Solution of the linearized couette-flow problem in a rarefied gas by the integral-diffusion method

In ordinary diffusion theory the transfer of properties is determined by the local gradients of the corresponding fields. As the mean free path increases, the flux density becomes an integral quantity and is determined by a neighborhood of the point under consideration of the order of a few mean free paths. In a previous article [1], the author proposed a model for a one-dimensional transfer process in linear rarefield-gas problems based on the analogy with radiative transfer. The same approach, though without directional averaging, is used in the present paper to analyze the linearized Couette flow problem. The solution obtained here has the properties of the solution obtained by more exact methods based on the solution of the Boltzmann equation [3-4].Nomenclature p_xy shear stress - c mean thermal velocity of molecules - 2/3 A mean free path - d half-width of channel - ±w₀ plate velocity - c nonequilibriumvalue of momentum flux density - y transverse coordinate - ratio of specific heats - W dimensionless velocity - P_xy shear stress scaled with respect to the shear stress in free-molecule flow - Y dimensionless coordinate - W₁(y) velocity distribution according to Millikan's solution - coefficient of viscosity - R Reynolds number - K Knudsen number