Analysis of nonlinear transport in Couette flow

Abstract

The nonlinear Bhatnagar, Gross, and Krook [Phys. Rev. 94, 511 (1954)] kinetic equation is solved for boundary conditions leading to planar Couette flow and heat transport. In the limit of zero Knudsen number but arbitrary uniformity parameter (shear rate), an exact ‘‘normal’’ solution is obtained. The velocity distribution function is illustrated explicitly for states far from equilibrium. At finite Knudsen number, the distribution function is obtained from numerical solution of a set of nonlinear, singular integral equations. Results are presented for a range of values of the Knudsen number and uniformity parameter. The approach to a normal state is studied with a determination of the hydrodynamic profiles, velocity slip, shear viscosity, and a nonlinear Burnett transport coefficient.