Analysis of nonlinear transport in Couette flow

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.