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. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

By comparing the consequences of Maxwell-Cattaneo's view on heat flux and the approximation of defining it as a class of conductors, we demonstrate that the latter choice leads to a non-physical result. Additionally, in the presence of heat-driven phase transitions, the Maxwell-Cattaneo equation can be considered as emerging from a balance of microstructural interactions, including the Guyer-Krumhansl equation.