Heat conduction and a porosity correction term for spherical and cubic particles in a simple cubic packing

Abstract

In this paper, to predict the effective thermal conductivity of two-phase systems from the value of the thermal conductivities of the constituent phases and the corresponding volume fractions, a theoretical model is developed by assuming the particles to be rigid and spherical in shape, having regular three-dimensional simple cubic geometry. In the literature there is a model in which particles are assumed to be rigid and cubic in shape and of the same geometry. A comparative study is made and it is observed that both models based upon rigid geometry produce deviations from experimental results. A modification is made to both the theoretical models by incorporating a single porosity correction term. The modified models are applied to a large number of samples having great differences in the thermal conductivities of the constituent phases. Comparisons of these models with different two-phase models have also been made in the literature. It is observed that there is close agreement between results from measured and modified models. Furthermore, the values predicted by the modified models show that, on the lower side of the volume fraction of the more highly conducting phase , the spherical particle model is better than the cubic particle model; on the other hand, for higher the cubic particle model predicts very well irrespective of the type of sample.