Microscopic Modeling of the Two-Temperature Model for Conduction in Heterogeneous Media

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.