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

Dadzie, Kokou (2013) A thermo-mechanically consistent Burnett regime continuum flow equation without Chapman-Enskog expansion. Journal of Fluid Mechanics, 716. pp. 6-11. ISSN 0022-1120

[img] PDF
Dadzie_SK_Pure_A_thermo_mechanically_consistent_Burnett_regime_continuum_flow...Chapman_Enskog_expansion_Feb_2013.pdf
Preprint

Download (179kB)
    [img] PDF
    Dadzie_SK_JFM_Rapids_Feb_2013.pdf
    Final Published Version

    Download (560kB)

      Abstract

      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.