Thermal Conductivities of MgO, Al2O3, and ZrO2 Powders to 850°C. II. Theoretical

A theoretical expression is presented to relate the effective thermal conductivity of statistically describable two-phase systems to the conductivities of the pure phases, the volume concentrations of the phases, and a shape factor. Auxiliary equations to relate bulk gas conductivity and small interparticle distance and to predict a radiation heat transfer contribution to effective thermal conductivity are also presented. The shape factor is a property of the discontinuous phase and is related to the two-phase system only through the volume balance of the phases. In the derivation of the expression no assumptions are made concerning particle shape, size, or spatial arrangement. However, the derivation is based on a simplified model in that the isotherms in the model are assumed to be planes perpendicular to the heat flow. In exact solutions of the heat flow equation, no assumptions are made regarding the heat flow or temperature pattern. On the other hand, exact solutions have been carried out only for simple shapes in fixed arrangements that seem to fall short of describing actual powder-gas systems.