To remove the paradox of classical Fourier theory relating to the instantaneous propagation of thermal disturbances, Cattaneo  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  previously obtained it but immediately eliminated the term involving the time derivative of the heat flux. It leads to a hyperbolic heat equation.
KeywordsHeat Conductor Constitutive Equation Internal Energy Relaxation Function Maxwell Relation
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