We propose a power-law based effective mean free path (MFP) model so that the Navier-Stokes-Fourier equations can be employed for the transition-regime flows typical of gas micro/nanodevices. The effective MFP model is derived for a system with planar wall confinement by taking into account the boundary limiting effects on the molecular free paths. Our model is validated against molecular dynamics simulation data and compared with other theoretical models. As gas transport properties can be related to the mean free path through kinetic theory, the Navier-Stokes-Fourier constitutive relations are then modified in order to better capture the flow behavior in the Knudsen layers close to surfaces. Our model is applied to fully developed isothermal pressure-driven (Poiseuille) and thermal creep gas flows in microchannels. The results show that our approach greatly improves the near-wall accuracy of the Navier-Stokes-Fourier equations, well beyond the slip-flow regime.
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e-mail: jason.reese@strath.ac.uk
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July 2011
Research Papers
Modeling of Knudsen Layer Effects in Micro/Nanoscale Gas Flows
Jason M Reese
Jason M Reese
Department of Mechanical Engineering,
e-mail: jason.reese@strath.ac.uk
University of Strathclyde
, Glasgow G1 1XJ, United Kingdom
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Jason M Reese
Department of Mechanical Engineering,
University of Strathclyde
, Glasgow G1 1XJ, United Kingdom
e-mail: jason.reese@strath.ac.uk
J. Fluids Eng. Jul 2011, 133(7): 071101 (10 pages)
Published Online: July 5, 2011
Article history
Received:
December 16, 2010
Accepted:
June 3, 2011
Online:
July 5, 2011
Published:
July 5, 2011
Citation
Dongari, N., Zhang, Y., and Reese, J. M. (July 5, 2011). "Modeling of Knudsen Layer Effects in Micro/Nanoscale Gas Flows." ASME. J. Fluids Eng. July 2011; 133(7): 071101. https://doi.org/10.1115/1.4004364
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