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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ASME 2008 6th International Conference on Nanochannels, Microchannels, and Minichannels
June 23–25, 2008
Darmstadt, Germany
Conference Sponsors:
- Nanotechnology Institute
ISBN:
0-7918-4834-5
PROCEEDINGS PAPER
An Extension to the Navier-Stokes-Fourier Equations by Considering Molecular Collisions With Boundaries
Erik J. Arlemark,
Erik J. Arlemark
University of Strathclyde, Glasgow, UK
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S. Kokou Dadzie,
S. Kokou Dadzie
University of Strathclyde, Glasgow, UK
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Jason M. Reese
Jason M. Reese
University of Strathclyde, Glasgow, UK
Search for other works by this author on:
Erik J. Arlemark
University of Strathclyde, Glasgow, UK
S. Kokou Dadzie
University of Strathclyde, Glasgow, UK
Jason M. Reese
University of Strathclyde, Glasgow, UK
Paper No:
ICNMM2008-62222, pp. 95-102; 8 pages
Published Online:
June 11, 2009
Citation
Arlemark, EJ, Dadzie, SK, & Reese, JM. "An Extension to the Navier-Stokes-Fourier Equations by Considering Molecular Collisions With Boundaries." Proceedings of the ASME 2008 6th International Conference on Nanochannels, Microchannels, and Minichannels. ASME 2008 6th International Conference on Nanochannels, Microchannels, and Minichannels. Darmstadt, Germany. June 23–25, 2008. pp. 95-102. ASME. https://doi.org/10.1115/ICNMM2008-62222
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