Dethermalization Theory: Thermal/Dielectric Analogy for Heat Flow Through Porosity in Composites

Abstract

The flow of heat in solids has long been known to possess an electric current analogy applicable to both steady state and transient flows. In the present work we assume a vector analogy between Fourier’s law and the classical electric displacement to develop a method of handling distributed porosity in composite materials subject to heat flow in a way analogous to dealing with distributed dielectric regions in solids subject to an external electric field. The effect of the geometry of “depolarization” regions in an electric displacement field and “demagnetization” regions in a magnetizing field can be carried over to the effect of “dethermalization” regions in a heat-flux field. The analogy provides a simple analytic way of determining the effects of porosity shape on thermal conductivity which can be significant and can violate the usual law of mixtures approach. For uniformly distributed porosity of known aspect ratio in a given region, the volume-fraction porosity of the region can then be evaluated from a simple measurement of the thermal diffusivity. This approach was originally successfully tested over a limited range of variables when the model was developed and has recently been validated to good accuracy over a large range of porosity aspect ratios.