Experimental and theoretical investigation on the performance of flexible thermoelectric generators with optimized geometry and copper foam

To address the low output performance of flexible thermoelectric generators (FTEGs) under wearable low-temperature-gradient conditions, this work presents a coupled structural design approach combining internal geometric optimization and external passive heat dissipation. Experimental measurements and finite-element simulations were performed to evaluate the effects of thermoelectric leg height (1.3–2.5 mm), array spacing (2–6 mm), and copper-foam pore density (40–80 PPI) on the performance of Bi₂Te₃-based FTEGs under thin-layer natural-convection conditions. Here, “thin-layer natural convection” refers to the passive cooling condition of a millimeter-scale wearable device/heat-sink assembly whose thickness is much smaller than the characteristic thermal boundary-layer scale of free convection in ambient air. The results show that increasing leg height enhances the equivalent thermal resistance of the thermoelectric module and increases the effective temperature difference across the legs, whereas increasing array spacing suppresses lateral heat leakage through the flexible substrate. The introduction of copper foam further improves cold-side heat dissipation, with the 80 PPI structure showing the best performance among the investigated heat-sink configurations. Within the investigated parameter range, the optimized configuration with a leg height of 2.5 mm, a spacing of 6 mm, and an 80 PPI copper-foam heat sink achieved an open-circuit voltage of 98.2 mV and the highest matched output power. These results provide a practical design guideline for wearable FTEGs operated under constrained natural-convection conditions.