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

Kokou Dadzie

Research output: Contribution to journalArticle

17 Citations (Scopus)
252 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)6-11
JournalJournal of Fluid Mechanics
Volume716
Early online date28 Jan 2013
DOIs
Publication statusPublished - Feb 2013

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continuum flow
flow equations
Hydrodynamics
hydrodynamics
expansion
Thermodynamics
Kinetic theory of gases
thermodynamics
kinetic theory
series expansion
gases
kinetic equations
continuums
perturbation
Kinetics
Gases

Keywords

  • kinetic theory
  • non-continuum effects
  • rarefied gas flows

Cite this

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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. 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.",
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language = "English",
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A thermo-mechanically consistent Burnett regime continuum flow equation without Chapman-Enskog expansion. / Dadzie, Kokou.

In: Journal of Fluid Mechanics, Vol. 716, 02.2013, p. 6-11.

Research output: Contribution to journalArticle

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AU - Dadzie, Kokou

PY - 2013/2

Y1 - 2013/2

N2 - 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.

AB - 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.

KW - kinetic theory

KW - non-continuum effects

KW - rarefied gas flows

U2 - 10.1017/jfm.2012.546

DO - 10.1017/jfm.2012.546

M3 - Article

VL - 716

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SN - 0022-1120

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