Geometric optimization for the thermoelectric generator with variable cross-section legs by coupling finite element method and optimization algorithm

Recently, several kinds of variable cross-section legs have been reported to improve the performance of thermoelectric generators (TEGs). This work further proposes an optimization study to maximize the output power of variable cross-section TEGs for solar energy utilization by coupling finite element method (FEM) and optimization algorithm. Six geometric variables along with the external load resistance are optimized by genetic algorithm (GA) and particle swarm optimization (PSO). Besides, Joule heating, Peltier effect, and Thomson effect are considered in the numerical model to improve the simulation accuracy. Optimization results show that distributions of the thermal resistance and the electrical resistance are significantly changed when the volumes of thermoelectric material remain constant. The optimized leg shape increases the temperature gradient in the high figure of merit (ZT) region by reducing the cross-section area. Although internal resistances of optimal TEGs are greater than those of rectangular TEGs, the improvement in electromotive force results in the enhancement of electrical performance. At heat flux of 35000 W m−2, 40000 W m−2, 45000 W m−2, and 50000 W m−2, temperature differences of optimal TEGs are increased by 12.77%, 18.36%, 41.93%, and 73.14%, while output powers are improved by 1.45%, 2.13%, 9.33%, and 20.13%, respectively.