A non-isothermal Couette slip gas flow

Abstract

A steady plane subsonic compressible non-isothermal Couette gas flow is analyzed for moderately high and low Reynolds numbers. The flow channel is formed by two plates in relative motion. Two cases are considered: (a) isothermal walls where the temperatures of the plates are equal and constant and (b) with constant but different plate temperatures. The Knudsen number is Kn a (c) 1/2 0.1, which corresponds to the slip and continuum flow. The flow is defined by continuity, Navier-Stokes and energy continuum equations, along with the velocity slip and the temperature jump first order boundary conditions. An analytical solution for velocity and temperature is obtained by developing a perturbation scheme. The first approximation corresponds to the continuum flow conditions, while the others represent the contribution of the rarefaction effect. In addition, a numerical solution of the problems is given to confirm the accuracy of the analytical results. The exact analytical solution, for constant viscosity and conductivity is found for the isothermal walls case as well. It is shown that it is entirely a substitution to the exact numerical solution for the isothermal walls case.