# Optimal Design of Wearable Micro Thermoelectric Generator Working in a Height-Confined Space
## 3 Results and Discussion
### Cooperative Optimization Design of the Overall Structure of TEG and Fin  
After determining the optimal number of fins for the highest equivalent convective heat transfer coefficient, we conducted further studies to investigate the effects of various geometric parameters on the performance of the device. Specifically, we explored the impact of the ratio of leg height to fin height (\(l/H\), where \(l+H=5\) mm), leg width (\(w\)), and number of leg pairs (\(N\)) on the maximum output power density per unit area (\(P_{\text{m1}}\)) (Figure 4) and the maximum output power density per unit mass (\(P_{\text{m2}}\)) (Figure 5) of the device, as well as the temperature difference at both ends of the device (\(\Delta T\)) (Figure S5).  
Figure 3: (**a**) Detailed drawing of corresponding parameters in finned radiator; (**b–e**) effect of temperature difference \(\theta\) and geometric parameters of finned heat sink on the equivalent convective heat transfer coefficient \(h_{\text{eff}}\) (**f**) relationship among the optimal number of fins, fin height \(H\), and temperature difference \(\theta\).  
Figure 4: The relationship among the maximum power density per unit area (\(P_{\rm m1}\)), leg width (\(w\)), and the ratio of leg height to fin height (\(l/H\)) with different number of leg pairs: (**a**) 2, (**b**) 4, (**c**) 8, (**d**) 16, and (**e**) 32.  
Notably, we observed that the temperature difference (\(\Delta T\)) decreased with an increase in both the number of leg pairs (\(N\)) and leg width (\(w\)), while it increased with an increase in \(l/H\) (Figure S5). The peak \(P_{\rm m1}\) corresponding to different \(l/H\) and \(w\) is marked with red  
Figure 5: The relationship among the maximum power density of per unit mass (\(P_{\rm m2}\)), leg width (\(w\)), and the ratio of leg height to fin height (\(l/H\)) with different number of leg pairs: (**a**) 2, (**b**) 4, (**c**) 8, (**d**) 16, and (**e**) 32.  
box in Figure 4. When \(N=2\), 4, the \(P_{\rm m1}\) tends to obtain optimal value at both large \(l\)/\(H\) and \(w\) (Figure 4a,b); When \(N=8\), the \(P_{\rm m1}\) first increases and then decreases with \(l\)/\(H\) as \(w\) = 0.3 mm, and the \(P_{\rm m1}\) monotonously increases with \(l\)/\(H\) as \(w\) = 0.4\(\sim\)0.6 mm (Figure 4c); However, the trends are different when \(N\) = 16, 32. The \(P_{\rm m1}\) increases monotonously with the increase of \(l\)/\(H\), and decreases monotonously with the increase of \(w\) (Figure 4d,e). Specifically, when \(N=16\), \(w\) = 0.3 mm, the optimal \(l\)/\(H\) is 2.5 (i.e., \(l\) = 3.57 mm, \(H\) = 1.43 mm), and the corresponding \(P_{\rm m1}\) reaches the highest value of 30.5 \(\mu\)W/cm\({}^{2}\). We compared the optimized simulation results with those previously reported in Table 1. As can be seen, radiators do greatly improve the performance of thermoelectric devices. Our optimized results are also at the forefront of research.  
In addition to the maximum output power density per unit area (\(P_{\rm m1}\)), we also evaluated the maximum output power density per unit mass (\(P_{\rm m2}\)) of the device, which is a crucial factor in determining the price-performance ratio of the device. (Here, we mainly calculated the weight of TE material.) As can be seen in Figure 5, the \(P_{\rm m2}\) of the device decreases monotonously with the increase of eg height-to-fin height ratio \(l\)/\(H\), leg width \(w\), and a number of leg pairs \(N\). Specifically, the peak \(P_{\rm m2}\) was observed when \(N=2\), \(l\)/\(H\) = 0.25 and \(w\) = 0.3 mm, reaching the highest value of 5.12 mW/g. The price-performance ratio of the device is an essential consideration for practical applications. Our results suggest that, from a cost perspective, it may be advantageous to choose a device with a lower \(l\)/\(H\), narrower leg width, and a smaller number of leg pairs to achieve a higher \(P_{\rm m2}\). These findings provide important insights for the design and optimization of thermoelectric devices with improved efficiency and cost-effectiveness.