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Energies 2021, 14, 204 2.2. Thermoelectric Unit Cell Design To simplify the proposed model, the system was divided into TEG system unit cells. The design of the TEG cell was modelled analytically by six governing Equations (1)–(6). Figure 2 shows the thermoelectric module placed between the heat exchanger (the hot side) and the heat sink (the cold side). Figure 2. The thermoelectric unit cell of the proposed design. Figure 2. The thermoelectric unit cell of the proposed design. • The steady-state heat flow is at a constant rate. sumptions: • The TEG module contact resistances are neglected. • The steady-state heat flow is at a constant rate. • The Thomson effect (which is the temperature-dependent material properties) is • The TEG module contact resistances are neglected. neglected. • The Thomson effect (which is the temperature-dependent material properties) is • The heat transfer that takes place by convection and radiation through the TEG module The governing equations of the system were formulated under the following assumptions: The governing equations of the system were formulated under the following as- neglected. is neglected. • The heat transfer that takes place by convection and radiation through the TEG The six governing equations are as follows: module is neglected. . 4 of 14 The six governing equations are as follows: . Qh = mhCpgas(Th.in − Th.out) (1) 𝑄 =𝑚𝐶𝑝 (𝑇 −𝑇 ) (1) . . . Q=ηhA (Th.in+Th.out)−T (2) h hhh(𝑇+𝑇)h 𝑄=𝜂h𝐴 .2 . −𝑇 (2) 22 α(Th − Tc) 1 α(Th − Tc) . Qh=n α R Th− R Re+Ke(Th−Tc) (3) 𝛼(+𝑇R−𝑇) 1 𝛼(𝑇+−R𝑇) Le2Le 𝑄=𝑛𝛼n𝑅 𝑇− n𝑅 𝑅+𝐾(𝑇−𝑇) (3) 𝑛+𝑅 2𝑛+𝑅2 . α(Th −Tc) 1α(Th −Tc) Qc=nα Tc+ Re+Ke(Th−Tc) (4) RL +Re 2 RL +Re 𝛼(𝑇 −𝑇) 1 𝛼(𝑇 −𝑇) 𝑄=𝑛𝛼n 𝑇+n 𝑅+𝐾(𝑇−𝑇) (4) 𝑅. 𝑅 2 (T +Tc.out) +𝑅 +𝑅 Q=hAT−c.in (5) 𝑛c c c c 𝑛 . . (𝑇.+𝑇.) Q𝑄==mhC𝐴p𝑇 −(T −T c c coolant c.out 2 c.in ) (65) Q. and mc are the mass flow rate of the exhaust gas and the cooling water in kg/s, respectively. is the heat input into the system, and Q. is the heat rejected from the system in Watts. m. hch . 𝑄=𝑚𝐶𝑝 (𝑇−𝑇) (6) . . C𝑄p is the shpeeactiifincphuetaitnotof ethitehesrysetxehmau, astngdas𝑄orifsotrhceohoelanttreinjekctJe/dkgfr·Kom. Tthe asnysdteTm inaWreathtse. c.in c.out 𝑚coolandtw𝑚aterarienltehteanmdaossutfleotwtermatpeeroaftuthreseixnhkaeulsvting,aasnadndsimthielacrloyo,lTingwanadterTinkga/rse,trhee- h.in h.out sinplecttaivnedlyo.u𝐶t𝑝letistetmhepsepreactuifriecshfeoarttohfeeeitxhearuesxthgauss. tTgaasnodrTforarceoothlaenjtuinctkiJo/nkgte·Km.p𝑇eratuarneds hc . 𝑇of theaTreEGthemcoodoulalentinwkaetelvrinin.leht iasntdheouhteleat teramnpseferratcuorefsfiicnieknetlvofine,itahnedr sthimeiclaorolyla,n𝑇t or . . athnede𝑇xhaustargeastihneWin/lemt a·nKd. AoutalentdteAmcpaerreathuerehsefaotrttrhaensefxehraurestasgafos.r 𝑇the𝑎h𝑛o𝑑t𝑇-sidaeresitnhke . 2h and cold-side heat exchanger, respectively. ηh is the overall heat sink efficiency, and n is the number of thermoelements inside the TEG. Ke is the TEG thermal conductance in W/K obtained from the TEG element geometric ratio and element thermal conductivity. Re is the TEG module electrical resistance in ohms obtained from the element geometric ratio and the element electrical resistivity. Finally, the six unknown variables from the .. governing equations are Qh, Qc, Th, Tc, Th.out, and Tc.out. It is also important to note that 2PDF Image | Thermoelectric Generator (TEG) System for Automotive Exhaust
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