High-order fluxes in heat transfer with phonons and electrons: application towavepropagation

We propose a theoretical model to study heat transfer at the nanoscale by means of high-order thermodynamic fluxes. The model is fully compatible with the model of heat transfer of extended irreversible thermodynamics, represents a generalization of the Guyer–Krumhansl proposal (Guyer & Krumhansl 1966 Phys. Rev. 148 ) and is able to deal with relaxational and non-local effects. It also accounts for the role played by the different heat carriers (electrons and/or lattice vibrations) and captures different heat-carrier temperatures. The proposed model is hyperbolic and is used to investigate the propagation of thermal waves.