European Journal of Mechanics B/Fluids 23 (2004) 709–726 Concise and accurate solutions to half-space binary-gas flow problems defined by the McCormack model and specular-diffuse wall conditions C.E. Siewert a,∗ , D. Valougeorgis b a Mathematics Department, North Carolina State University, Raleigh, NC 27695-8205, USA b Department of Mechanical and Industrial Engineering, University of Thessaly, Volos, 38334, Greece Received 10 August 2003; received in revised form 6 December 2003; accepted 9 December 2003 Available online 15 January 2004 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.  2003 Elsevier SAS. All rights reserved. 1. Introduction The study of slip phenomena in gas flows over plane boundaries is of major importance in gas dynamics, especially when the flow is in the transition or in the slip regimes [1,2]. In the transition regime the application of the Boltzmann equation (BE) or of kinetic model equations is necessary to describe the thermal creep and the mechanocaloric effects. In addition, in the slip regime the determination of the appropriate slip boundary conditions to be coupled with the hydrodynamic continuum equations should be obtained from the solution of kinetic type equations (BE or suitable models). The fundamental theoretical significance and the great practical importance of the slip coefficients easily justify the interest in this area of research. Most work in this regard has been focused on the case of a single gas [3–6]; however, the case of gas mixtures has also received some significant attention [7–12]. Efforts are now being made [13–18] to extend early work on gas mixtures in order to solve complicated binary gas problems in an efficient and accurate manner. This is achieved by adapting well-developed techniques for single-component gases to gas mixtures. The renewed interest in these problems is justified by the basic need of a thorough understanding of micro and mesoscale transport phenomena in mixtures due to an increasing number of technological applications [19,20]. One of the major difficulties in dealing with gas mixtures is the large number of parameters (concentration ratios, molecular masses and diameters, gas-surface accommodation coefficients, intermolecular laws and forces), which are involved in the * Corresponding author. E-mail address: siewert@ncsu.edu (C.E. Siewert). 0997-7546/$ – see front matter  2003 Elsevier SAS. All rights reserved. doi:10.1016/j.euromechflu.2003.12.002