Abstract
This paper presents the numerical comparison in the solution of the hyperbolic transport Equation that models the heat flux in thermoelectric materials at nanometric length scales when the wave propagation of heat dominates the diffusive transport described by Fourier’s law. The widely used standard finite difference method fails in well-reproducing some of the physics presented in such systems at that length scale level. As an alternative, the spectral methods assure a well representation of wave behavior of heat given their spectral convergence.
Highlights
The research activity in the area of thermoelectricity began with the discoveries of Seebek, Peltier and Thomsom in the early 1800’s
We focus in this work on the problem of heat transport in thermoelectric thin films taking into account two important features of the heat transport in the nanoscale, namely, memory and nonlocal effects and the experimentally observed reduction of the thermal conductivity in nanoscopic devices
The hyperbolic heat transport partial differential Equation representing the thermoelectric problem in thin films was solved on a discrete grid system using a finite difference and a spectral collocation scheme
Summary
The research activity in the area of thermoelectricity began with the discoveries of Seebek, Peltier and Thomsom in the early 1800’s. Superlattices made with crystalline materials appear as good thermoelectrics since they manage to scatter phonons without diminishing the electrical conductivity [1]. We focus in this work on the problem of heat transport in thermoelectric thin films taking into account two important features of the heat transport in the nanoscale, namely, memory and nonlocal effects and the experimentally observed reduction of the thermal conductivity in nanoscopic devices. It is worth mentioning that a proper description of heat transport in that kind of problems is not possible without including the above distinctive features of the nanoscale transport considered in this work
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