Engineering Mechanics

Proceedings Vol. 29 (2023)

ENGINEERING MECHANICS 2023

Copyright © 2023 Institute of Thermomechanics of the Czech Academy of Sciences, Prague

 

Sladek J., Sladek V.
pages 227 - 230, full text

The Seebeck effect is utilized in the thermoelectric materials to convert the waste heat directly to electricity. A high electrical conductivity, low thermal conductivity and high Seebeck coefficient are desirable for high thermoelectric conversion efficiency. For generation of a large voltage it is needed to keep sustained large temperature gradients. Therefore, some research efforts are devoted to develop thermoelectric composites with low thermal and high electric conductivities. Earlier research on macro- sized structures has not been successful. Nanotechnology open a door to reduce thermal conductivity without affecting the electrical conductivity. The heat transfer is realized by "larger" phonons than electrons responsible for the electric conduction. The scattering of phonons is increased in nano-sized structures and the thermal conductivity is reduced owing to the mean:free path of phonons becoming comparable with the size of sample. Then, the classical Fourier heat conduction model appears to be insufficient because of ignoring size effects. To consider the size effect an advanced continuum model for heat transfer is developed here with including second order temperature gradients in constitutive law. The governing equations involve higher-order derivatives of field variables. Therefore, it is necessary to develop also a powerful computational tool to solve general boundary-value problems. The mixed finite element method (FEM) is developed in this paper.

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