Higher-order effects in rarefied channel flows

The regularized 13 moment (R13) equations and their boundary conditions are considered for plane channel flows. Chapman-Enskog scaling based on the Knudsen number is used to reduce the equations. The reduced equations yield second-order slip conditions, and allow us to describe the characteristic dip in the temperature profile observed in force driven flow. Due to the scaling, the R13 equations' ability to describe Knudsen layers is lost. Solutions with Knudsen layers are discussed as well, and it is shown that these give a better match to direct solutions of the Boltzmann equations than the reduced equations without Knudsen layers. For a radiatively heated gas the R13 equations predict a dependence of the average gas temperature on the Knudsen number with a distinct minimum around Kn = 0.2 , similar to the well-known Knudsen minimum for Poiseuille flow.