Effective Thermal Properties of Layered Systems Under the Parabolic and Hyperbolic Heat Conduction Models Using Pulsed Heat Sources

Abstract

In this work, transient heat transport in a flat layered system, with interface thermal resistance, is analyzed, under the approach of the Cattaneo–Vernotte hyperbolic heat conduction model using the thermal quadrupole method. For a single semi-infinite layer, analytical formulas useful in the determination of its thermal relaxation time as well as its thermal effusivity are obtained. For a composite-layered system, in the long time regime and under a Dirichlet boundary condition, the well-known effective thermal resistance formula and a novel expression for the effective thermal relaxation time are derived, while for a Neumann problem, only a heat capacity identity is found. In contrast in the short time regime, under both Dirichlet and Neumann conditions, an expression that involves the effective thermal diffusivity and relaxation time as a function of the time is derived. In this time regime and under the Fourier approach, a formula for the effective thermal diffusivity in terms of the time, the thermal properties of the individual layers and its interface thermal resistance is obtained. It is shown that these results can be useful in the development of experimental methodologies to perform the thermal characterization of materials in the time domain.