Pressure and temperature driven fully-developed rarefied gas flow in a channel with uniform injection/suction through its permeable walls

Abstract The pressure and temperature driven fully-developed rarefied gas flow between two parallel permeable plates, with uniform gas injection and suction from the bottom and top plates respectively, is investigated, based on the linearized Shakhov (S) model and the linearized Boltzmann equation (BE). Both flow configurations are characterized by the gas rarefaction parameter and the injection/suction velocity magnitude. Computational results for the so-called kinetic coefficients, as well as for the macroscopic quantities are provided in a wide range of the two parameters. The Onsager-Casimir reciprocity relation between the mechanocaloric and thermal creep coefficients has been proven to hold for arbitrary values of the injection velocity and has been used to validate the accuracy of the obtained results. It is shown that, the kinetic coefficients and macroscopic quantities are significantly affected as the injection velocity is increased. In addition, the kinetic results properly recover the corresponding analytical solutions in the free molecular and slip regimes. The examined prototype rarefied injection/suction flows may be useful to the investigation of more complex and realistic flow configurations in channels of various cross-sections with permeable walls where the injection velocity is not constant in the whole flow domain.