Volume 89,   № 5

COMPUTATION OF THE HEAT FLUX IN A CYLINDRICAL DUCT WITHIN THE FRAMEWORK OF THE KINETIC APPROACH


Within the framework of the kinetic approach, the authors have solved the problem on rarefi ed-gas fl ow in a cylindrical duct in the presence of the longitudinal temperature gradient. The Williams kinetic equation was used
as the basic equation, and the diffuse-refl ection model, as the boundary condition on the duct wall. This enabled the authors to consider the solution of the problem in linearized form. To fi nd a linear correction to the locally
equilibrium distribution function, the problem was reduced to solution of a linear homogeneous partial differential equation of fi rst order. A solution to the latter was constructed with the method of characteristics. With account taken of the obtained solution and on the basis of the statistical meaning of the distribution function of gas molecules by coordinates and velocities, the authors constructed the profi le of the heat-fl ux vector in the duct and computed the heat fl ux through the duct cross section. A numerical analysis of fi nal expressions was made. A comparison with analogous results obtained with the discrete-ordinates method has shown that the solution procedure proposed in the work leads to correct results in a wide range of values of the duct radius

Within the framework of the kinetic approach, the authors have solved the problem on rarefi ed-gas fl ow in a cylindrical duct in the presence of the longitudinal temperature gradient. The Williams kinetic equation was used
as the basic equation, and the diffuse-refl ection model, as the boundary condition on the duct wall. This enabled the authors to consider the solution of the problem in linearized form. To fi nd a linear correction to the locally
equilibrium distribution function, the problem was reduced to solution of a linear homogeneous partial differential equation of fi rst order. A solution to the latter was constructed with the method of characteristics. With account taken of the obtained solution and on the basis of the statistical meaning of the distribution function of gas molecules by coordinates and velocities, the authors constructed the profi le of the heat-fl ux vector in the duct and computed the heat fl ux through the duct cross section. A numerical analysis of fi nal expressions was made. A comparison with analogous results obtained with the discrete-ordinates method has shown that the solution procedure proposed in the work leads to correct results in a wide range of values of the duct radius
Author:  O. V. Germider, V. N. Popov, and A. A. Yushkanov
Keywords:  Boltzmann kinetic equation, model kinetic equations, method of characteristics, gas flow in a cylindrical duct.
Page:  1338

O. V. Germider, V. N. Popov, and A. A. Yushkanov .  COMPUTATION OF THE HEAT FLUX IN A CYLINDRICAL DUCT WITHIN THE FRAMEWORK OF THE KINETIC APPROACH //Journal of engineering physics and thermophysics. №5. Volume 89, № 5. P. 1338.


Back to list