Application of High Moment Theory to the Plane Couette Flow

In this paper we make use of 26 field equations derived by the moment method to describe the stationary plane Couette flow for dense and rarefied gases. In such high moment theories one needs more boundary conditions than can be controlled experimentally. We employ a new minimax principle for the entropy production to determine the remaining boundary conditions. There results a heat flux in the direction of the flow, proportional to the curvature of the velocity field. Such a heat flux confirms results from molecular dynamics, it vanishes in a dense gas.