단원자 희박기체에서의 열전달 해석을 위한 모델 카이네틱 방정식의 직접 해석 기법

Abstract

In the present study, the heat conduction process in a monatomic rarefied gas was investigated based on the solution of the kinetic relaxation models for various Knudsen numbers. Generalization of the equilibrium distribution function in the model kinetic equation allows the correct estimation of the heat flux for arbitrary Prandtl numbers. The kinetic model equations in terms of newly defined density distribution functions are used to investigate two-dimensional heat transfer flows between two infinite walls of constant temperature ratio. The macroscopic flow variables were recovered by the integration of the resultant distribution functions with respect to longitudinal velocities. The steady solutions obtained by means of the current methodology are in good agreement with the solutions of the direct numerical analysis for the full Boltzmann equation. The temperature jumps at the solid surfaces were successfully evaluated from the deviation of the resultant distribution functions from local equilibrium states. It is concluded that the temperature jumps near the solid boundaries increase as the parameter for the rarefaction of the flow increases. This paper deals with the numerical simulation of the natural convection in a two-dimensional square filled with a monatomic gas. It is clearly shown that increasing the Knudsen number of the flow results in the increment of the relative jumps at the solid wall boundary.