Frequency-modulated hyperbolic heat transport and effective thermal properties in layered systems

Abstract

In this work heat transport in layered systems is analyzed using a hyperbolic heat conduction equation and considering a modulated heat source for both Dirichlet and Neumann boundary conditions. In the thermally thin case, with Dirichlet boundary condition, the well known effective thermal resistance formula is derived; while for Neumann problem only a heat capacity identity is found, due to the fact that in this case this boundary condition cannot become asymptotically steady when modulation frequency goes to zero. In contrast in the thermally thick regime, heat transport shows a strong enhancement when hyperbolic effects are considered. For this thermal regime, an analytical expression, for both Dirichlet and Neumann conditions, is obtained for the effective thermal diffusivity of the whole system in terms of the thermal properties of the individual layers. It is shown that the magnifying effects on the effective thermal diffusivity are especially remarkable when the thermalization time and the thermal relaxation time are comparable. The limits of applicability of our equation, in the thermally thick regime are shown to provide useful and simple results in the characterization of layered systems. Enhancement in thermal transport and in the effective thermal diffusivity is a direct consequence of having taken into account the fundamental role of the thermal relaxation time in addition to the thermal diffusivity and thermal effusivity of the composing layers. It is shown that our results can be reduced to the ones obtained using Fourier heat diffusion equation, when the thermal relaxation times tend to zero.