A perturbation-based solution of Burnett equations for gaseous flow in a long microchannel

Abstract

In this paper, an analytical investigation of two-dimensional conventional Burnett equations has been undertaken for gaseous flow through a long microchannel. The analytical solution is obtained by using perturbation analysis around the classical Navier–Stokes solution with appropriate boundary conditions. The perturbation expansion is employed with the smallness parameter $\unicode[STIX]{x1D716}$, taken as the ratio of height to length of the microchannel. The solution for pressure is obtained by solving the cross-stream momentum equation while the velocity distribution is obtained from the streamwise momentum equation. The resulting ordinary differential equations in pressure and velocity are third-order and second-order, respectively. The required boundary conditions for pressure are obtained from direct simulation Monte Carlo (DSMC) data. The obtained analytical solution matches the available DSMC solution well. This is perhaps the first analytical solution of the Burnett equations using the perturbation approach.