The prediction of the thermal conductivity of two and three phase solid heterogeneous mixtures

Abstract

A theoretical technique to predict the thermal conductivity of heterogeneous solid mixtures has been developed. Tsao's model for predicting the thermal conductivity of two phase solid mixtures has been modified and extended. The technique of this paper does not require experimental data on the mean and standard deviations of the one dimensional porosity function describing the distribution of the discontinuous phase as is the case with Tsao's model. A parabolic distribution of the discontinuous phase is assumed and the constants of the parabolic distribution are determined by analysis and presented as a function of the discontinuous phase volume fraction. Thus, the need for values of the mean and standard deviations is circumvented. The equivalent thermal conductivity of a unit cube of the mixture is derived in terms of the distribution function, and the thermal conductivity of the constituents. The technique is shown to predict thermal conductivity values within 8 per cent of available experimental data.