Exact and approximate Maxwell-Cattaneo-type descriptions of heat conduction: A comparative analysis

We compare consequences of Maxwell-Cattaneo’s view on the heat flux and the choice of considering its approximation as an exact relation defining per se a class of conductors. In particular, we prove that this last choice leads to a non-physical result. Furthermore, at variance of the common way of justifying the Maxwell-Cattaneo equation as a memory-type constitutive structure, we show how in the presence of heat-driven phase transitions it can be considered as emerging (under appropriate conditions) from a balance of microstructural interactions, which includes also the Guyer-Krumhansl equation.