Exact and approximate Maxwell-Cattaneo-type descriptions of heat conduction: A comparative analysis. (August 2021) - Capriz, Gianfranco; Wilmanski, Krzysztof; Mariano, Paolo Maria
Highlights: We discuss the dependence of energy on the heat flux in non-Fourier heat conduction. We prove that a model for second-order heat conductors is physically unacceptable. We show how Cattaneo and Guyer-Krumhansl equations can be derived from a balance of microstructural interactions under appropriate internal constraints. Abstract: 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.