Exponential Porosity Dependence of Thermal Conductivity

The porosity dependence or thermal conductivity is of general interest in many fields of science and technology (ceramics, metals, foods). It cannot be decribed by universal Function, because porosity is only one of many microstructural parameters. When measured data are not available, a tough estimate is often needed for engineering design. We show that the power-law expressions and other relations commonly used for this purpose, provide predictions that are too high and valid only for exceptional microstructures. We propose exponential behavior, in the sense of a modified exponential relation, which is shown to be closer to reality for the majority of microstructures occuring in real materials. Nevertheless, even this prediction is often too high, especially in the case of partially sintered microstructures, due to non-convex pore shape. We indicate a reasonable definition of a concavity-convexity parameter which may serve as a measure to quantify this shape effect.