Analytical solution of the Burnett equations for gaseous flow in a long microchannel

摘要

This paper presents an analytical solution of the Burnett equations for gaseous flow in a long microchannel. A non-dimensional analysis is first undertaken to reduce the governing equations into somewhat simplified differential equations, which are solved to obtain the pressure and velocity fields. The exact solution for pressure has been obtained by solving the cross-stream momentum equation, while the solution for velocity is obtained from the streamwise momentum equation. The required boundary conditions are obtained from the direct simulation Monte Carlo (DSMC) method. The obtained analytical solution is compared with the available DSMC and perturbation based solutions, and found to agree well. The work is particularly significant because analytical solutions of the Burnett equations are currently known in only a very few cases. The present analytical solution opens the possibility for further analysis by employing the expressions for pressure and velocity provided here.