A nonlinear model of thermoelectricity with two temperatures: Application to quasicrystalline nanowires
efficiency of the thermoelectric generator
multi-temperature theory of fluid mixtures
The joint transport of heat and electric current is called a thermoelectric effect. The aim of the paper is to describe the nonlinear thermoelectric coupling in quasi-crystals, materials that are located at the borderline between metals and semiconductors. Guided by the relevance of nonlinear effects at the nanometric length scales, it is assumed that the thermoelectric transport is due to the combined flows of phonons and electrons, whose thermodynamic properties are somewhat different. The analysis pertains to materials with no production of the electric charge per unit volume (that excludes doped semiconductors or systems where positive ions naturally appear). One allows the near equilibrium and equilibrium temperatures of phonon and electron components to the heat flux to be different. Thermodynamic compatibility of the obtained transport equations, that are additionally coupled to constitutive equations for the heat flux, is investigated to yield the non-negative entropy production in the process. Here, appropriate macroscopic transport equations come from the so-called thermo-mass theory. The efficiency of the thermoelectric coupling in quasicrystalline nanowires is estimated. The authors note that accounting for two different temperature scales seems clear from the theoretical viewpoint, but currently there is no experimental evidence confirming the existence of different phonon and electron temperature labels. As such, the paper can be regarded as the first effort towards a mathematical model to describe thermoelectric effects at nanoscale, capable of providing hints toward a detailed experimental scrutiny.
scientific article; zbMATH DE number 6578054