Optimal performance and entropy generation transition from micro to nanoscaled thermoelectric layers

Abstract

In this paper we address the heat and electric charge transport in a thermoelectric thin layer. The analysis is based on hyperbolic type equations describing the time evolution of dissipative flows including size effects on the thermal and electric conductivities. We explore the effects of the layer width on the time evolution of the system and, particularly, on the thermal figure of merit and the entropy generation. We find a transition between two dynamic regimes controlled by the system’s size when going from the micro to the nanometric scale of lengths. The transition is featured by a marked increasing of the thermal figure of merit and the total entropy generation. The low entropy generation regime is dominated by the diffusive transport of heat and the regime with high entropy generation values by wave energy transfer (this last corresponding to the nanometric scale). We use here the spectral methods of solution which assure a well representation of wave behaviour of heat given their spectral convergence.