Analytical solution of a gas sliding problem using a new kinetic equation

A new kinetic equation leading to a correct (true) value of the Prandtl number (Pr) is derived. Based on this equation, an analytical solution to the gas sliding problem is obtained and the isothermal and thermal sliding velocities are calculated, the corresponding formulas being derived in an explicit form. The results of numerical calculations indicate that the proposed model is compatible with the existing theories: the results obtained for the thermal sliding fall between data calculated within the framework of the Bhatnagar-Gross- Kruck (BGK) model with constant collisional frequency and the BGK model with constant mean free path. The new model can be referred to as a model with an intermediate character of the collisional frequency as the function of the velocity of molecules. An important advantage of the proposed model is the presence of a parameter that may correspond to the true Prandtl number. The values of the sliding coefficients K-sl and K-Tsl in this kinetic model possess essentially a new qualitative status. Indeed, the "old" quantities were obtained using a model with incorrect Prandtl number and had to be recalculated for the correct Pr value, this procedure introducing an element of uncertainty. The results obtained using the proposed model, involving the correct Pr value, are free of this dis advantage. (C) 2000 MAIK ''Nauka/Interperiodica".