Heat flow and temperature and density distributions in a rarefied gas between parallel plates with different temperatures. Finite-difference analysis of the nonlinear Boltzmann equation for hard-sphere molecules

Heat flow and temperature and density distributions in a rarefied gas between two parallel plates at rest with different uniform temperatures are analyzed numerically on the basis of the full nonlinear Boltzmann equation for hard-sphere molecules and the Maxwell-type boundary condition by a finite difference method where the collision term is computed direct numerically. The accurate results are presented for the case in the density measurement by Teagan and Springer [Phys. Fluids 11, 497 (1968)], where the temperature ratio is 1.326, the value of the accommodation coefficient is 0.826, and the ratio of mean free path to plate spacing (Knudsen number Kn) is 0.0658≤Kn≤0.7582. It is found that there is a considerable difference between the present density distribution and the experimental data. The reason for this discrepancy is also discussed. The accurate numerical results of the linearized problem are also presented for comparison.