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Energies 2021, 14, 204 5 of 14 Energies 2021, 14, 204 6 of 15 the electrical current which appears in similar work found in the literature is replaced in the current study by using the term ฮฑ(ThโTc) in Equations (3) and (4) to present the relationship . between the heat input Q indicated by Lee [17]. Subsequently, the power output can be calculated as: The friction factor is: The total volume flow rate total is: The efficiency of the TEG module is given by: ๐๔ฑ = ๐๐ด Pout where U is the velocity. ฮทTE = . The pressure drop is calculated by: Qh 2.3. Heat Sink 4๐๐ฟ ๐๐ข๔ฐ ๔ฒ RL +Re n 4๐ด . ๔ฑ๔ต and heat rejection Q versus the electrical load resistance, as h ๐ท=c (16) ๔ฒ 2(๐๔ต +๐ค๔ต) . . ๔ฑฐ๔ฐ ๐ = ๔ต 1.58 ln(๐ ๔ฑฟ ) โ 3.28๔ตก (17) Qh = Pout + Qc (7) 2๐๐ฟ ๐บ๔ฐ The heat sinkโs function is to abso๐ทrb an2d rejec๐ทt he๐at into the surrounding air by โ๐ = = ๔ฒ๔ฒ (19) increasing the heat transfer surface area with fins and spines [18]. This sectionโs main The optimum fin spacing ๐ง๔ฒ can be calculated as: objective is to present the design of a heat sink that can absorb the maximum possible ๔ฒ waste heat coming from the exhaust. To do so, t๔ฑฐh๔ฒe/๔ฐ fin๔ฑฐthickness t and the fin spacing z ๐๔ฒ = 3.24๐ ๐๔ต ๐๐ ๔ฒ๐ฟ f (20f) were optimized. Figure 3 illustrates the heat sink and its design parameters. (18) (8) Figure 3. Forced convection multiple fin array. Figure 3. Forced convection multiple fin array. The overall thermal resistance of the heat sink is given by: 2.4. Effective Material Properties 1 Most TEG module manufacturers do not provide the thermoelectric material prop- Rt = erties. Moreover, the thermoelectric ideal equatitons (i.e., Equations (3) and (4)) do con- ฮทhA (9) sider neither the effect of contact resistance nor the Thomson effect. To resolve these short- The overall efficiency of the heat sink is: comings, the effective material properties presented by Weera et al. [19] were used, where ๔ฐฐAf ๔ฐฑ๔ฑ ๔ฑ these properties were back-calculated from the manufacturerโs maximum parameters. Be- ฮท=1โn 1โฮท sides the virtue of directly obtaining the required matef rial properties, this methodโs ad- vantage is demonstrated in accounting for the errors associated with neglecting the con- tact rTehsiestaontacleasraenadisTchaolcmuslaotnedefbfeyc:ts. The effective thermal conductivity is given by: Moreover, the single fin area is given by: At (10) A=n๔ฑ 2๔ฑL+t๔ฑb +Lz๔ฑ (11) t fH๔ฑSf โ ๐ผโ ๐ =๐โ๐งโ (21) The effective electrical resistivity is g๔ฑiven by๔ฑ: Af =2 L+tf bHS (12) 4๔ฑฑ๐ด๔ฑฒ๐๔ฒ ๐โ = ๐ฟ ๔ฒ๔ฒ๔ฒค (22) ๐(๐ผ๔ฒ๔ฒ๔ฒค)๔ฐPDF Image | Thermoelectric Generator (TEG) System for Automotive Exhaust
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