GENERAL PROBLEMS IN THE THEORY OF TRANSFER
TEMPERATURE FLUCTUATIONS OF MOLECULAR AND PHOTON GASES IN A CYLINDRICAL TUBE OF SMALL RADIUS
A. N. Morozov and A. V. Skripkin
UDC 519.21; 536.2
A study has been made of equilibrium temperature fl uctuations of molecular and photon gases in a cavity that is bounded by a cylindrical surface and is in a condensed medium with a high thermal conductivity. It has been shown that the indicated fl uctuations belong to the class of non-Markovian random processes and require stochastic integral equations for their description. Basic statistical characteristics of the change in the cavity temperature, including characteristic functions and spectral densities of fl uctuation power, have been determined.
Keywords: medium with a microstructure, thermal conductivity, non-Markovian process, integral stochastic equation.
PAGE 261
ELECTRODYNAMICS OF DIFFUSION IN CONDENSED PHYSICOCHEMICAL SYSTEMS
V. V. Leonov
UDC 530.1:536.7:539.3
Consideration has been given to the electrodynamic aspects of stationary diffusion mass transfer in condensed media with the aim of improving electrometric approaches to determination of the physicochemical properties of substances in a condensed state.
Keywords: electrodynamics, diffusion, condensed state, stationary diffusion mass transfer.
PAGE 270
TRANSFER PROCESSES IN RHEOLOGICAL MEDIA
A GENERALIZED MODEL OF A THERMAL SHOCK TO VISCOELASTIC BODIES BASED ON THE MAXWELL AND KELVIN RHEOLOGICAL MODELS
É. M. Kartashov
UDC 593.3
The thermal response of viscoelastic bodies to a thermal shock has been considered within the framework of the generalized model of an infi nite viscoelastic region bounded from the inside by either a plane or a spherical or a cylindrical surface. The infl uence of the geometry factor of the boundary surface of the indicated region on the magnitude of thermoviscoelastic stresses originating in it and on the characteristic features of a viscoelastic medium has been investigated based on the Maxwell and Kelvin linear rheological models.
Keywords: thermal shock, viscoelastic body, Maxwell and Kelvin linear rheological models, generalized model, stresses.
PAGE 277
RHEOLOGICAL AND MICROSTRUCTURAL FEATURES OF PHASE TRANSITIONS IN COMPOSITE POLYMER MATERIALS BASED ON TAR AND POLYETHYLENE
M. Yu. Dolomatov, S. V. Dezortsev, R. Z. Bakhtizin, B. R. Kharisov, and I. R. Nigmatullinaa
UDC 541.1+541.6+539.2
The change in the structure of tar- and polyethylene-based petroleum and polymer systems has been investigated by the methods of viscosity measurement and atomic force scanning microscopy. It has been established that the structural change of a composite petroleum and polymer thermoplastic material in the region of phase transitions of the 2nd kind results from the collapse of polymer coils and the formation of globules that subsequently aggregate. It has been shown using atomic-force-microscopy that a volume superlattice is formed from polymer globules in thermoplastic petroleum polymers in the region of phase transition of the 2nd kind.
Keywords: phase transition of the 2nd kind, petroleum polymer, polymer globule, polymer coil, material′s structure.
PAGE 289
REFLECTION AND TRANSMISSION BETWEEN TWO MICROPOLAR THERMOELASTIC HALF-SPACES WITH THREE-PHASE-LAG MODEL
R. Kumar, M. Kaur, and S. C. Rajvanshic
UDC 536.21
The present investigation is concerned with the refl ection and transmission of plane waves at an interface between two micropolar thermoelastic half-spaces with different micropolarity and thermoelastic properties. The three-phaselag theory of thermoelasticity developed by Roychoudhuri is used to study the phenomena mentioned. The refl ection and transmission coeffi cients of a longitudinal displacement wave, thermal wave, and two coupled transverse displacement and microrotational waves are derived for different incident waves. The amplitude ratios for different refl ected and transmitted waves vs. the angle of incidence are calculated numerically for various thermoelasticity models. Their graphical representations are given.
Keywords: micropolar thermoelasticity, three-phase-lag thermoelasticity, amplitude ratios, refl ection, transmission.
PAGE 295
HEAT AND MASS TRANSFER IN COMBUSTION PROCESSES
FEATURES OF THE DETONATION OF EXPLOSIVE AEROSUSPENSIONS
A. V. Pinaev
UDC 534.222.2
The detonation activity of aerosuspensions of particles of a secondary explosive (pentaerythritol tetranitrate) with a mean-volume density of 0.14–1.28 mg/cm3 at the initial pressure of the air in a shock tube of 0.01–0.3 MPa was considered. The dependence of the structure and the main parameters of the detonation wave in an explosive aerosuspension on the concentration of the explosive in it and the initial air pressure as well as the mechanism of propagation of this wave were investigated. The critical (lowest) mean-volume density of an explosive aerosuspension, at which its detonation is still possible, was determined experimentally for different initial air pressures.
Keywords: limit and mechanism of detonation, velocity of detonation propagation, secondary explosive, critical density of explosive aerosuspension.
PAGE 308
ON THE PROBLEM OF CONTROL OF THE AMPLITUDE OF SELF-OSCILLATIONS OF A SINGING FLAME
V. V. Gotsulenko and V. N. Gotsulenko
UDC 629.7:533.6.001
The character of change in the amplitude of self-oscillations of the fl ame in a combustion chamber, which are excited as a result of the phenomenological delay of combustion of the fuel in it, with variation of the chambers’s wave resistance and outfl ow of the combustion products at a constant pressure through a throttling orifi ce and a converging nozzle has been determined. It has been established that when the combustion products fl ow out through the converging nozzle, the viscous-friction resistance decreases with increase in the mass fl ow rate of the combustion products. This leads to instability of the steady-state combustion mode..
Keywords: combustion chamber, fuel-combustion delay, self-oscillations, limiting cycle, negative resistance, singing fl ame.
PAGE 319
INFLUENCE OF CATALYST PARTICLE SIZE ON THE CRITICAL CONDITIONS OF CATALYTIC OXIDATION OF GASES
V. V. Kalinchak, A. S. Chernenko, and V. V. Kalugin
UDC 536.46
A method of determination of the critical conditions of catalytic surface ignition and fi ring of small contents of gases in a mixture ofconstantcomposition on a catalyst particle in the form of the dependence of the gas-mixture temperature on the particle size has been proposed. It has been shown that heat exchange by radiation with surrounding bodies that are cold relative to the gas mixture gives rise to a minimum on the dependences under study and to the upper limit for regions of self-ignition and fi ring on the catalyst diameter. Limiting conditions for catalytic self-ignition and fi ring of gases have been obtained.
Keywords: catalyst particle, self-ignition, fi ring, critical conditions, heat exchange by radiation.
PAGE 325
SELF-PROPAGATING HIGH-TEMPERATURE SYNTHESIS IN THE Ti–C–Ni–Mo SYSTEM ON APPLICATION OF POWERFUL ULTRASOUND
M. M. Kulak and B. B. Khina
UDC 536.46:534.29
An experimental setup has been developed and a study has been made of the self-propagating high-temperature synthesis in a Ti–C–Ni–Mo system under the conditions of action of ultrasonic vibrations. The infl uence of the amplitude of ultrasonic vibrations on the combustion rate and temperature and on the phase composition and structure of the derivedcomposite material based on titanium carbide with a metal binder has been determined. The heat-transfer coeffi cient on the surface of a sample for vibrations at ultrasound frequency has been evaluated. Consideration has been given to possible mechanisms of infl uence of ultrasonic vibrations on the process of selfpropagating high-temperature synthesis. It has been shown that the reduction in the synthesis temperature is due to the cooling of the sample because of the forced convection of the surrounding gas, whereas the change in the structure of the synthesized material is related to the change in the conditions of high-temperature heterogeneous interaction in the wave of self-propagating high-temperature synthesis.
Keywords: self-propagating high-temperature synthesis, ultrasonic vibrations, structure formation, grain size, cermet, titanium carbide, metal binder.
PAGE 333
HYDROGASDYNAMICS IN TECHNOLOGICAL PROCESSES
INVESTIGATION OF THE PRESSURE DISTRIBUTION IN A FLOW OF A VISCOUS FLUID IN A PIPELINE UNDER HYDRAULIC-SHOCK CONDITIONS WITH ACCOUNT FOR THE RELAXATION PROPERTIES OF THE FLUID
I. V. Kudinov and V. A. Kudinov
UDC 536.21 (075)
An exact analytical solution of the hyperbolic equation defi ning the pressure distribution in a viscous fl uid fl owing in a pipeline under the conditions of a hydraulic shock with account for the relaxation properties of the fl uid has been obtained. It was established, based on acomparison of calculation and experimentaldata, that the relaxation properties of such a fl uid determine the degree of nonstationarity of its fl ow and, hence, the wall friction of the fl uid or its shear stress. It is shown that, in the case of nonstationary movement of a viscous fl uid in a pipeline under hydraulic-shock conditions, the pressure jump caused by the hydraulic shock differs markedly in form (it is longer in time) from that in the case of quasi-stationary movement of this fl uid under the identical conditions. The same effect (although weaker) was detected for decrease in the indicated pressure jump.
Keywords: viscous fl uid, hydraulic shock, nonstationary process, hyperbolic equation, hydrodynamical resistance, relaxation coeffi cients.
PAGE 344
DEHYDRATION OF IONS BY CUMULATION IN LIQUID MICROLAYERS
V. Ya. Khentov, V. M. Gasanov, and Yu. V. Vlasov
UDC 532.62+541.182.2
It has been established that bubble collapse on a liquid surface is accompanied by cumulation with droplet formation. The cumulation process, which is, nonstationary, has been investigated experimentally. It has been shown that the liquid of cumulative droplets is characterized by a lower value of the surface tension as compared to the bulk liquid. Consequently, the surface layer of droplets is enriched with electrolyte to a greater extent than the surface layer of the bulk liquid. This process is explained by the partial dehydration of ions bycumulation.
Keywords: cumulation, dehydration, fractionation, surface tension, gas bubble.
PAGE 355
COUPLING BETWEEN VELOCITIES IN A RADIAL SUPERCHARGER
V. N. Pavlechko and O. A. Petrov
UDC 621.65.01
We have analyzed the velocities of the medium and impeller in a radial supercharger with consideration of the Coriolis acceleration. We have derived an expression for determining the angular velocity of the medium that differs from the angular velocity of the impeller. Dependences have been obtained to determine the velocity of the medium at the exit from the impeller on the inclination angle of the supercharger blades and their coupling with the circumferential velocity of the impeller in the absence of energy losses. Graphical dependences of velocities on the inclination angle of the blades at different ratios of inside radius to outside radius have been constructed.
Keywords: radial supercharger, Coriolis acceleration, angular velocity of a medium, coupling between velocities.
PAGE 359
CALCULATING THE FLOWS OF A ONE-VELOCITY VISCOUS HEAT-CONDUCTING MIXTURE
V. S. Surov
UDC 532.529.5
One-dimensional fl ows in foamy and bubble gas–liquid mixtures have been investigated by the nodal method of characteristics with account for their viscous and heat-conducting properties.
Keywords: one-velocity multicomponent viscous heat-conducting mixture, hyperbolic systems of partial differential equations, numerical simulation.
PAGE 367
GODUNOV METHOD FOR CALCULATING MULTICOMPONENT HETEROGENEOUS MEDIUM FLOWS
V. S. Surov
UDC 532.529.5
The modifi ed Godunov method intended for integrating the nondivergent systems that describe a multivelocity heterogeneous mixture fl ow is presented. The linearized Riemann solver has been used in solving the Riemann problems.
Keywords: multivelocity multicomponent heterogeneous medium, hyperbolic systems of nondivergent form, modifi ed Godunov method, approximate Riemann solver, numerical simulation.
PAGE 376
INFLUENCE OF FLOW ROTATION WITHIN A COOLING TOWER ON THE AERODYNAMIC INTERACTION WITH CROSSWIND FLOW
M. M. Hemmasian Kashani and K. V. Dobrego
UDC 536.42:661.426
Environmental crosswind changes the aerodynamic pattern inside a cooling tower, destroys uniform and axisymmetric distribution of fl ow at its inlet and outlet, and may degrade fi ll zone performance. In this paper, the effect of fl ow rotation in the over-shower zone of a natural draft cooling tower (NDCT) on the aerodynamic interaction with crosswind is studied numerically. The 3D geometry of an actual NDCT and three models of induced rotation velocity fi elds are utilized for simulation. It is demonstrated that fl ow rotation results in homogenization of the aerodynamic fi eld in the over-shower zone. The inhomogeneity of the velocity fi eld in the outlet cross section decreases linearly with rotation intensifi cation. The effect of main stream switching under strong wind conditions is found. It is shown that even moderate fl ow rotation eliminates this effect.
Keywords: cooling tower, over-shower zone, crosswind, numerical simulation.
PAGE 385
INFLUENCE OF MAIN CHARACTERISTIC FEATURES OF SPOT WELDING ON WELDED CONNECTION/JOINT STRENGTH
Firas M. F. Al Quran, M. I. Matarneh, and A. G. Belik
UDC 669.295
To provide the required quality of welded connection in spot welding, an investigation of the infl uence of characteristic features of welding conditions on the welded connection strength and choice of the best process parameters are carried out.
Keywords: spot welding, pressing force, welding current.
PAGE 394
THEORETICAL AND EXPERIMENTAL ANALYSIS OF THE HIGH-VELOCITY INTERACTION OF SOLID BODIES IN WATER
A. N. Ishchenko, S. A. Afanas′eva, V. V. Burkin, A. S. D′yachkovskii, E. N. Zykov, L. V. Korol′kov, R. Yu. Monakhov, A. A. Rodionov, M. V. Khabibullin, and A. V. Chupasheva
UDC 539.3
Methods of estimating the penetrating ability of a metal striker into an aquatic medium and its interaction with obstacles in it have been developed. The penetration of a needle-shaped metal body into a water with a high velocity and its interaction with a metal obstacle found in it was investigated and calculated within the framework of continuum mechanics with the use of an elastoplastic model for defi nition of the solid body with account for its destruction and a hydrodynamic model for the water. It has been established that in the case where the indicated striker enters into the water with a velocity of 1.0–2.5 km/s, the developed-cavitation regime is realized, the head of the striker is subjected to the plastic deformation, and, in some cases, it is destroyed.
Keywords: water, striker, obstacle, mathematical simulation, high-velocity penetration, destruction.
PAGE 399
ADHESION AND HYDRODYNAMIC DRIFT OF SETTLINGS IN HEAT-TRANSFER CHANNELS
B. Ya. Kamenetskii*
UDC 532.5; 621.18
We have calculated the values of the hydrodynamic drift of the substance and the degree of adhesion of the layer from the results of experiments in the case of settling and dissolution of sulfate CaSO4 on the inner surface of heated tubes. It has been established that with increasing lifetime of the layer of settlings the substance drift decreases due to the rapid increase in the adhesion and strengthening of the layer.
Keywords: heat-transfer channel, aqueous solution of impurity, concentrated pressure, formation of settlings, rate of increase in the surface temperature, thermal resistance of the layer, calcium sulfate, layer dissolution time, dynamic pressure, adhesion of layers.
PAGE 409
CONDITIONS OF STABILIZATION OF THE PLASMA JET IN A VORTEX CHAMBER
G. V. Tkachenko and B. A. Uryukov
UDC 537.527
The stabilization of a plasma jet in a vortex chamber as a result of the return of the turbulent moles coming out of this jet and back into it was analyzed with account for the nonuniformity of the circumferential velocity of the vortex, the heat transfer, and the appearance of associated masses in this chamber. For the purpose of determining the dependence of the critical Richardson number in the indicated chamber on the physical and thermodynamic parameters of the moles and the vortex fl ow in it, a system of equations was derived and solved numerically. The calculation results obtained were compared with the corresponding experimental data.
Keywords: vortex chamber, stabilization of a plasma jet, turbulent mole, associated mass, Richardson number.
PAGE 413
STRENGTH OF A REINFORCED-CONCRETE COMMERCIAL OBJECT ON HIGH-VELOCITY IMPACT WITH A MODEL PROJECTILE
N. N. Belov, N. T. Yugov, S. A. Afanas′eva, and A. A. Yugov
UDC 539.3
The processes of impact interaction of model projectiles (including those carrying an explosive) with concrete, reinforced-concrete, and steel-concrete plates simulating structures of commercial objects have been investigated by a theoretical-experimental method. An analysis of structural strength has been made in the range of impact velocities 300–1500 m/s at different angles of incidence. Results of mathematical modeling of the impact interaction between a projectile of mass 200 kg and a commercial object representing a three-storied building with a basement space have been given..
Keywords: computer simulation, high-velocity impact, destruction, concrete, reinforced concrete.
PAGE 420
HEAT AND MASS TRANSFER IN DISPERSED AND POROUS MEDIA
DETERMINATION OF THE HYDRAULIC PARAMETERS OF TWO-PHASE VAPOR-LIQUID FLOW IN POROUS HIGH-THERMAL-CONDUCTIVITY MATERIALS
UDC 532.685:536.24
A. P. Lukisha
This paper presents the calculation data for the functions of relative phase permeabilities, the parameter of saturation for a porous material with the liquid phase and the two-phase parameter, as well as of the true speeds of fi ltration of the liquid and vapor phases of the porous material obtained with the use of a combination and analysis of two existing methods for calculating the hydrodynamical drag in the two-phase vapor-liquid fl ow in porous media — the Masket–Laverette and Lockhart–Martinelli methods. It has been shown that the dependence of the above quantities on the main regime-design parameters of porous heat-transfer elements is more complex and multiparametric than was thought before. On the basis of the calculation data, an interpolation dependence has been obtained for determining the parameter of saturation of porous samples with the liquid phase depending on the main regimedesign parameters of the model.
Keywords: hydrodynamics, two-phase vapor-liquid fl ows, porous materials, relative phase permeability model.
PAGE 427
COMPARISON OF THE RESULTS OF EXPERIMENTAL INVESTIGATIONS OF A VIBROFLUIDIZED BED WITH CALCULATIONS BY A GRANULAR GAS HYDRODYNAMIC MODEL
UDC 519.87:66.096.5
N. S. Orlova
A comparison has been made between the results of numerical calculations of the vibrofl uidization process of relatively large dolomite and fi ne glass particles by a granular gas hydrodynamic model and the corresponding experimental data. Good agreement is observed between the numerical calculations and the experimental data in the case of vibrofl uidization of relatively thin layers of the above materials. On the basis of the obtained results, the fi eld of use of the granular gas hydrodynamic model for describing the vibrofl uidization process has been determined..
Keywords: granular gas hydrodynamic model, vibrofl uidization, large and fi ne particles.
PAGE 443
ANALYSIS OF THE EFFECT EXERTED BY THE INITIAL TEMPERATURE OF ATOMIZED WATER ON THE INTEGRAL CHARACTERISTICS OF ITS EVAPORATION DURING MOTION THROUGH THE ZONE OF "HOT" GASES
UDC 536.4
R. S. Volkov, G. V. Kuznetsov, and P. A. Strizhak
We have carried out an experimental investigation of the integral characteristics of atomized water evaporation during its motion through high-temperature combustion products using a fl ame of fi xed height as an example and a high-response measurement system of two-phase vapor-liquid fl ow diagnostics. The scales of the infl uence of the initial liquid temperature on the intensity of phase transition in the region of the combustion zone at different atomization parameters have been established. Approximate relations for the dependences of the evaporated fraction of atomized liquid on its initial temperature and droplet size have been formulated.
Keywords: evaporation, heat and mass transfer, high-temperature gases, combustion products, flame, atomized water, droplet, jet, flow.
PAGE 450
NANOSTRUCTURES
USE OF NEUTRAL-NETWORK APPROXIMATION FOR PREDICTION OF THE MICROHARDNESS OF NANOCOMPOSITE COATINGS
UDC 538.9
S. G. Valyukhov, A. V. Kretinin, and O. V. Stognei
Results of experimental investigations into the microhardness of metal–ceramic nanocomposite coatings have been approximated with the apparatus of artifi cial neural networks. A neutral-network dependence of the microhardness on the concentration of the metal phase and microhardnesses of "pure" phases has been obtained. An algorithm of employment of a neural network for calculation of the microhardness of nanocomposites has been presented..
Keywords: microhardness, composite coatings, artifi cial neural networks.
PAGE 459
SIZE EFFECT IN EVAPORATION OF ATOMS (MOLECULES) FROM AEROSOL NANOPARTICLES
UDC 541.182
V. V. Levdanskii, J. Smolik, and V. Zdimal
The infl uence of the size effect on evaporation of atoms (molecules) from aerosol nanoparticles has been investigated theoretically.
Keywords: nanoparticles, evaporation, size effect.
PAGE 469
THERMODYNAMICS OF METAL COMPOSITES BASED ON POLYVINYLCHLORIDE
UDC 536.63 – 677.494
B. B. Kolupaev, T. G. Lyashuk, and B. S. Kolupaev
We present the results of experimental investigations of the thermodynamic properties of composites based on
polyvinylchloride and copper nanoparticles obtained by electrical explosion of the conductor. It has been established that the thermodynamic potentials H and G in determining the system parameters (s, T, p, V) depend nonlinearly on the temperature and content of the fi ller. β- and α-relaxation transitions as a general phenomenon characteristic of the fl uctuation structure of polyvinylchloride are observed thereby. The introduction of a nanodispersed metal fi ller into polyvinylchloride increases the amount of activation energy and the time of "settled" life of the structural
elements, changing the thermodynamic stability of the composite.
Keywords: potential, stability determinant, entropy capacity, structural element, phase space.
PAGE 474
THERMOPHYSICAL PROPERTIES
CONTACT HEAT CONDUCTIVITY UNDER CONDITIONS OF HIGH-TEMPERATURE HEAT TRANSFER IN FIBROUS HEAT-INSULATING MATERIALS
UDC 536.2.08
P. S. Grinchuk
A mathematical model for calculating the effective heat conductivity of fi brous materials at high temperatures and variable density has been suggested and substantiated. Consideration is focused basically on accounting for heat conduction in the solid phase of a fi brous material. The calculated results were compared with experimental data that demonstrated a good accuracy of the proposed model. The effective heat conductivity of a fi brous heat-insulating material has been calculated as a function of density for a number of temperatures within the range from 200 to 1000oC.
Keywords: fi brous heat-insulating materials, effective heat conductivity, contact heat exchange.
PAGE 481
NEW TECHNOLOGIES OF SYMMETRIC-WAVE MULTICOLOR THERMOMETRY AND THEIR METROLOGICAL CHARACTERISTICS
UDC 526.521.3
L.F. Zhukov and A. L. Kornienko
The influence of the optical characteristics of multicolor thermometry on its methodical and instrumental errors was investigated and, on the basis of the investigations performed, a new direction of symmetric-wave multicolor pyrometry of radiation, including linear and universal thermometric technologies, has been developed. It is shown that, in the case where the spectral distribution of the radiating capacity of a body is linear, the methodical error in determining its temperature by the method of linear symmetric-wave pyrometry of radiation is close to zero and is practically determined by the discreteness of the selection of temperatures of this body. The errors in measuring the temperature of the majority of materials, e.g., tungsten, by the method of linear symmetric-wave thermometry are 9.1–25.0, 5.9–6.8, and 2.4–3.3 times smaller than those given by classical energy, spectral-ratio and polychromatic pyrometries of radiation. The universal thermometry method proposed allows one to eliminate the methodical error, predominating in optical thermometry, in determining the temperatures of bodies with different linear and nonlinear spectral distributions of their radiating capacity. The residual instrumental error given by linear and universal symmetric-wave pyrometries of radiation of a body does not exceed the error in measuring its initial monochromatic radiation temperatures, i.e., 0.2–0.5%.
Keywords: temperature, symmetric-wave multicolor pyrometry, radiating capacity, methodical and instrumental errors.
PAGE 489
UNCERTAINTY PRINCIPLE IN METROLOGY AND STATISTICS: ALGORITHMS AND APPLICATIONS
UDC 519.23:53.089.6
E. V. Chernukho
We have formulated the uncertainty principle from the viewpoint of metrological and statistical problems. A comparison between the error and uncertainty paradigms has been made. The possibility of applying the uncertainty principle to the processing of experimental measurement data has been analyzed.
Keywords: uncertainty principle, error paradigm, uncertainty function, rank measure, estimation of parameters.
PAGE 498
HEAT CONDUCTION AND HEAT TRANSFER IN TECHNOLOGICAL PROCESSES
MODELING OF THE TEMPERATURE FIELD OF A CONTINUOUSLY CAST INGOT WITH DETERMINATION OF THE POSITION OF THE PHASE-TRANSITION BOUNDARY
UDC 536.248.2:51-74
A. I. Borodin and A. A. Ivanova
Heat transfer in an ingot in pulling it through the crystallizer in the process of continuous casting of steel is modeled by two different methods: in the classical formulation of the Stefan problem and on condition that a two-phase buffer zone exists between the liquid core of the ingot and its solid shell. A comparison of the obtained results is made using
a standard slab crystallizer as an example.
Keywords: continuous casting of steel, crystallizer, modeling of heat transfer, ingot, Stefan problem, generalized formulation, two-phase zone, liquidus, solidus.
PAGE 507