Numerical analysis of the Poiseuille flow and the thermal transpiration of a rarefied gas through a pipe with a rectangular cross section based on the linearized Boltzmann equation for a hard sphere molecular gas

Abstract

Poiseuille flow and the thermal transpiration of a rarefied gas through a long straight pipe with a rectangular cross section are analyzed numerically based on the linearized Boltzmann equation for a hard sphere molecular gas. A deterministic numerical analysis based on the finite difference is carried out, where the collision integral is evaluated with the aid of the numerical kernel method [Y. Sone et al., Phys. Fluids A 1, 363 (1989)]. The numerical solution, the mass flow rate as well as the macroscopic variables, is presented and discussed for a wide range of the Knudsen number and various aspect ratios of the cross section.