Spectral and Finite Difference Solutions of the Hyperbolic Heat Transport Equation for Thermoelectric Thin Films

Aldo Figueroa, Federico Vázquez

Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Cuernavaca, México.

DOI: 10.4236/am.2013.410A3004                

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.

Keywords

Thermoelectric Cooling; Ballistic Regime; Spectral Chebyshev Collocation Method

Conflicts of Interest

The authors declare no conflicts of interest.

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