Solution of the Problem of the Couette Flow for a Fermi Gas with Almost Specular Boundary Conditions

Abstract

A solution of the Couette problem for a Fermi gas is constructed. The kinetic Bhatnagar–Gross–Krook (BGK) equation is used. Almost specular boundary conditions are considered. Formulas for the mass flux and the heat flux of the gas are obtained. These fluxes are proportional to the difference of the tangential momentum accommodation coefficients of the molecules. An expression for the viscous drag force acting on the walls of the channel is also found. An analysis of the macroparameters of the gas is performed. The limit to classical gases is taken. The obtained results are found to go over to the known results in this limit.