Analytic solution to the Williams equation in the Poiseuille flow problem using mirror-diffuse model of interaction of gas molecules with the channel walls

An analytic (in the form of the Neumann series) solution to the Williams equation in the Poiseuille flow problem has been constructed using the kinetic approach. For the boundary condition on the channel walls, the mirror-diffusion model is used. Taking into account the constructed distribution function for various values of the channel width and the coefficient of accommodation of the tangential momentum of gas molecules by the channel walls, the value of the mass flow rate per unit width of the channel is calculated. Comparison with analogous results obtained by numerical methods is carried out. The results obtained upon transition to the hydrodynamic regime and to nearly hydrodynamic regimes of the gas flow are analyzed.