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Application of a High-Order Macroscopic Approach to Force-Driven Poiseuille Flow in the Slip and Transition Regimes

[+] Author Affiliations
Simon Mizzi, Xiao-Jun Gu, David R. Emerson

STFC Daresbury Laboratory, Warrington, England, UK

Robert W. Barber

SFTC Daresbury Laboratory, Warrington, England, UK

Jason M. Reese

University of Strathclyde, Glasgow, Scotland, UK

Paper No. MNHT2008-52203, pp. 1341-1350; 10 pages
doi:10.1115/MNHT2008-52203
From:
  • ASME 2008 First International Conference on Micro/Nanoscale Heat Transfer
  • ASME 2008 First International Conference on Micro/Nanoscale Heat Transfer, Parts A and B
  • Tainan, Taiwan, June 6–9, 2008
  • Conference Sponsors: Nanotechnology Institute
  • ISBN: 0-7918-4292-4 | eISBN: 0-7918-3813-7
  • Copyright © 2008 by ASME

abstract

In this paper various extended macroscopic models are described and applied to force-driven Poiseuille flow. In particular, details are given for the regularized Grad 13- and 20-moment equations. Extended macroscopic models have, until recently, been limited by the uncertainity surrounding the prescription of boundary conditions on solid-walls. The gas-solid wall interaction plays an important role in describing the dynamics of confined gaseous flows. This problem is tackled in the context of the moment equations whereby the simplified Maxwell microscopic formalism is used to derive boundary conditions for a given moment equation set. The proposed governing equations and boundary conditions are applied to force-driven Poiseuille flow where anomalous thermal behavior is observed as the Knudsen number increases. Results are compared to DSMC data and it is established that the proposed extended macroscopic models can capture this non-intuitive behavior. However, the models show some quantitative disparity in representing this behavior. It is proposed that this is addressed by development of a consistent theory of molecular collision geometries in the extended hydro-dynamic model or by the utilization of more extended moment sets.

Copyright © 2008 by ASME

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