A High Order Modification on the Analytic Solution of 2-D Microchannel Gaseous Flows

Abstract

A new analytic solution of the Navier-Stokes equations for two-dimensional microchannel flows is presented. The solution is based on the concept of the continuum approach using the Chapman-Enskog method, but built upon the proposal to introduce a hyperbolic tangent function of Kn number in the power series of the distribution function and slip boundary condition. The solution of the Navier-Stokes equations is extended successfully to the transition flow regime. The analytic solutions are compared with results of the DSMC in both slip flow and transition flow regimes. Satisfactory agreements on the velocity profiles and pressure distributions have been achieved.