Rarefied Gas Channel Flows for Three Molecular Models

An analytic solution of the Boltzmann equation for the problem of a rarefied gas flowing between two parallel, infinite plates is developed for three different molecular models. They are the (1) Bhatnagar-Gross-Krook model, (2) hard-sphere model, and (3) Maxwellian model. The half-range moment method, which is used in the analysis for the three models, yields satisfactory results (with the expected minimum in the volume flow rate) for the transition, slip, and continuum regions. For the Bhatnagar-Gross-Krook model, the Willis iteration method provides good results for the near-free-molecular region even when, as a first guess, the first approximation by the half-range moment method is used. The comparisons between the analytic results and the experimental data indicate that the Bhatnagar-Gross-Krook model is a satisfactory approximation to the collision integral for the purpose of this study, and that the Maxwellian model provides an upper limit for the volume flow rate, and the hard-sphere model, a lower limit.