Concise and accurate solutions to half-space binary-gas flow problems defined by the McCormack model and specular-diffuse wall conditions

Abstract

An analytical version of the discrete-ordinates method (the ADO method) is used to establish concise and particularly accurate solutions to the viscous-slip and the half-space thermal-creep problems for a binary gas mixture. The kinetic equations used to describe the flow are based on the McCormack model for mixtures. In addition to a computation of the viscous-slip and thermal-slip coefficients, for the case of Maxwell boundary conditions for each of the two species, the velocity, heat-flow and shear-stress profiles are established for both types of particles. Numerical results are reported for three binary mixtures (Ne–Ar, He–Ar and He–Xe) with various molar concentrations. The complete solution requires only a (matrix) eigenvalue/eigenvector routine and the solution of a system of linear algebraic equations, and thus the algorithm is considered especially easy to use. The developed (FORTRAN) code requires typically less than 0.1 seconds on a 1.2 GHz Pentium-based PC to solve both problems.