Poiseuille-type flow of a rarefied gas between two parallel plates driven by a uniform external force

Abstract

A unidirectional flow of a rarefied gas between two parallel plates driven by a uniform external force is investigated on the basis of kinetic theory with special interest in the behavior in the near continuum regime. The Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation and the diffuse reflection boundary condition are employed as the basic system. First, a systematic asymptotic analysis of the basic system for small Knudsen numbers is carried out, and a system of fluid-dynamic-type equations and their boundary conditions are derived up to the second order in the Knudsen number. Then, an accurate numerical analysis of the original BGK system is performed for a wide range of the Knudsen number by means of a finite-difference method. The behavior of the gas, such as the non-Navier-Stokes effects in the near continuum regime, is clarified on the basis of the fluid-dynamic-type system as well as the numerical solution of the BGK system.