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Energies 2021, 14, 204 9 of 14 temperature of 90 ◦C and flow rate of 0.237 kg/s. In order to simplify the approach towards the presented results, the analysis and experimental work were conducted on one TEG unit cell where the hot inlet air and cooling water temperatures were averaged in the middle of the whole system, assuming a linear change of the temperatures along the whole system as proven by Fagehi [2]. After the power output and power density of the unit cell were determined, the result of the whole system was extrapolated using the obtained power density of the unit cell. 4.1. Prediction of Effective Material Properties To establish the accuracy of the effective material properties as in Equations (21)–(24), a commercial thermoelectric module was tested, with the results of the module performance shown in Table 1 and Figure 7. The results show the relationship between voltage and output power versus hot junction temperature for predicted values using effective material properties and manufacturer’s data. A comparison of the predicted results with the manufacturer’s data shows an excellent agreement, indicating the validity of the effective material properties approach. The calculated effective material properties are shown in Table 1. Figure 7 shows a comparison between the predicted performance using the effective material properties and the manufacturer’s performance. Table 1. The results of effective material properties for (TMG-127-1.0-0.8) at Th = 200 ◦C, Tc = 30 ◦C, n=127, Ae =1mm2,andLe =1.35mm. Energies 2021, 14, 204 Vmax =3.0V α∗=314.96μ·V Input Parameters (from Manufacturer) Imax =3.0A Wmax =5.1W Effective Material Properties ηmp =4.8% z∗=1.492×10−31 k∗=0.03 W ρ∗=2.23×10−3Ω·cm Kcm·K K 10 of 15 Figure 7. Comparison between the predicted performance using the effective material properties Figure 7. Comparison between the predicted performance using the effective material properties and the manufacturer’s performance. and the manufacturer’s performance. TableTh1.eTheartesuinltks’osftoeftfaelcthiveeatmtraatenrsiafelrproapterwtieasfcoarl(cTuMlaGte-d12b7-y1.o0p-0t.i8m)aizti𝑇ng=th2e00fin°Ct,h𝑇ick=ness 30°C, 𝑛=127, 𝐴 =1mm,and 𝐿 =1.35mm. using Equations(9)–(19), and was found to be 2 mm, as shown in Figure 8. Moreover, the optimum fin spacing was independently calculated using Equation (20), and was found to Input Parameters (from Manufacturer) be 1.35 mm. The total heat transfer rate at optimum fin spacing and thickness was 166 W. 𝑉 =3.0V 𝐼 =3.0A 𝑊 =5.1W 𝜂 =4.8% The pressure drop along the whole system had a significant effect on automotive engine Effective Material Properties performance and fuel consumption, and was found to be 0.27 Pa—well below the limit of ∗ μ.V∗ W∗ ∗ 1 812 Pa indicated by Kumar et al. [20].𝜌 = 2.23 × 10 Ω. cm 𝛼 =314.96 K 𝑘 =0.03cm.K 𝑧 =1.492×10 K The heat sink’s total heat transfer rate was calculated by optimizing the fin thickness using Equations (9)–(19), and was found to be 2 mm, as shown in Figure 8. Moreover, the optimum fin spacing was independently calculated using Equation (20), and was found to be 1.35 mm. The total heat transfer rate at optimum fin spacing and thickness was 166PDF Image | Thermoelectric Generator (TEG) System for Automotive Exhaust
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