Geometry optimization of a thermoelectric generator with temperature-dependent properties

Maximizing the power delivered by a thermoelectric generator (TEG) (with an internal resistance RTE) can be achieved by optimizing its design taking into account the external load (with a resistance of RL). In the present work, the evolution of the thermoelectric (TE) properties of the materials along the leg was considered. By considering a fixed heat rate on the hot side, the powers delivered by various TEGs were assessed by varying the length of the legs. After that, analytical approach was detailed based on the mathematical formulas governing the thermal and electrical transports. This approach revealed that the ratio m = RL/RTE is between the most commonly claimed values (1 and (1 + zT)1/2). Our variable properties model reveals that the optimal design requires lower cost than that considered by equaling RTE and RL (m = 1). This finding turns out to be more and more valid for materials which present a linear variation of temperature with position.