Energy Efficiency of Anisotropic Thermoelectric Materials Under Three-Dimensional Conditions

The figure of merit parameter (Z) for an anisotropic thermoelectric (TE) material is dependent on direction, and the highest Z has been used to characterize the energy conversion efficiency of anisotropic TE materials. It is, however, not clear whether the material properties in other directions also play a role in the TE generator efficiency. This work presents a three-dimensional (3D) model to investigate the direction dependence of energy efficiency for orthotropic TE materials. It is analytically proved that the peak efficiency is a function of Z in the leg direction, the thermal conductivity (separate from that in Z) in the leg direction and the thermal conductivities in the lateral directions, but is independent of lateral electrical conductivities. Numerical examples indicate that the energy efficiency is insensitive to the lateral thermal conductivities, but increases with an increase in the thermal conductivity in the leg direction for a fixed Z in the leg direction. Moreover, the efficiency of an orthotropic material with the leg in a lower Z direction may become higher than that with the leg along the highest Z direction, depending on the thermal conductivity in the leg direction, which indicates that orienting the highest Z direction along the leg may not necessarily achieve the highest TE generator efficiency. The effects of anisotropy on the efficiency are coupled with heat loss along the lateral surface and become less significant for small surface heat transfer coefficients.