Applications of new boundary conditions for the Boltzmann equation derived from a kinetic model of gas-surface interaction

Recently, new models of the boundary condition for the Boltzmann equation were proposed on the basis of a kinetic model of gas-surface interactions [K. Aoki et al., Phys. Rev. E 106, 035306 (2022)2470-004510.1103/PhysRevE.106.035306]. In the present paper, the kernel representations of the models are given, and the models are applied to some basic problems of a rarefied gas between two parallel plates. To be more specific, the heat transfer between the plates with different temperatures, plane Couette flow, and plane Poiseuille flow driven by an external force are numerically investigated by using the Bhatnagar-Gross-Krook model of the Boltzmann equation and the new models of the boundary condition. The results are compared with those based on the conventional Maxwell-type boundary condition. It is shown that when the interaction of gas and solid molecules is strong, the results based on the new models tend to approach those based on the diffuse reflection. However, when the interaction is not strong, the former results deviate from those based on the Maxwell-type condition with a constant accommodation coefficient.