Thermal conductmty of disordered heterogeneous media from the microstructure

It is generally desired to predict the effective conductivity of porous and other composite media from the phase conductivities and the details of the microstructure; one can then relate changes in the microstructure to changes in the effective property. The purpose of this article is to review the rigorous approaches that have been employed to attack this problem, with an emphasis on significant developments in the last five years. In particular, we discuss approximation methods, series-expansion techniques, rigorous bounding methods, and, to a lesser extent, percolation theory and renormalization-group theory. Recent advances in the Statistical characterization of the microstructure of the heterogeneous medium is described. Progress in the calculation of expressions for the effective conductivity that depend upon such microstructural Information is reviewed. It is shown that such approaches can lead to accurate estimates of the effective conductivity for a wide range of phase conductivities and volume fractions. The predicted values of the effective property, for certain models described here, are compared to available experimental data.