A three-dimensional analytical model for performance evaluation of thermoelectric generators

A three-dimensional (3D) theoretical model for thermoelectric generators (TEGs) has been developed in this paper, yielding analytical solutions for power output and energy conversion efficiency. The model comprehensively considers convective heat transfer between the thermoelectric legs and their ambient environment, as well as 3D heat conduction within the ceramic substrates. Numerical results reveal the significant influence of convective heat loss from the legs' surfaces on efficiency, especially for taller legs or higher heat convection coefficient, while having a minimal impact on power output for the constant temperature boundaries. It is shown that neglecting 3D heat conduction within the ceramic substrates leads to a substantial overestimation of TEG performance. Additionally, the complex 3D heat conduction problem for TEGs can be simplified into a more manageable 1D model with only minor adjustments to classical TEG theory. This is achieved by introducing analytical expressions for a dimensionless impact factor to quantify convective heat loss from the legs’ surfaces and the effective thermal conductance of the ceramic substrates. The proposed model serves as a valuable tool for simplifying the modeling process and optimizing the design of actual TEGs.