Optimization and Prediction of Water-Cooling Conditions for Thermoelectric Waste Heat Recovery

Industrial waste heat recovery is an important approach for improving energy utilization efficiency and reducing environmental impacts. Thermoelectric devices can directly convert waste heat into electricity, but their practical application is limited by relatively low output power. Active water cooling can enhance the power generation performance of thermoelectric devices, but the pumping power may reduce the net output power. In this study, a water-cooling thermoelectric device is investigated under constant heat input conditions using three-dimensional numerical simulations and a semi-analytical prediction model. The effects of cooling water inlet temperature and flow rate on the thermal response, electrical output, heat transfer behavior, and net output power are systematically analyzed. The results show that increasing the cooling water flow rate increases the gross electrical power but also increases pumping power, resulting in an optimal flow rate of approximately 3 m/s to maximize the net output power. At inlet temperatures of 24 °C, 28 °C, and 32 °C, the maximum net output powers are 51.46 W, 49.89 W, and 48.68 W, respectively. A prediction model for cooling water input conditions is further developed based on energy balance and convective heat transfer correlations, and the predicted velocities agree with the numerical results with relative errors below 2%.