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 effects, 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 diffusion 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 briefly analyzed for metallic nanowires.