Model equations in rarefied gas dynamics: Viscous-slip and thermal-slip coefficients

Abstract

Various model equations are used to define the viscous-slip and the thermal-slip coefficients in rarefied gas dynamics. More specifically, the BGK model, the S model, the variable collision model and the CES model are used to establish the slip coefficients basic to Kramers’ problem and the half-space problem of thermal creep. While the most general results are developed from use of the Maxwell boundary condition, results for the BGK model and the S model as defined by the Cercignani–Lampis boundary condition are also reported. An analytical discrete-ordinates method is used to establish the reported numerical results, and when available results from a numerical solution of the linearized Boltzmann equation are used as reference values. In addition to the numerical work based on model equations, the important issue of how to define meaningful ways (appropriate mean-free paths) to compare the results for the various models is discussed.