The McCormack model: channel flow of a binary gas mixture driven by temperature, pressure and density gradients

Abstract

An analytical version of the discrete-ordinates method (the ADO method) is used to establish concise and particularly accurate solutions to the problems of Poiseuille flow, thermal-creep flow and diffusion flow for a binary gas mixture confined between parallel walls. The kinetic equations used to describe the flow are based on the McCormack model for mixtures. The analysis yields, for the general (specular-diffuse) case of Maxwell boundary conditions for each of the two species, the velocity, heat-flow and shear-stress profiles for both types of particles. Numerical results are reported for two binary mixtures (Ne–Ar and He–Xe) with various molar concentrations. The complete solution requires only a (matrix) eigenvalue/eigenvector routine and a solver 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 a second on a 2.2 GHz Pentium IV machine to solve all three problems.