Numerical analysis of thermally generated flow based on the kinetic approach

Two-dimensional thermally generated gas flow between two saw-tooth like surfaces is numerically investigated using the kinetic approach based on the S-model of the Boltzmann equation. An implicit scheme for the solution of the S-model kinetic equation, optimized for the use of massive parallelization in both physical and velocities spaces, is applied. Both surfaces are assumed to be isothermal and kept at different temperatures. Top peaks are shifted with respect to bottom peaks in the x-direction. Temperature gradients between the surfaces and the asymmetric distribution of peaks along surfaces lead to an occurrence of tangential temperature gradients along the surfaces, causing a thermal creep flow in the x-direction. Rarefaction effect on the thermal transportation flow is estimated by varying Knudsen number from 0.04 to 40, i.e. covering slip, transition and free-molecular regimes. The influence of surface geometry, such as the shift between top and bottom peaks, the length of periodic pattern, on flow is analyzed. It is found that rarefaction, as well as a geometry configuration have a crucial effect on the occurrence of gas flow.