Correlation functions for predicting properties of heterogeneous materials. IV. Effective thermal conductivity of two-phase solids

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Abstract
The Beran bounds on the effective thermal conductivity of a statistically homogeneous and isotropic heterogeneous material require a knowledge of several three‐point correlation functions. These bounds are evaluated here for two‐phase materials, using the correlation functions developed in Paper II of this series. The resultant bounds are compared with experimental data on the effective thermal conductivity of air‐saturated porous sandstone (phase thermal conductivity ratio of 80 : 1) and air‐saturated firebrick (ratio of 60 : 1), and with the less restrictive Hashin‐Shtrikman bounds which do not require any knowledge of correlation functions. It is shown that the Beran bounds are a significant improvement over the Hashin‐Shtrikman bounds, with the greatest improvement occurring for low‐phase thermal conductivity ratios.