The recently developed thermodynamically constrained averaging theory is briefly summarized as a tool for the building of rigorous macroscale models of transport phenomena in complex systems. The specific case of thermal transport in a single-fluid-phase porous medium system is considered. Key results from the application of this theory are used to develop a simplified entropy inequality, which is in turn used to guide the development of closure relations. The decomposition of exchange terms is considered, and closed models for internal energy are derived for the case of nonequilibrium and local thermal equilibrium conditions. Since all variables are expressed in terms of precisely defined averages of microscale quantities, the resultant models can be compared with highly resolved microscale simulations to determine the range of validity of the upscaled models.
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e-mail: graywg@unc.edu
e-mail: casey_miller@unc.edu
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Thermodynamically Constrained Averaging Theory Approach for Heat Transport in Single-Fluid-Phase Porous Medium Systems
William G. Gray,
William G. Gray
Department of Environmental Sciences and Engineering,
e-mail: graywg@unc.edu
University of North Carolina
, Chapel Hill, NC 27599-7431
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Cass T. Miller
Cass T. Miller
Department of Environmental Sciences and Engineering,
e-mail: casey_miller@unc.edu
University of North Carolina
, Chapel Hill, NC 27599-7431
Search for other works by this author on:
William G. Gray
Department of Environmental Sciences and Engineering,
University of North Carolina
, Chapel Hill, NC 27599-7431e-mail: graywg@unc.edu
Cass T. Miller
Department of Environmental Sciences and Engineering,
University of North Carolina
, Chapel Hill, NC 27599-7431e-mail: casey_miller@unc.edu
J. Heat Transfer. Oct 2009, 131(10): 101002 (14 pages)
Published Online: July 28, 2009
Article history
Received:
September 9, 2008
Revised:
November 3, 2008
Published:
July 28, 2009
Citation
Gray, W. G., and Miller, C. T. (July 28, 2009). "Thermodynamically Constrained Averaging Theory Approach for Heat Transport in Single-Fluid-Phase Porous Medium Systems." ASME. J. Heat Transfer. October 2009; 131(10): 101002. https://doi.org/10.1115/1.3160539
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