Nonlocal heat transport with phonons and electrons: Application to metallic nanowires

In the framework of Extended Irreversible Thermodynamics we develop a model for coupled heat conduction by phonons and electrons. Particular emphasis is given to nonlocal eects, which may arise when the mean-free paths of phonons and/or electrons are comparable to the size of the system. As particular cases, we recover two parabolic equations of the Guyer-Krumhansl type which model the concurrent presence of the diusion of heat superposed to the propagation of heat waves, and two hyperbolic equations of the Maxwell-Cattaneo type. In the latter case, the phase speed of temperature waves is calculated. The size dependence of the Wiedemann-Franz law is brie y analyzed for metallic nanowires.