Phonon-electron coupling and nonlocal heat transport in Bi⁠2Te⁠3 nanowires

A hydrodynamical model of heat transfer with phonons and electrons is applied to infer the steady-state temperature profile in a Bi⁠2Te⁠3 nanowire. Our analysis is concerned with systems which allow for different temperatures of phonons and electrons. Along with the approach of the kinetic theory, the phonons and the electrons are regarded as a gas-like mixture flowing through the crystal lattice. The coupling between phonons and electrons is taken into account by an additional term in the partial balances of energy of the components of the mixture. The compatibility of the model with the second law of thermodynamics is investigated in view of the requirement of positive entropy production, and of a nonlocal constitutive equation for the entropy flux.