Failures of the Burnett and super-Burnett equations in steady state processes

Linearized Burnett and super-Burnett equations are considered for steady state Couette flow. It is shown that the linear super-Burnett equations lead to periodic velocity and temperature curves, i.e. unphysical solutions. The problem is discussed as well for the so-called augmented Burnett equations by Zhong et al. (AIAA Journal 31, 1036-1043 (1993)), and for the recently introduced regularized 13 moment equations (R13) of Struchtrup and Torrilhon (Phys. Fluids 15(9), 2668-2680 (2003) ). It is shown that both theories exhibit proper Knudsen boundary layers for velocity and temperature. However, the heat flux parallel to the wall has different signs for the Burnett and the R13 equations, and a comparison with DSMC results shows that only the R13 equations predict the proper sign.