Comparative study of the Boltzmann and McCormack equations for Couette and Fourier flows of binary gaseous mixtures

We evaluate the accuracy of the McCormack model by comparing its solutions for Couette and Fourier flows of binary gaseous mixtures with results from the linearized Boltzmann equation. Numerical simulations of Ne-Ar and He-Xe gas mixtures are carried out from slip to near free-molecular flow regimes for different values of the molar concentration. Our numerical results show that while there are only small differences in the shear stress in Couette flow and the heat flux in Fourier flow, calculated from the two kinetic equations, differences in other macroscopic quantities can be very large, especially in free-molecular flow regime. Moreover, the difference between results from the two models increases with the molecular mass ratio and the molar concentration of the heavier species. Finally, the applicability of the McCormack model, which was derived for linearized flows only, is investigated by comparing its solutions with those from the Boltzmann equation for Fourier flow with large wall-temperature ratios.