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The process of heat conduction, with allowance made for the lag effect, is considered. A postulate of extended irreversible thermodynamics is suggested, according to which the entropy is a function of the internal energy and its time derivatives (up to the third derivative, inclusive). On the basis of the developed thermodynamic formalism, a third-order heat conduction equation is derived, generalizing the known dual-phase-lag model equation. A mathematical model of heat conduction in a package of heat-conducting plates is built, leading to the considered third-order equation. By numerical modeling it is shown that this equation describes heat wave propagation.

Extended Irreversible Thermodynamics and Generalization of the Dual-Phase-Lag Model in Heat Transfer