Internal and external simultaneous optimization of an irreversible thermoelectric generator for maximum power output

A generalized finite-time thermodynamic model of irreversible multi-element thermoelectric generator is established taking into account inner and external factors. The inner effects include Seebeck effect, Fourier effect, Joule effect and Thomson effect. The irreversibility is caused by the finite-rate heat transfer between the heat reservoirs and the device. The theoretical iterative functions of the hot and cold junction temperatures and energy equations are obtained. The model is applied to the analysis of a multi-element thermoelectric generator, which is made of typical thermoelectric materials. It is found that, for given other parameters, there is an optimal electrical current, an optimal length of thermoelectric elements and an optimal ratio of thermal conductance allocation corresponding to the maximum power output. Thus, internal and external simultaneous multivariable optimizations are performed for a maximum power output. The effects of several important parameters on the optimal variables are analyzed in detail. The comparison between the optimized power and the non-optimized power shows that the multivariable optimization is necessary and effective for various working conditions. The model and optimization conclusions obtained herein can be applied to not only the analysis and optimization but also the design of thermoelectric generators. © The Author 2012. Published by Oxford University Press. All rights reserved.