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Abstract
In this paper we propose a model for micro gas flows consisting of the NavierStokesFourier 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/strainrate and heatflux/ temperaturegradient 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.
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.
Original language  English 

Title of host publication  Proceedings of the 6th International Conference on Nanochannels, Microchannels, and Minichannels 
Pages  95102 
Number of pages  7 
Publication status  Published  23 Jul 2008 
Keywords
 micro gas flows
 navier stokes equations
 mean free path
 non linear constitutive relationships
 velocity slip
 knudsen layer
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Projects
 1 Finished

BEYOND NAVIERSTOKES: MEETING THE CHALLENGE OF NONEQUILIBRIUM GAS DYNAMICS
Reese, J. & McInnes, C.
EPSRC (Engineering and Physical Sciences Research Council)
1/10/05 → 31/01/10
Project: Research