Comparison of Kinetic Theory Analyses of Linearized Couette Flow

Abstract

Linearized Couette flow is considered for Knudsen numbers ranging from zero to unity using Krook's kinetic model. The velocity and stress are calculated from the numerical solution of an integral equation for the velocity. By comparison with independent calculations the relative error of these results is estimated as less than 0.2%. For the particular case of slip flow, the constant in the boundary condition is evaluated from a numerical quadrature. The accuracy of several analytic methods is compared with particular emphasis on the method of Gross, Jackson, and Ziering and that of Lees. Using previous results obtained for Knudsen numbers greater than unity it is confirmed that some form of iteration, based on an integral equation formulation, is needed to give accurate results in the nearly free molecular regime. Further, such an iteration significantly increases the accuracy of the results over the entire transition regime down to Knudsen numbers as low as one third.