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

Published online by Cambridge University Press:  28 January 2013

S. Kokou Dadzie
S. Kokou Dadzie*
Affiliation:
Department of Engineering and Applied Physics, Glyndŵr University, Mold Road, Wrexham LL11 2AW, UK
*
†Email address for correspondence: k.dadzie@glyndwr.ac.uk
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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. A close comparison with the conventional Burnett hydrodynamic set of equations is made and the linear stabilities around an equilibrium point under small perturbations are presented.

JFM classification

Rarefied Gas Flow: Kinetic theory Micro-/Nano-fluid dynamics: Non-continuum effects Rarefied Gas Flow: Rarefied Gas Flow
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 716 , 10 February 2013 , R6
Copyright
©2013 Cambridge University Press

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