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.

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.