A study of unidirectional versus tridirectional heat flux models and the effect of particle size on heat conduction in composite solids

The effect of the assumption of unidirectional heat flux was determined for a well‐known unit cell model used to predict effective thermal conductivities of particulate composites. Predictions obtained for the condition of unidirectional heat flux were compared with those obtained for the more rigorous case of tridirectional heat flux. The latter case required a digital simulation of the model to obtain three‐dimensional temperature distributions. Comparisons were made for two different values of pure component thermal conductivity ratio and for a broad range of phase compositions. Results in each case suggest that the unidirectional heat flux assumption is not a serious limitation. Experimental studies were made of the effects of composition, particle size, and pure component thermal properties on the effective thermal conductivity of three different composite systems. Cylindrical samples of each system were cast from various proportions of their basic constituents. Effective thermal conductivities were calculated from effective thermal diffusivities. The latter were obtained experimentally from the thermal response of the center of each composite sample as it was cooled from room temperature to 0°C. by means of an agitated ice bath. Effective conductivities so obtained were compared with conductivities predicted by the tridirectional simulation and three previously published models. Results show that a recent model that utilizes unidirectional heat flux but permits random phase distribution provides the best predictions of the experimental data presented in this work. Results of the particle size study indicate that there is a minimum ratio of system dimension to particle dimension below which a particulate composite can no longer be considered macroscopically homogeneous and isotropic.