Poiseuille flow and thermal transpiration of a rarefied gas between plane parallel walls with nonuniform surface properties: integral equation approach

Poiseuille flow and thermal transpiration of a rarefied gas between plane parallel walls with nonuniform surface properties are studied on the basis of kinetic theory. Specifically, one of the walls is a diffuse reflection boundary, and the other wall is a Maxwell-type boundary whose accommodation coefficient has a periodic distribution in the direction perpendicular to the flow. The behavior of the gas is studied on the basis of the linearized Bhatnagar-Gross-Krook-Welander model of the Boltzmann equation. The extended integral equation for the macroscopic flow velocity is derived for the analysis at large Knudsen numbers, and is numerically solved. Features in the dependence of the mass flow rate on the distribution of the accommodation coefficient observed in the previous study (Doi 2015 ASME J. Fluids. Eng. 137 101103) were found to hold over a quite wide range of the Knudsen number up to 1000. A successive approximation method of the solution for a large Knudsen number is numerically tested using the integral equation.