Heat Conductors

Giovambattista Amendola, Mauro Fabrizio and John Golden
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Giovambattista Amendola: University of Pisa, Dipartimento di Matematica
Mauro Fabrizio: University of Bologna, Dipartimento di Matematica
John Golden: Technological University - Dublin, Grangegorman Campus

Chapter Chapter 9 in Thermodynamics of Materials with Memory, 2021, pp 219-235 from Springer

Abstract: Abstract To remove the paradox of classical Fourier theory relating to the instantaneous propagation of thermal disturbances, Cattaneo [59] suggested a generalized Fourier law, which he justified by means of statistical considerations. This constitutive equation relates the heat flux, its time derivative, and the temperature Temperature gradient gradient. It is referred to as the Cattaneo–Maxwell relation Heat flow Cattaneo–Maxwell theory , since Maxwell [254] previously obtained it but immediately eliminated the term involving the time derivative of the heat flux. It leads to a hyperbolic Hyperbolicity heat equation.

Date: 2021
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DOI: 10.1007/978-3-030-80534-0_9

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