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TECHNICAL BRIEFS

A Closure Model for Transient Heat Conduction in Porous Media

[+] Author and Article Information
C. T. Hsu

Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

J. Heat Transfer 121(3), 733-739 (Aug 01, 1999) (7 pages) doi:10.1115/1.2826043 History: Received March 31, 1997; Revised March 25, 1999; Online December 05, 2007

Abstract

Equations governing the transient heat conduction in porous materials consisting of solids and fluids of different thermal properties were derived with a volumetric average scheme under the assumption of nonthermal equilibrium. The derivation leads to a macroscopic two-equation system which requires the closure modeling of new unknown terms due to interfacial transport, namely, the tortuosity term and the interfacial heat transfer term. Closure relations were obtained from the microscopic equations for temperature fluctuation under quasi-steady assumption. The closure coefficients appeared in the closure relations then depend on the media geometry as well as thermal properties. To demonstrate these dependencies, the closure coefficient for the thermal tortuosity is evaluated based on the effective stagnant thermal conductivity model proposed by Hsu et al. (1995) for periodically packed cubes, and the coefficient for interfacial heat transfer based on a quasi-steady heat conduction of dispersed spheres immersed in fluids. The salient features as well as the applicability and limitation of the newly proposed transient heat conduction model were discussed.

Copyright © 1999 by The American Society of Mechanical Engineers
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