A thermo-mechanically consistent Burnett regime continuum flow equation without Chapman-Enskog expansion

Chapman-Enskog expansion is the orthodox approach to derive continuum flow models from Boltzmann’s kinetic equation for dilute gases. Beyond the Navier-Stokes-Fourier order, these models known as Burnett hydrodynamic-regime equations violate a number of fundamental mechanical and thermodynamic principles in their original forms. This has generated a widely investigated problem in the kinetic theory of gases. In this short article, we derive a Burnett hydrodynamic-regime continuum model that is systematically consistent with all known mechanical and thermodynamic principles without using any series’ expansion. Close comparison with the conventional Burnett hydrodynamic set of equations is considered and their linear stabilities around an equilibrium point under small perturbations are presented.