Variational methods, bounds and size effects for two-phase composites with coupled heat and mass transport processes at the two-phase interface

Abstract

New variational principles are developed for the effective heat conductivity tensor of anisotropic two-phase composites in the presence of coupled mass and heat transport processes at the two-phase interface. We focus on physical situations where an imposed temperature gradient causes impurities or lattice defects to concentrate on the two-phase interface and diffuse along it. This is accompanied by the release and absorption of heat as the impurities, respectively, enter or leave the interface. We investigate the effect of the inclusion geometry on the overall thermal conductivity. For randomly distributed inclusions new size effects are given in terms of the inclusion size distribution and nearest neighbor distribution function for the included phase.