# High-Performance Wearable Bi\({}_{2}\)Te\({}_{3}\)-Based Thermoelectric Generator
## 3 Results and Discussion  
### Effective Temperature Difference of TEGs under Different Convective Heat Transfer Coefficients  
Figure 2 shows the temperature field of the TE devices with convective heat transfer coefficients at the cold end of 5, 50, 100, and 200 W/(m\({}^{2}\)\({}^{\circ}\)C), respectively. When the ambient temperature \(T_{\text{air}}\) is 25 \({}^{\circ}\)C, the maximum device temperature \(T_{\text{max}}\) is 37 \({}^{\circ}\)C, while the minimum device temperature \(T_{\text{min}}\) decreases with the increase in convective heat transfer coefficient. In a typical wearable scenario, the natural convection heat transfer coefficient of air is 5 W/(m\({}^{2}\)\({}^{\circ}\)C), the minimum temperature \(T_{\text{min}}\) of the device is 36.899 \({}^{\circ}\)C at this time, and the average temperature difference \(\Delta T\) is 0.1 \({}^{\circ}\)C. In the case of forced convection heat transfer, the air convection heat transfer coefficient is 50 W/(m\({}^{2}\)\({}^{\circ}\)C), the minimum temperature \(T_{\text{min}}\) of the device is 36.06 \({}^{\circ}\)C, and the average temperature difference \(\Delta T\) is 0.94 \({}^{\circ}\)C. When the convective heat transfer coefficient increases to 50 W/(m\({}^{2}\)\({}^{\circ}\)C), the minimum temperature \(T_{\text{min}}\) of the device is 35.255 \({}^{\circ}\)C and the average temperature difference \(\Delta T\) is 1.75 \({}^{\circ}\)C. When the convective heat transfer coefficient increases to 200 W/(m\({}^{2}\)\({}^{\circ}\)C), the minimum device temperature \(T_{\text{min}}\) is 33.946 \({}^{\circ}\)C and the average temperature difference \(\Delta T\) is 3.05 \({}^{\circ}\)C.  
As shown in Figure 2, increasing convective heat transfer coefficient \(h\) at the cold end leads to an increase in temperature difference between two ends of the device, which provides guidance for optimizing power generation performance of the device in a wearable scenario. Figure 2: Temperature field of TEG with different convective heat transfer coefficients at the cold end. (**A**) \(h\) = 5 W/(m\({}^{2. }\)\({}^{\circ}\)C); (**B**) \(h\) = 50 W/(m\({}^{2. }\)\({}^{\circ}\)C); (**C**) \(h\) = 100 W/(m\({}^{2. }\)\({}^{\circ}\)C); (**D**) \(h\) = 200 W/(m\({}^{2.}\)\({}^{\circ}\)C). Power Generation Performance Optimization of TEGs under Different Convective Heat Transfer Coefficients  
Figure 3 shows the \(P_{\text{out}}\) and \(U_{\text{oc}}\) of a TEG with different leg lengths under \(h\) = 5, 50, 100, and 200 W/(m\({}^{2}\)\({}^{\circ}\)C) at the cold end. The results show that the \(P_{\text{out}}\) increases and then decreases as the current increases. Both the maximum \(P_{\text{out}}\) and \(U_{\text{oc}}\) increase gradually with the increase in \(h\) and TE leg length. At \(h\) = 5 W/(m\({}^{2}\)\({}^{\circ}\)C), the maximum \(P_{\text{out}}\) of the TEGs with leg length \(L\) of 0.48 mm, 0.88 mm, 1.38 mm, and 1.88 mm are 0.039 \(\mu\)W, 0.074 \(\mu\)W, 0.117 \(\mu\)W, and 0.161 \(\mu\)W, and the \(U_{\text{oc}}\) of the TEGs is 0.583 mV, 1.07 mV, 1.67 mV, and 2.26 mV, respectively (Figure 3A). The maximum \(P_{\text{out}}\) and \(U_{\text{oc}}\) of the TEG with a leg length of 1.88 mm are 4.1 and 3.9 times higher than those of the \(L\) = 0.48 mm TEG, respectively. As the convective heat transfer coefficient \(h\) increases to 50 W/(m\({}^{2}\)\({}^{\circ}\)C), the maximum output power \(P_{\text{out}}\) of the four TEGs is 3.71 \(\mu\)W, 6.85 \(\mu\)W, 10.5 \(\mu\)W, and 13.8 \(\mu\)W, and the open-circuit voltage \(U_{\text{oc}}\) of the devices is 5.67 mV, 10.2 mV, 15.5 mV, and 20.6 mV (Figure 3B), respectively. The maximum \(P_{\text{out}}\) and \(U_{\text{oc}}\) of the TEG with the longest TE leg are both about three-four times higher than those with the shortest TE leg.