Simple analytic model for optimally sizing thermoelectric generator module arrays for waste heat recovery

Thermoelectric generators (TEGs) are commonly used in waste heat recovery (WHR) applications. Counter-intuitively, recent studies have demonstrated that there is an optimal number of TEG modules to use in a WHR system for maximum power output. General rules for identifying this limit have not yet been proposed. In this study, a simple analytic model is derived to describe WHR systems, and predict the optimal TEG module array size. This model incorporates a new thermal-fluid figure of merit (H_T), which accounts for coupled effects of TEG module thermal conductance, heat exchanger performances, and coupling fluid stream thermal capacity rates. The model is experimentally validated with data from a small-scale test facility. The model is used to predict performance trends of (1) TEG arrays with varying module counts at low and high fluid thermal capacity rates, (2) TEG arrays with fixed overall heat exchanger conductances (UAs) and UAs proportional to module-count, and (3) multi-row TEG arrays. Guidelines for selecting optimal numbers of TEG modules are recommended for these cases. The application of this model is illustrated through analysis of a vehicle WHR system. This analytic model can guide preliminary WHR system designs, which can be refined with sophisticated computational and experimental approaches.