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Heat Conductors

In: Thermodynamics of Materials with Memory

Author

Listed:
  • Giovambattista Amendola

    (University of Pisa, Dipartimento di Matematica Applicata “U. Dini”)

  • Mauro Fabrizio

    (University of Bologna, Dipartimento di Matematica)

  • John Murrough Golden

    (Dublin Institute of Technology, School of Mathematical Sciences)

Abstract

To remove the paradox of classical Fourier theory relating to the instantaneous propagation of thermal disturbances, Cattaneo [29] 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 gradient. It is referred to as the Cattaneo–Maxwell relation, since Maxwell [170] previously obtained it but immediately eliminated the term involving the time derivative of the heat flux. It leads to a hyperbolic heat equation.

Suggested Citation

  • Giovambattista Amendola & Mauro Fabrizio & John Murrough Golden, 2012. "Heat Conductors," Springer Books, in: Thermodynamics of Materials with Memory, chapter 0, pages 199-216, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-1692-0_8
    DOI: 10.1007/978-1-4614-1692-0_8
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