Exact and approximate Maxwell-Cattaneo-type descriptions of heat conduction: A comparative analysis. (August 2021)

• Record Type: Journal Article
• Authors: Capriz, Gianfranco; Wilmanski, Krzysztof; Mariano, Paolo Maria
• Is Part Of: International journal of heat and mass transfer. Volume 175(2021)
• Publication Date: 2021-08
• Subjects: Finite speed heat propagation -- Heat-driven phase transitions -- Non-Fourier heat conduction -- The Maxwell-Cattaneo model; Heat -- Transmission -- Periodicals; Mass transfer -- Periodicals; Chaleur -- Transmission -- Périodiques; Transfert de masse -- Périodiques; Electronic journals; 621.4022
• DOI: 10.1016/j.ijheatmasstransfer.2021.121362
• Languages: English
• ISSNs: 0017-9310

Abstract

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.