Nonlinear Knudsen boundary layer on an infinitely thin permeable membrane

The state of a gas in the neighborhood of an infinitely thin permeable membrane whose sides have different temperatures is investigated. The dimensions of orifices in the membrane are much less than the mean molecular free path. The gas temperatures and pressures on both sides of the membrane outside the nonlinear Knudsen layers adjacent to the membrane and variations in these parameters in the Knudsen layers are determined. The investigation is carried out by solving the Boltzmann kinetic equation by means of the direct simulation Monte-Carlo method. The semiempirical Maxwell method is also used for consideration of the molecular flows on both sides of the membrane when analyzing the temperatures and the pressures. The solution to the nonlinear problem is compared with the solution to the linear problem of a jump temperature near a nonisothermal porous body obtained earlier.