Macroscopic Conduction Models by Volume Averaging for Two-Phase Systems

Abstract

The aim here is to describe macroscopic models of conductive heat transfer within systems comprising two solid phases, using the method of volume averaging. The presentation of this technique largely stems from work by Carbonell, Quintard, and Whitaker [1–3]. The macroscopic conservation equations are set up under the assumption of local thermal equilibrium, leading to a model governed by a single equation. The effective thermal conductivity of the equivalent medium is obtained by solving the associated closure problems. The case where thermal equilibrium does not pertain, leading to a model with two energy conservation equations, is discussed briefly.