An extension to the Navier-Stokes-Fourier equations by considering molecular collisions with boundaries

E.J. Arlemark, S.K. Dadzie, J.M. Reese

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

1 Citation (Scopus)

Abstract

In this paper we propose a model for micro gas flows consisting of the Navier-Stokes-Fourier equations (NSF) extended by a description of molecular collisions with solid boundaries and discontinuous velocity slip and temperature jump boundary conditions. By considering the molecular collisions with the solid boundaries in gas flows we capture some of the near wall effects that the conventional NSF with linear stress/strain-rate and heat-flux/ temperature-gradient relationships seem to be unable to describe. The model that we propose incorporates the molecular collisions with solid boundaries as an extension to the conventional definition of the average travelling distance of molecules before experiencing intermolecular collisions (the mean free path). By considering both of these types of collisions we obtain an effective mean free path expression, which varies with distance to surfaces. The effective mean free path is proposed to be used to obtain new definitions of effective viscosity and effective thermal conductivity, which will extend the applicability of NSF equations to higher Knudsen numbers.
We show results of simple flow cases that are solved using this extended NSF model and discuss limitations to the model due to various assumptions. We also mention interesting ideas for further development of the model based on a more detailed gas description.
LanguageEnglish
Title of host publicationProceedings of the 6th International Conference on Nanochannels, Microchannels, and Minichannels
Pages95-102
Number of pages7
Publication statusPublished - 23 Jul 2008

Fingerprint

Navier-Stokes
Collision
Gas Flow
Path
Flow of gases
Effective Conductivity
Knudsen number
Strain Rate
Thermal Conductivity
Heat Flux
Model
Slip
Thermal gradients
Heat flux
Strain rate
Thermal conductivity
Viscosity
Jump
Molecules
Boundary conditions

Keywords

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

Cite this

Arlemark, E. J., Dadzie, S. K., & Reese, J. M. (2008). An extension to the Navier-Stokes-Fourier equations by considering molecular collisions with boundaries. In Proceedings of the 6th International Conference on Nanochannels, Microchannels, and Minichannels (pp. 95-102)
Arlemark, E.J. ; Dadzie, S.K. ; Reese, J.M. / An extension to the Navier-Stokes-Fourier equations by considering molecular collisions with boundaries. Proceedings of the 6th International Conference on Nanochannels, Microchannels, and Minichannels. 2008. pp. 95-102
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Arlemark, EJ, Dadzie, SK & Reese, JM 2008, An extension to the Navier-Stokes-Fourier equations by considering molecular collisions with boundaries. in Proceedings of the 6th International Conference on Nanochannels, Microchannels, and Minichannels. pp. 95-102.

An extension to the Navier-Stokes-Fourier equations by considering molecular collisions with boundaries. / Arlemark, E.J.; Dadzie, S.K.; Reese, J.M.

Proceedings of the 6th International Conference on Nanochannels, Microchannels, and Minichannels. 2008. p. 95-102.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

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N2 - In this paper we propose a model for micro gas flows consisting of the Navier-Stokes-Fourier equations (NSF) extended by a description of molecular collisions with solid boundaries and discontinuous velocity slip and temperature jump boundary conditions. By considering the molecular collisions with the solid boundaries in gas flows we capture some of the near wall effects that the conventional NSF with linear stress/strain-rate and heat-flux/ temperature-gradient relationships seem to be unable to describe. The model that we propose incorporates the molecular collisions with solid boundaries as an extension to the conventional definition of the average travelling distance of molecules before experiencing intermolecular collisions (the mean free path). By considering both of these types of collisions we obtain an effective mean free path expression, which varies with distance to surfaces. The effective mean free path is proposed to be used to obtain new definitions of effective viscosity and effective thermal conductivity, which will extend the applicability of NSF equations to higher Knudsen numbers.We show results of simple flow cases that are solved using this extended NSF model and discuss limitations to the model due to various assumptions. We also mention interesting ideas for further development of the model based on a more detailed gas description.

AB - In this paper we propose a model for micro gas flows consisting of the Navier-Stokes-Fourier equations (NSF) extended by a description of molecular collisions with solid boundaries and discontinuous velocity slip and temperature jump boundary conditions. By considering the molecular collisions with the solid boundaries in gas flows we capture some of the near wall effects that the conventional NSF with linear stress/strain-rate and heat-flux/ temperature-gradient relationships seem to be unable to describe. The model that we propose incorporates the molecular collisions with solid boundaries as an extension to the conventional definition of the average travelling distance of molecules before experiencing intermolecular collisions (the mean free path). By considering both of these types of collisions we obtain an effective mean free path expression, which varies with distance to surfaces. The effective mean free path is proposed to be used to obtain new definitions of effective viscosity and effective thermal conductivity, which will extend the applicability of NSF equations to higher Knudsen numbers.We show results of simple flow cases that are solved using this extended NSF model and discuss limitations to the model due to various assumptions. We also mention interesting ideas for further development of the model based on a more detailed gas description.

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Arlemark EJ, Dadzie SK, Reese JM. An extension to the Navier-Stokes-Fourier equations by considering molecular collisions with boundaries. In Proceedings of the 6th International Conference on Nanochannels, Microchannels, and Minichannels. 2008. p. 95-102