheating liquid with a tempo of 10⁶-10⁷ K/sec an anomalously high sensitivity of a heat flux to the test conditions has been discovered. The peculiarities of heat exchange are due to the steep temperature dependence of the bubble formation rate. The first bubbles appear and coalesce on a relatively more heated section of the wall. Further the vapor font propagates along the heater following the motion of the isotherm corresponding to intensive nucleation. The model explains the time nonmonotonic dependence of a heat flux.

L.V. PLETNEV, N.I. GAMAYUNOV, V.M. ZAMYATIN
COMPUTER SIMULATION OF THE PROCESS OF EVAPORATION INTO VACUUM
Mogilev Machine Building Institute, Mogilev, Belarus; Tver State Technical University, Tver, Russia; Centerprogramsystem (TsPS), Tver, Russia

RUSing the Monte Carlo method we suggest an approach to solving the problem of finding the velocity and energy distribution functions of atoms and their components in a Knudsen layer depending on the condensed phase temperature and magnitude of the potential barrier. We found distributions for the fluxes of particles that had escaped from the condensed phase surface into vacuum. Evaporation of a monoatomic condensed phase and Maxwellian velocity distribution of atoms in the condensed phase were considered.

B.G. POKUSAEV , E.A. TAIROV, D.A. KAZENIN , L.V. SYSKOV
STUDY OF SUBCOOLED WATER BOILING AT PULSED HEAT RELEASE
Institute of Energy Systems, Irkutsk, Russia; Moscow State University of Engineering Ecology, Moscow, Russia

Results of experimental study of nonstationary boiling of water subcooled below the saturation temperature at pulsed heat release in a vertical tubular heater 9 mm in diameter are presented. Interrelation of variations in the heating-surface temperature and pressure in the volume with evolution in the structure of steam-liquid wall layer is shown on the basis of visualization of the dynamic process. The experimental data obtained in the range of pressures 0.037-0.3 MPa, heating rates of heat liberating wall 2000-6500 K/sec and water subcooling 5-110 K are generalized. An approximate theoretical model of the initial boiling of water is described.

V.M. POLYAEV, B.V. KICHATOV
BOILING OF LIQUID ON SURFACES WITH POROUS COATING
N.E.Bauman Moscow State Technical University, Moscow, Russia

We suggest a model of liquid boiling on surfaces with porous coatings. Quantitative evaluations are made, from a single point of view, of basic laws governing the process of boiling of solutions and pure components on surfaces with porous coatings. The effect of the orientation of the surface with respect to the gravity field on heat transfer intensity has been made.

N.A. PRIBATURIN, S.I. LEZHNIN, V.A. FEDOROV
PHYSICAL MODEL OF THERMAL HYDRAULIC AUTOFLUCTUATIONS IN VAPOR CONDENSATION INSIDE A PIPE
Institute of Thermophysics, Siberian Branch of the Russia Academy of Sciences, Novosibirsk, Russia

The appearance of pressure pulsations on complete water vapor condensation inside a pipe, the outer surface of which is intensely cooled by cold water, is analyzed. The experiments of a model one-tube heat exchanger and industrial condenser are carried out. The existence of two modes of pressure pulsations is found. It has been fixed, that the frequencies of these modes depend on an inclination of the channel to horizon, density of a heat flux, presence of noncondensed gas, and of static pressure. The physical model of pressure fluctuations occurrence are developed. The qualitative conformity of experiment and calculation is shown.

A.A. SHAPOVAL
TOWARDS SIMULATION OF THE PROCESSES OF HEAT EXCHANGE IN BOILING ON SURFACES WITH DISORDERED POROUS STRUCTURES
Institute of Problems of Materials Science, National Academy of Sciences of the Ukraine, Kiev, Ukraine

An approximate semi-empirical model of heat transfer in boiling of water and organic liquids on surfaces with porous disordered structures are presented. The model makes it possible to interpret the influence of geometric, structural, and thermophysical characteristics of porous structures in heat transfer. The thermophysical calculation of heat transfer for a porous surface is possible. The essence of the model is the following. The thermal resistance of heat transfer have three components. The magnitudes of the components change with modification of heat flux. The order of calculation of every component is presented. An empirical formula is suggested for calculating the characteristic value.

A.A. SHAPOVAL, A.G. KOSTORNOV
CONCERNING THE EFFECT OF THE CHARACTERISTICS OF POROUS STRUCTURES OF METALLIC FIBERS ON BOILING UP OF WATER UNDER THE CONDITIONS TYPICAL FOR HEAT PIPES AND THERMOSIPHONS
Institute of Problems of Materials Science, National Academy of Sciences of the Ukraine, Kiev, Ukraine

The results of experimental investigations of the influence of parameters of metallic fibrous structures in initial boiling of water are presented. The investigations were performed under the conditions of free motion of liquid, typical for thermosiphons, and under the condictions of capillary transport, typical for heat pipes. The empirical formulas are obtained. They make it possible to calculate difference of temperatures in initial boiling. It is found that the characteristics of porous structures exert a weak influence on the difference of temperatures in initial boiling. This influence is insignificant.

S.E. TARASEVICH
HEAT TRANSFER FROM A WALL TO THE LIQUID FILM SURFACE THROUGH A STEAM GAP IN POST-BURNOUT BOILING IN A CHANNEL WITH FLOW SWIRLING
Kazan State Technical University, Kazan, Russia

The character of heat exchange in evaporation of a swirled liquid film depends significantly on heat transfer in a steam gap. Using the developed and tested model, the author carried out a numerical analysis of heat transfer in the steam gap. It was established that heat transfer from a wall to steam play the main role in evaporation, since superheated steam moves to the central steam flow. The analysis of the influence of the Re number on heat transfer was carried out.

B.R. TAUASAROV
SIMULATION OF MOTION AND HEAT AND MASS TRANSFER OF A PARTICLE IN A TURBULENT GAS FLOW
M.Auezov South-Kazakhstan State University, Shymkent, Kazakhstan

Motion of particles in a turbulent gas flow is considered provided that their diameter and turbulence scale are of the same order of magnitude. The mathematical model is developed with allowance for oscillation components of gas velocity in the vicinity of a moving particle and with allowance for lifting force induced by both averaged rotation of turbulence pulsations and gradient of longitudinal gas velocity near the apparatus walls too. Trajectories and local heat and mass transfer coefficients under evaporation of a droplet in a turbulent gas flow have been studied in a numerical experiment based on the proposed model. The results of the work are likely to be of certain importance to engineering calculations of apparatuses for processing gas-liquid droplets systems.

V.I.TIMOSHPOL'SKII, G.A.ANISOVICH, YU.A.SAMOILOVICH, I.A.TRUSOVA, A.P.BRODSKII, I.A.PAVLYUCHENKOV
MODELING OF NONLINEAR PROCESSES OF SOLIDIFICATION, COOLING AND HEATING ON THE BASIS OF THE PROBLEMS OF SAVING ENERGY IN MECHANICAL ENGINEERING AND METALLURGY
Belarusian State Polytechnic Academy, Minsk, Belarus; Department of Physical and Technical Sciences, National Academy of Sciences of Belarus, Minsk, Belarus

Fundamental investigations are carried out in the field of the processes of crystallization, solidification, cooling, and heating of steel based on physicochecmical modeling of real process and in the conditions of operating technologies on a number of leading metallurgical complexes supplied with modern equipment, including up-to-date heating and thermal furnaces. Record indices were achieved in the world and European practice of operation of metallurgical units by introduction of the author's works.

A.N. VARAVA, A.V. DEDOV, A.T. KOMOV, V.V. TSUKANOV, S.A. SHCHEGLOV
CRITICAL HEAT LOADS IN BOILING UNDER THE CONDITIONS OF SWIRLED SUBCOOLED FLOW
Moscow Power Engineering Institute (Technical University), Moscow, Russia

The results of experimental studies of critical heat transfer in boiling of a subcooled swirled flow as well as a physical model of the crisis based on modeling of the drying-out of a liquid microlayer are presented. The investigation is performed with application to the program of thermonuclear research. Comparison of predicted results with experimental data exhibits a satisfactory agreement.

V.V. VERKHOVSKII. G.N. DANILOVA, A.V. TIKHONOV
HEAT TRANSFER AND PARAMETERS OF BOILING PROCESS ON SURFACES WITH ARTIFICIAL VAPOR NUCLEATION CENTERS
St.Petersburg State Academy of Cold and Foodstuff Technologies, St.Petersburg, Russia

Physical and mathematical model of boiling heat transfer on enhanced surfaces is given. Bubble departing diameter and frequency measurements are necessary for further calculation. Tests with R 113, R 141b and R 123a were carried out. Calculations, based on the model proposed, are in good agreement with different test data of the present authors and those taken from the literature.

V.E. VINOGRADOV, P.A. PAVLOV
EXTENSION OF LIMITING LIQUID SUPERHEATS INTO THE REGION OF NEGATIVE PRESSURES
Institute of Thermophysics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia

The explosive boiling-up of a number of organic liquids (nhexane, n-heptane, benzene, toluene, acetone, ethyl alcohol, isobutyl alcohol) and water in a wave of negative pressure with an amplitude of up to -15 MPa has been investigated by experiment. Dependences of the limiting - superheat temperature of the liquids under study on the negative - pressure value have been measured. The paper shows the continuity of the lines of attainable superheat of organic liquids in the range of pressures from critical to -15 MPa. Time dependences of the density of a heat flow from a platinum heater to a liquid at the stage of intensive fluctuation nucleation in the region of negative pressures have been obtained.

A.A. VOLOSHKO
BOILING HEAT TRANSFER OF LIQUIDS UNDER THE CONDITIONS OF DYNAMIC ACCELERATIONS
Astrakhan Scientific Research and Design Institute of Gas, Astrakhan, Russia

The paper presents the results of investigations of the influence exerted by dynamic accelerations on the conditions of vapor phase formation. Characteristic distributions of liquid temperature and saturation temperature over the height of a liquid layer on a heating surface at different dynamic accelerations are shown. It is shown that with increase in dynamic acceleration at a constant temperature of the heating surface different forms of heat transfer are observed: from developed nucleate boiling to free convection of liquid.

V.V. YAGOV
BUBBLE BOILING HEAT TRANSFER - POSSIBILITIES OF THEORETICAL ANALYSIS
Moscow Power Engineering Institute, Moscow, Russia

An analysis of the newest numerical investigations of elementary processes of bubble boiling (growth of a single bubble, flow and evaporation of thin liquid films at the nucleation center) is given. It is shown that these investigations, despite their usefulness for the understanding of the process, cannot be used for engineering calculations. In this respect, the development of approximate theories of bubble boiling that reflect substantial interrelations between the governing parameters is most advantageous. To refine computational boiling heat transfer equations, it is most important to substantiate theoretically the dependence of the number density of nucleation sites on the temperature difference and properties of phases.

Z.ZH. ZHANABAEV, A.ZH. TURMUKHAMBETOV
FRACTAL NATURE OF HEAT EXCHANGE IN TWO-PHASE MEDIA
E.A.Buketov Karaganda State University, Karaganda, Kazakhstan

From the analysis of experimental results a conclusion was drawn about the fractal nature of turbulent structures generated in a gaseous-liquid medium. Geometrical (fractal) and physical (multifractal) models of self-similar evolution of isotropic and anisotropic structures were suggested. Ultimate index values of criterion dependence degree of heat exchange are determined. Theoretical description of increasing as well as decreasing heat exchange intensity vs. growing gas content, which is observed in experiments, is presented.

E.G. ZAULICHNYI
INTENSIFICATION OF CONVECTIVE HEAT TRANSFER BY BUBBLING OF LIQUIDS
Institute of the Problems of Power Engineering, National Academy of Sciences of Belarus, Minsk, Belarus

Results of theoretical and experimental investigations of using high intensive exchangers as bubblers for delivering the energy of compressed air into refrigerant and hot agent are presented. Coefficients of heat and mass transfer increase by a factor of 100 KOP for the systems developed increase by a factor of 2 in comparison with traditional refrigeration systems.