# Optimal Design of Wearable Micro Thermoelectric Generator Working in a Height-Confined Space
## 4 Conclusions  
In this work, we optimized the design and integrated manufacturing of a wearable micro-thermoelectric generator in a height-confined space. The effects of geometric parameters of thermoelectric generator (TEG) on the number of fins and fin height are systematically studied by numerical simulation. The optimal number of fins to obtain the highest equivalent convective heat transfer coefficient was determined under different fin heights. Our findings reveal that the geometric size of the device has a negligible effect on the heat dissipation capacity of the heat sink, and the optimal number of fins decreases gradually as the fin height increases. Moreover, a co-design of TEG and fin topological structure was performed to examine the influence of the ratio of leg height to fin height (\(l/H\)), leg width (\(w\)), and number of thermoelectric leg pairs (\(N\)) on the maximum output power density per unit area (\(P_{\text{m1}}\)), and the maximum output power density per unit mass (\(P_{\text{m2}}\)) of the device. Notably, when \(N=16\), \(w=0.3\) mm, \(l/H=2.5\) (i.e., \(l=3.57\) mm and \(H=1.43\) mm), and \(P_{\text{m1}}\) reaches the maximum value of \(30.5\)\(\mu\)W/cm\({}^{2}\); When \(N=2\), \(l/H=0.25\) and \(w=0.3\) mm, \(P_{\text{m2}}\) reaches a maximum value of \(5.12\) mW/g. To verify the simulation results, we have fabricated micro-TEGs and measured the open-circuit voltages of TEGs with different thermoelectric leg heights (\(l=0.49\) mm, \(l=1.38\) mm, and \(l=1.88\) mm). The measured values were consistent  
Figure 6: Open-circuit voltage and maximum power density of per unit mass (\(P_{\text{m2}}\)) of micro-TEGs with different leg heights: (**a**) \(l=0.49\) mm, (**b**) \(l=1.38\) mm, (**c**) \(l=1.88\) mm. with the simulated values. Additionally, we found that \(P_{\text{m2}}\) reached a maximum value of 0.44 mW/g when \(N=2\), \(l=0.49\) mm, \(H=3.74\) mm, and \(w=0.85\) mm. Overall, our study provides insights into the optimal design of wearable micro thermoelectric generators working in a height-confined space and highlights the importance of co-designing TEGs and fin topological structures for optimizing their performance. Additionally, future improvements in material properties and the development of advanced technological means will result in less restrictive optimization strategies. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app13106156/s1](https://www.mdpi.com/article/10.3390/app13106156/s1)]([https://www.mdpi.com/article/10.3390/app13106156/s1](https://www.mdpi.com/article/10.3390/app13106156/s1)), Figure S1: Temperature dependent properties of p-type Bi\({}_{0.4}\)Sb\({}_{1.6}\)Te\({}_{3}\) and n-type Bi\({}_{2}\)Se\({}_{0.2}\)Te\({}_{2.8}\) thermoelectric materials: (a) absolute value of Seebeck coefficient; (b) electrical conductivity; (c) thermal conductivity; Figure S2: The manufacturing process flow chart of the micro device; Figure S3: The relationship among the convective heat transfer coefficient per unit area (\(h_{\text{a}}\)), fin height (\(H\)) and number of fins under different temperature difference (\(\theta\)) between fin base and the ambient: (a) \(\theta=4\) K, (b) \(\theta=5\) K, (c) \(\theta=6\) K, (d) \(\theta=7\) K, and (e) \(\theta=8\) K; Figure S4: The relationship among the equivalent convective heat transfer coefficient (\(h_{\text{eff}}\)), fin height (\(H\)) and number of fins under different temperature difference (\(\theta\)) between fin base and the ambient: (a) \(\theta=4\) K, (b) \(\theta=5\) K, (c) \(\theta=6\) K, (d) \(\theta=7\) K, and (e) \(\theta=8\) K; Figure S5: The relationship among the temperature difference between the two ends of the device (\(\Delta\)T), the ratio of leg height to fin height (I/H), leg width (w) with different number of leg pairs: (a) 2, (b) 4, (c) 8, (d) 16, and (e) 32. [PERSON] and [PERSON] contributed equally to this work. Conceptualization, X.T. and Q.Z. ; simulation, K.T., Y.X. and K.H. ; investigation, K.T. and J.W.