Heat conduction in multiphase systems—I: Theory and experiment for two-phase systems

The method of volume averaging is applied to the process of transient heat conduction in two- and three-phase systems, and a closure scheme is developed that allows for direct determination of the thermal conductivity tensor. Previous experimental studies have been extended to cover a wide range of parameters and for two-phase systems values of the effective thermal conductivity have been measured for conductivity ratios as high as κ = kσ/kβ = 8000. Here kσ is the conductivity of the discontinuous phase and kβ is the conductivity of the continuous phase. For large values of κ a combined numerical and perturbation method was used to predict the effective thermal conductivity. Good agreement between theory and experiment is obtained; however, the particle-particle contact was treated in an empirical manner.