Determination of thermal properties for hyperbolic heat transport using a frequency-modulated excitation source

Abstract

The hyperbolic Cattaneo–Vernotte equation has been proposed as an alternative to generalize the Fourier law of heat transfer. The determination of the thermal properties under the hyperbolic approach is a subject of research that deserves an extensive analysis. The development of new methodologies to detect the hyperbolic effects and measure the thermal properties is scarce. One of the most powerful techniques that have shown to provide useful results consists in exciting the physical system using a modulated thermal excitation. In this paper the heat transfer induced by this kind of sources is studied, through a system formed by a semi-infinite layer in contact with a finite one. It is shown that there exist frequency ranges in which the real and imaginary part of the modulated temperature exhibit characteristic and strong oscillations. When the thermal effusivities of the layers are quite different, 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. The theoretical basis for the development of a hyperbolic thermal-wave resonator has also been derived.