Replacement relations for thermal conductivities of heterogeneous materials having different matrices

We derive explicit closed form relation between thermal (or electrical) conductivities of two matrix composite materials having the same microstructure and inhomogeneities, but different matrices. The relation is verified numerically and by comparison with experimental data available in literature. We also discuss a possible application of this replacement relation which allows one to evaluate conductive properties of particles in a matrix composite - the problem of crucial importance in geophysics, mechanics of nanocomposites, biomechanics, etc.