A Simple, Versatile Conduction Shape Factor for Heterogenous Materials

Heat flow in heterogeneous materials is of interest to engineers and scientists in a range of applications. In this paper a simplified conduction shape factor which may be used for a range of particle geometries is proposed. The shape factor may be employed using a modification of Maxwell’s effective conductivity model. Numerical simulations were performed for ellipses and ellipsoids that demonstrated that the shape factor is effective for both individual and multiple ellipses or ellipsoids up to volume fractions of 0.32, with differences between the simulated and predicted effective thermal conductivities being of the order of 1 %.