Microscopic modeling of the two-temperature model for conduction in heterogeneous media

Reference:

Rees, D. A. S., 2010. Microscopic modeling of the two-temperature model for conduction in heterogeneous media. Journal of Porous Media, 13 (2), pp. 125-143.

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Official URL:

http://dx.doi.org/10.1615/JPorMedia.v13.i2.40

Abstract

We consider conduction in a two-phase composite solid or, equivalently, a stagnant porous medium saturated with a single fluid. In particular, we derive and calculate values for the interphase heat transfer coefficient, h, which multiplies the source/sink terms in the two-energy model for conduction in a porous medium. On allowing a uniform heat generation to take place within one of the phases, it is possible to determine h from the difference in the average temperatures of the two phases after the decay of transients. An exact analytical expression is obtained for periodic striped media, which suggests that a new nondimensional parameter might usefully be defined. Exact numerical solutions are obtained for randomly striped media. Precise expressions are also found for the two-dimensional checkerboard pattern and its three-dimensional analogue. We also consider other types of two-dimensional periodic media, and finally, randomly constituted media are analyzed. © 2010 Begell House, Inc.

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