Effective thermal conductivity of real two-phase systems using resistor model with ellipsoidal inclusions

Abstract

A theoretical model has been developed for real two-phase system assuming linear flow of heat flux lines having ellipsoidal particles arranged in a three-dimensional cubic array. The arrangement has been divided into unit cells, each of which contains an ellipsoid. The resistor model has been applied to determine the effective thermal conductivity (ETC) of the unit cell. To take account of random packing of the phases, non-uniform shape of the particles and non-linear flow of heat flux lines in real systems, incorporating an empirical correction factor in place of physical porosity modifies an expression for ETC. An effort is made to correlate it in terms of the ratio of thermal conductivities of the constituents and the physical porosity. Theoretical expression so obtained has been tested on a large number of samples cited in the literature and found that the values predicted are quite close to the experimental results. Comparison of our model with different models cited in the literature has also been made.