Weakly rarefied gas flows between nonuniformly heated parallel plates

The aim of this research is to establish the validity of the predictions of the theory of slow nonisothermal flows, to study the limits of applicability (with respect to the Knudsen number) of the conclusions reached and to determine the effect of the Knudsen layers on these flows on the basis of a numerical investigation of slow nonisothermal weakly rarefied gas flow in a plane infinite channel with weakly nonequilibrium heating of the walls and a finite wall temperature difference. The gas flow is described by a relaxation transport equation. The results obtained show how quickly, as the Knudsen number decreases, the solutions of the transport equation outside the Knudsen layers tend to the solution of the equations of gas dynamics of slow nonisothermal flows (and not to the solution of the Navier-Stokes equations).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 115–121, January–February, 1988.     

Heat transfer in a very rarefied gas

A one-dimensional problem of heat transfer in a rarefied gas is considered. It relates to the nonmonotonic variation of the heat flux between two plates when the temperature of one of them is reduced. Attention is drawn to a paradox that arises in this problem if the interaction of the molecules of the gas with the surface is described by means of accommodation coefficients.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1. pp. 195–198, January–February, 1980.     

Heat and mass transfer in laminar flow between parallel porous plates

Summary The problem of heat transfer in a two-dimensional porous channel has been discussed by Terrill [6] for small suction at the walls. In [6] the heat transfer problem of a discontinuous change in wall temperature was solved. In the present paper the solution of Terrill for small suction at the walls is revised and the whole problem is extended to the cases of large suction and large injection at the walls. It is found that, for all values of the Reynolds number R, the limiting Nusselt number Nu increases with increasing R.Nomenclature stream function - 2h channel width - x, y distances measured parallel and perpendicular to the channel walls respectively - U velocity of fluid at x=0 - V constant velocity of fluid at the wall - =y/h nondimensional distance perpendicular to the channel walls - f() function defined in equation (1) - coefficient of kinematic viscosity - R=Vh/ suction Reynolds number - density of fluid - C _p specific heat at constant pressure - K thermal conductivity - T temperature - x=x ₀ position where temperature of walls changes - T ₀, T ₁ temperature of walls for x<x ₀, x>x ₀ respectively - = (T – T ₁)/T ₀ – T ₁) nondimensional temperature - =x/h nondimensional distance along channel - R ^* = Uh/v channel Reynolds number - Pr = C _p/K Prandtl number - _n eigenvalues - B _n() eigenfunctions - B _n ⁽⁰⁾ , () eigenfunctions for R=0 - B ₀ ⁽ⁱ⁾ , B ₀ ⁽ⁱⁱ⁾ ... change in eigenfunctions when R0 and small - K _n constants given by equation (13) - h heat transfer coefficient - Nu Nusselt number - _m mean temperature - C _n constants given by equation (18) - perturbation parameter - B _0i () perturbation approximations to B ₀() - Q = B ₀/ ₀ derivative of eigenfunction with respect to eigenvalue - z nondimensional distance perpendicular to the channel walls - F(z) function defined by (54)     

Heat transfer from a heated sphere in a rarefied gas at rest

We consider the problem of heat transfer from a slightly heated sphere in a resting rarefied gas. We assume that the Krook equation is valid in this case. Two forms of the basic equations are presented, and relations are given which are obtained as a result of calculations of the heat flux and the temperature jump at the sphere surface as a function of a parameter which is inversely proportional to the Knudsen number. The results obtained are compared with results given by the known approximate theories.In conclusion the author wishes to thank M. N. Kogan for proposing the problem and for numerous discussions.     

Motion of a rarefied gas between infinite plane-parallel emitting and absorbing surfaces

The problem of the motion of a rarefied gas between infinite plane-parallel emitting and absorbing surfaces is solved numerically on the basis of the Boltzmann kinetic equation.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 176–178, March–April, 1972.     

Heat transfer to laminar flow between parallel plates with a prescribed wall heat flux

Summary The first three eigenvalues and constants, as well as asymptotic expressions for these quantities, are presented for heat transfer to laminar flow between parallel flat plates with a symmetrically prescribed wall heat flux.     

Heat transfer from a sphere in the intermediate dynamics region of a rarefied gas

The results are given of the experimental study of convective heat transfer from a sphere in a low-density subsonic stream. Generalizing the results obtained and earlier known data for sub-and supersonic velocities, we suggest approximate formulas for calculating heat transfer from a sphere under any streamline flow conditions of a rarefied gas.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 170-172, March-April, 1972.     

Heat transfer and equilibrium temperature of a sphere in a supersonic rarefied gas flow

Some results are presented of experimental studies of the equilibrium temperature and heat transfer of a sphere in a supersonic rarefied air flow.The notations D sphere diameter - u, , T,,l, freestream parameters (u is velocity, density, T the thermodynamic temperature,l the molecular mean free path, the viscosity coefficient, the thermal conductivity) - T₀ temperature of the adiabatically stagnated stream - T_e mean equilibrium temperature of the sphere - T_w surface temperature of the cold sphere (T_we) - mean heat transfer coefficient - _e air thermal conductivity at the temperature T_e - P Prandtl number - M Mach number     

Magnetohydrodynamic heat transfer in two-phase flow between parallel plates

This study dealt with two-phase magnetohydrodynamic (MHD) flow and heat transfer in a parallel-plate channel. Both phases were incompressible and the flow was assumed to be steady, one-dimensional and fully developed. The present study was expected to be useful in the understanding of the effect of the presence of slag layers on the heat transfer characteristics of a coal-fired MHD generator.The problem was investigated, in which one of the two fluids was assumed to be electrically non-conducting. The transport properties of the two fluids were taken to be constant, and the plates were assumed to be maintained at constant and equal temperatures. In this case, the governing differential equations were linear, and an exact solution was obtained. Results were presented for various height and viscosity ratios for the two fluids and for two values of the electric field loading parameter. The governing equations were also solved numerically in order to verify the exact solution.     

Subsonic rarefied gas flow over a rack of flat transverse plates

Parameters of a rarefied gas flow through a rack of flat plates aligned across the flow are studied by means of the joint numerical solution of the Boltzmann and Navier-Stokes equations. A subsonic flow regime is considered. The changes in flow characteristics are calculated as functions of the free-stream velocity and plate temperature. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 59–67, January–February, 2008.     

On the frame dependence of constitutive equations. I. Heat transfer through a rarefied gas between two rotating cylinders

To verify the principle of material frame indifference a numerical calculation of the heat flux field in a rotating gas has been carried out based on the kinetic equation over wide ranges of gas rarefaction and angular velocity. It has been confirmed that a radial gradient of the temperature causes a tangential heat flux. Also, it has been found that the radial heat flux is affected by the rotation.On temporary leave from Department of Physics, Urals State University, 620083 Ekaterinburg, Russia     

Heat transfer in the cylindrical rarefied Couette flow

The efficiency of the self-similar interpolation method is demonstrated with reference to the solution of the problem of heat transfer in a rarefied gas between two coaxial cylinders rotating relative one another. The analytical solution of the problem is compared with the results obtained by direct statistical simulation. The most interesting result is the energy flux nonmonotonicity and the reversal of its sign with variation in the Knudsen number.