Thermal wave oscillations and thermal relaxation time determination in a hyperbolic heat transport model

Abstract

One of the major challenges in the study of thermal transport and its analysis, based on the hyperbolic model associated with Cattaneo equation, is the fact that it is necessary to determine the thermal relaxation time for the analyzed materials. This parameter has been an elusive physical quantity to be determined experimentally even though it is of crucial importance in heat transport. In this paper a system formed by a semi-infinite layer in contact with a finite one, that is excited by a modulated heat source is studied. It is shown that a frequency range can be found in which the amplitude and phase of the spatial component of the oscillatory surface temperature show strong oscillations when the thermal relaxation time of the finite layer is close to its thermalization time. When the thermal effusivities of the layers are quite different or their thermal relaxation times are similar, it is shown that simple analytical expressions for the values of the maxima and minima of the oscillations as well as for the frequencies, at which they occur, are obtained. These results were used to establish a methodology to determine the thermal relaxation time as well as additional thermal properties of the finite layer.