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A continuum model of gas flows with localized density variations

Author

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  • Dadzie, S. Kokou
  • Reese, Jason M.
  • McInnes, Colin R.

Abstract

We discuss the kinetic representation of gases and the derivation of macroscopic equations governing the thermomechanical behavior of a dilute gas viewed at the macroscopic level as a continuous medium. We introduce an approach to kinetic theory where spatial distributions of the molecules are incorporated through a mean-free-volume argument. The new kinetic equation derived contains an extra term involving the evolution of this volume, which we attribute to changes in the thermodynamic properties of the medium. Our kinetic equation leads to a macroscopic set of continuum equations in which the gradients of thermodynamic properties, in particular density gradients, impact on diffusive fluxes. New transport terms bearing both convective and diffusive natures arise and are interpreted as purely macroscopic expansion or compression. Our new model is useful for describing gas flows that display non-local-thermodynamic-equilibrium (rarefied gas flows), flows with relatively large variations of macroscopic properties, and/or highly compressible fluid flows.

Suggested Citation

  • Dadzie, S. Kokou & Reese, Jason M. & McInnes, Colin R., 2008. "A continuum model of gas flows with localized density variations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6079-6094.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:24:p:6079-6094
    DOI: 10.1016/j.physa.2008.07.009
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    References listed on IDEAS

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    1. Brenner, Howard, 2005. "Navier–Stokes revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(1), pages 60-132.
    2. Cohen, E.G.D., 1983. "Kinetic theory of non-equilibrium fluids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 118(1), pages 17-42.
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    Cited by:

    1. Svärd, Magnus, 2018. "A new Eulerian model for viscous and heat conducting compressible flows," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 350-375.

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