The role of thermal effusivity in heat exchange between finite-sized bodies

Abstract

Thermal effusivity is a thermophysical property of materials that combines thermal conductivity and volumetric heat capacity. Thermal effusivity is often interpreted in terms of a body's ability to exchange heat when brought in contact with another body at a different temperature, and is relevant in thermal property measurements, such as the transient plane source method as well as in energy harvesting and thermal management. Well-known theoretical models show that thermal effusivity is the only thermophysical property that governs heat exchange between two semi-infinite bodies. In contrast, there is a lack of work on heat exchange between bodies of finite thickness, which may be a relevant consideration in several practical scenarios. This work presents an analytical solution for heat exchange between two finite bodies initially at different temperatures. The effect of thermal contact resistance is accounted for. Results from this work are shown to approach semi-infinite results when the layer thickness becomes large. It is shown that while the heat flux for finite thickness in general depends on both thermal effusivity and thermal diffusivity, exclusive dependence on effusivity may occur under certain conditions, particularly for poorly conducting materials. The sensitivity of interfacial heat flux on these thermal properties is examined in the regimes in which most materials of interest lie. The limits in which the semi-infinite approximation is reasonable are determined. A practical problem is solved as an illustration. This work improves the fundamental understanding of thermal effusivity and thermal interaction between finite-sized bodies, and may find applications in a variety of engineering problems such as thermal property measurement, energy harvesting and thermal management.