Couette and Poiseuille microflows: Analytical solutions for regularized 13-moment equations

The regularized 13-moment equations for rarefied gas flows are considered for planar microchannel flows. The governing equations and corresponding kinetic boundary conditions are partly linearized, such that analytical solutions become feasible. The nonlinear terms include contributions of the shear stress and shear rate, which describe the coupling between velocity and temperature fields. Solutions for Couette and force-driven Poiseuille flows show good agreement with direct simulation Monte Carlo data. Typical rarefaction effects, e.g., heat flux parallel to the wall and the characteristic dip in the temperature profile in Poiseuille flow, are reproduced accurately. Furthermore, boundary effects such as velocity slip, temperature jump, and Knudsen boundary layers are predicted correctly.