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Energies 2021, 14, 204 6 of 14 The heat transfer coefficient is given by: h = NuKw Dh The turbulent flow Nusselt number inside a duct is: f (Re − 1000)Pr (13) (14) (15) (16) (17) (18) (19) (20) The Reynold’s number is: 1+12.72 Pr −1 Re = UwDh N=2 u f0.5 2/3 υw The hydraulic diameter is calculated as: Dh = 4Acw 2(bw +wb) The friction factor is: The total volume flow rate total is: where U is the velocity. The pressure drop is calculated by: 4fL ρu2m 2fL G2 ∆P=Dh 2=Dhρ Theoptimumfinspacingzf canbecalculatedas: Zf =3.24Re−1/2Pr−14L 2.4. Effective Material Properties f = [1.58 ln(Re) − 3.28]−2 Vt = U A Most TEG module manufacturers do not provide the thermoelectric material proper- ties. Moreover, the thermoelectric ideal equations (i.e., Equations (3) and (4)) do consider neither the effect of contact resistance nor the Thomson effect. To resolve these shortcom- ings, the effective material properties presented by Weera et al. [19] were used, where these properties were back-calculated from the manufacturer’s maximum parameters. Besides the virtue of directly obtaining the required material properties, this method’s advantage is demonstrated in accounting for the errors associated with neglecting the contact resistances and Thomson effects. The effective thermal conductivity is given by: ∗ α∗2 k=∗∗ (21) ρz The effective electrical resistivity is given by: ρ∗= L max (22) n(Imax)2 L 4 A W.PDF Image | Thermoelectric Generator (TEG) System for Automotive Exhaust
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