Analytic solution to the problem of the couette flow in a plane channel with infinitely large parallel walls

Abstract

An analytic (in the form of a Neuman series) solution to the problem of the Couette flow in a plane channel with infinitely large parallel walls is constructed using the kinetic approach in the isothermal approximation. For the basic equation, the Bhatnagar-Gross-Krook (BGK) model of the kinetic Boltzmann equation is used, while the boundary condition is determined by the diffuse reflection model. The mass flux through half the channel thickness in the direction parallel to the channel walls as well as the nonzero component of the viscous stress tensor are calculated taking into account the constructed distribution function. The results are compared with analogous data obtained by numerical methods.