Heat Conductors

  • Giovambattista Amendola
  • Mauro Fabrizio
  • John Murrough Golden


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.


Heat Conductor Constitutive Equation Internal Energy Relaxation Function Maxwell Relation 
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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Giovambattista Amendola
    • 1
  • Mauro Fabrizio
    • 2
  • John Murrough Golden
    • 3
  1. 1.Dipartimento di Matematica Applicata “U. Dini”University of PisaPisaItaly
  2. 2.Dipartimento di MatematicaUniversity of BolognaBolognaItaly
  3. 3.School of Mathematical SciencesDublin Institute of TechnologyDublin 8Ireland

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