Analytical solution of plane Poiseuille flow within Burnett hydrodynamics

Abstract

In the current paper, low-speed isothermal microscale gas flows have been investigated utilizing the augmented Burnett equations. There has been limited success to analytically solve the Burnett equations till date. We propose an analytical solution to Burnett equations, which is shown to satisfy the full set of augmented Burnett equations up to Kn of 2.2 with an error of 1 %. Detailed validation shows that the solution represents the integral flow parameters accurately up to Kn ~ 2.2 and local field properties up to Kn ~ 0.5. The range over which the proposed Burnett analytical solution is applicable is substantially better than existing analytical solutions, without incorporating any wall scaling functions into constitutive relations and variation of slip coefficients in the boundary conditions. Normalized mass flow rate, friction factor, and axial velocity profile results show very good agreement with the experimental and simulation data. The analytical solution is also able to predict the change in the curvature of streamwise pressure profile.