Temperature Distribution in a Non-Prismatic Thermoelectric Leg and the Energy Conversion Efficiency

It has been proposed that asymmetric thermoelectric (TE) legs may enhance the TE energy conversion efficiency. This work presents an analytical model for the temperature field in non-prismatic TE legs and the energy conversion efficiency. Different from the models available in the literature, the present one-dimensional (1D) heat equation for thermal conduction in non-prismatic legs is derived from the general three-dimensional energy and charge balance laws and the thermoelectric constitutive relations considering Joule heating and the Seebeck effect on the heat flow. The temperature field in a TE leg with an arbitrary gradient of the cross sectional area is obtained using the 1D heat equation. The temperature field and energy conversion efficiency are calculated for exponential and quadratic Bi2Te3 legs as well as an exponential PbTe leg. The numerical results indicate that leg tapering has minimal effects on the temperature distribution in and energy efficiency of the non-prismatic leg under the prescribed cold and hot side temperatures boundary conditions provided that the volume of the leg remains the same. The energy efficiency of the tapered leg, however, can be significantly increased under the prescribed hot side heat flux condition. Finally, a simple estimate on the limitation of the 1D models for non-prismatic legs is discussed.