An extension to the Navier-Stokes equations to incorporate gas molecular collisions with boundaries

Erik J. Arlemark, S. Kokou Dadzie, Jason M. Reese

Research output: Contribution to journalArticle

31 Citations (Scopus)

Abstract

We investigate a model for micro-gas-flows consisting of the Navier-Stokes equations extended to include a description of molecular collisions with solid boundaries, together with first and second order velocity slip boundary conditions. By considering molecular collisions affected by boundaries in gas flows we capture some of the near-wall affects that the conventional Navier-Stokes equations with a linear stress/strain-rate relationship are unable to describe. Our model is expressed through a geometry-dependent mean-free-path yielding a new viscosity expression, which makes the stress/strain-rate constitutive relationship non-linear. Test cases consisting of Couette and Poiseuille flows are solved using these extended Navier-Stokes equations, and we compare the resulting velocity profiles with conventional Navier-Stokes solutions and those from the BGK kinetic model. The Poiseuille mass flow-rate results are compared with results from the BGK-model and experimental data, for various degrees of rarefaction. We assess the range of applicability of our model and show that it can extend the applicability of conventional fluid dynamic techniques into the early continuum-transition regime. We also discuss the limitations of our model due to its various physical assumptions, and we outline ideas for further development.
LanguageEnglish
Pages041006-1-041006-8
Number of pages8
JournalJournal of Heat Transfer
Volume132
Issue number4
DOIs
Publication statusPublished - 1 Apr 2010

Fingerprint

molecular collisions
Navier-Stokes equation
Navier Stokes equations
Gases
gases
strain rate
gas flow
Flow of gases
BGK model
Strain rate
rarefaction
Couette flow
mass flow rate
fluid dynamics
laminar flow
mean free path
Fluid dynamics
slip
velocity distribution
viscosity

Keywords

  • micro gas flows
  • navier stokes equations
  • mean free path
  • non linear constitutive relationships
  • velocity slip
  • knudsen layer

Cite this

Arlemark, Erik J. ; Dadzie, S. Kokou ; Reese, Jason M. / An extension to the Navier-Stokes equations to incorporate gas molecular collisions with boundaries. In: Journal of Heat Transfer. 2010 ; Vol. 132, No. 4. pp. 041006-1-041006-8.
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An extension to the Navier-Stokes equations to incorporate gas molecular collisions with boundaries. / Arlemark, Erik J.; Dadzie, S. Kokou; Reese, Jason M.

In: Journal of Heat Transfer, Vol. 132, No. 4, 01.04.2010, p. 041006-1-041006-8.

Research output: Contribution to journalArticle

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