Thermal characterization of granular materials using a thermal-wave resonant cavity under the dual-phase lag model of heat conduction

The process of heat transport in granular materials has generated a great deal of controversy. It has been claimed that the process is affected not only by the thermal conductivity, diffusivity and heat capacity, but also additional parameters in the form of time-phase lags must be considered. These quantities permit to take into account the thermal inertia and the micro-structural interactions of the media in such a way that they establish the non-simultaneity between the temperature and the heat flux. A highly successful model that takes into account these effects is known as the dual-phase lag model of heat conduction. It constitutes an approach that generalizes and overcomes the limitations of the classical Fourier law of heat transport. One of the most sensitive techniques for measuring thermal properties is the thermal-wave resonant cavity, which is formed by three layers. The one in the middle is semi solid, liquid or gas, whose thickness can be changed moving one of the external layers. In order to study the material in the middle, a modulated heat source is applied to one of the external layers, and the changes of temperature are registered at the surface of any of the external layers. This methodology has provided high accuracy results for the thermal properties of liquids, gases and nanofluids in the context of Fourier heat diffusion equation. However results for granular materials using this methodology are scarce and the role of the phase lags in heat transport has not been fully explored. In this work, the theoretical basis for the development of a thermal-wave resonant cavity based on dual-phase lag model is studied. It is shown that this system could be used to measure not only the thermal diffusivity but also the time-phase lags of granular materials, by performing a suitable thickness scan of the cavity. It is shown that the results obtained can be a highly useful in the development of experimental methodologies revealing the possibility of non-Fourier heat transport and how the thermal characterization of granular materials can be performed.