Poiseuille flow of a rarefied gas in a cylindrical tube: Solution of linearized Boltzmann equation

The existence of a minimum in the cylindrical Poiseuille flow of a rarefied gas has been known since the experiments of Knudsen [Ann. Phys. 4, 75 (1909)]. Previously, the phenomenon has been studied with models of the Boltzmann equation, but results for the Boltzmann equation itself have not been reported. In the present paper, proceeding from recent studies, first the SN numerical algorithm for solving the linearized Boltzmann equation for the cylindircal geometry is outlined. Then, explicit numerical results for a rigid sphere gas and the boundary condition of diffuse specular reflection are obtained. The results show a minimum of the flow rate, and generally, provide a good description of the experimental data.