We present an analytic model and optimization of impingement heat transfer in fluid-to-fluid heat exchangers with integrating a thermoelectric (TE) generator between the hot and cold fluid flows. In power generation systems, designing for maximum power output generally involves balancing the external thermal resistances while the generator contacts the hot and cold temperature reservoirs. In fluid-to-fluid heat exchangers, fluid temperatures are not constant or uniform. They gradually change along the flow direction. In general, counter-flow heat exchangers outperform parallel flow configurations in maximizing TE power generation using internal fluid flows. We show here the performance of our impingement model compared with a counter-flow configuration as the base line.

To obtain the maximum power output from practical thermoelectric materials (ZT values are 1.2–1.8), the enhancement of liquid-to-wall heat transfer is significant. An array of traditional impinging jet orifices provides a uniformly planar and focused heat transfer process that spatially targets the TE elements. This approach provides more uniform hot and cold side temperatures among the TE elements. We investigate the impact of introducing impingement orifices directly at the locations of the TE elements. The major focus of this work is the trade-off between the advantage of increasing power generation by impingement and the disadvantage of introducing additional pressure drop.

Decreasing the external thermal resistances yields not only a larger maximum power output but also requires thinner TE elements. This enables lower cost per power generation capacity approaching the 0.2–0.3 $/W range as well as a more lightweight design. We report here the associated cost impacts for the impinging jet arrangement.

Design optimization depends on the specific constraints and parameters, such as TE material and substrate thickness, flow design to avoid the stagnation, and required exit temperatures. In some cases, active pumping by an additional actuator can augment the enhancement, while a fraction of generated power is consumed for the actuation. In the paper, we show examples of gas and liquid flow cases.

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