Enhanced heat transfer characteristics and performance of composite thermoelectric devices

Transcription

1 Advancd omputational thods and Exprimnts in Hat Transfr XII 5 Enhancd hat transfr charactristics and prformanc of composit thrmolctric dvics. K. hyu, B. V. K. Rddy,. Barry & J. Li partmnt of chanical Enginring and atrials Scinc, Univrsity of Pittsburgh, USA Abstract Thrmolctric lmnts mad of smiconductor slics layrd onto highly conducting intr-connctor matrials ar trmd as omposit Thrmolctric vic (TE. An intgratd TE (ite is a TE with flow channls drilld through an intr-connctor, it acts as a hat xchangr, dircting th hat transfr btwn th fluid stram and lmnt lgs. In this work, thrmolctric prformanc of such lmnts in trms of powr output P 0, hat input Q h, convrsion fficincy η, lctric currnt and Ohmic and Sbck voltags for various hot surfac tmpraturs T h, load rsistancs R L and smiconductor slic sizs d has bn invstigatd using both analytical and numrical mthods. Th thrmolctric prformanc of TE has bn compard with a gomtrically quivalnt convntional TE lmnt. For an optimum load rsistanc R optml, an incras in T h showd a substantial incras in P 0 and a minor incras in Q h. At T h 550K and 350 K, th optimum η for TE, % and 9% rspctivly lssr and narly four-fold incras in P 0 as compard to th convntional TE is obsrvd. Th smiconductor slic siz d has a significant ffct on th TE prformanc: an obsrvd incras in both P 0 and Q h and dcras in η is a rsult of dcrasing d. At fixd d 5 mm and hot stram inlt tmpratur (450 K valus, th singl-stag ite showd fiv-tims in P 0 and two-fold in η for a flow rat R 500 compard to th valus at R 00. Ths novl TEs hlp xtract largr amounts of wast hat, rduc thrmal strsss and minimiz smiconductor matrial usag as compard to convntional TEs. Kywords: thrmolctrics, wast hat rcovry, convntional, composit, intgrat, analytical solutions, numrical mthods, convrsion fficincy, powr output, voltag, currnt. ISSN (on-lin WIT Transactions on Enginring Scincs, Vol 75, 0 WIT Prss doi:0.495/ht00

2 6 Advancd omputational thods and Exprimnts in Hat Transfr XII Introduction Th high dmand for nrgy rsults in trmndous incras in carbon missions and wast hat rlasd into th atmosphr. It is stimatd that approximatly two-thirds of th supplid input nrgy in fossil-ful powr plants, automobils, stl furnacs, glass mills, industrial hating and cooling systms is rjctd as a wast hat to th surroundings. Thrfor, thr is a nd to xplor th novl tchnologis which must b nvironmntally frindly, small siz, stabl and rliabl. Thrmolctric solid-stat tchnology is on of th viabl tchnologis to xtract nrgy from wast hat and also hlps to mitigat carbon foot-print and grn-hous gas missions. Thrmolctric dvics ar constructd by joining two dissimilar lctrically and thrmally conductiv matrials at a junction. Using th Sbck ffct, ths dvics work as lctric powr gnrators whn th two junctions ar xposd to a tmpratur diffrntial []. Sinc 950, th us of smiconductors has rsultd in major advancs in thrmolctric powr gnration. With th prsnt thrmolctric matrials having figurs of mrit ZT.5, th convrsion fficincis 5-0% in powr gnration can b achivd. Howvr, an incras in fficincy for dirct hat-to-lctricity ar sought through th mthods of nanostructuring and fabrication [, 3], novl bulk dsigns such as cascading [4], multistag [5] and sgmntd [6 8] TEs and us of nw matrials []. Using cascading TEs, Kaib t al. [4] showd that an fficincy of.% can b achivd with hot sid tmpratur T h 550º and cold sid tmpratur T c 30º. Ovr a tmpratur rang of K, ran t al. [6] dvlopd a sgmntd TE and obtaind a convrsion fficincy of 5%. orovr, for T h 973 K and T c 300 K, El-Gnk t al. [7] showd a pak convrsion fficincis of 6.69% and 7.4% for skuttrudit and SiG sgmntd thrmolctric gnrators, rspctivly. ran and Lagrandur [8] also rcntly invstigatd th sgmntd TEs in automotiv wast hat rcovry systms and achivd a powr output of 5W oprating at inlt xhaust gas tmpratur of 650º. Ovr th past fw dcads, TEs hav bn xtnsivly studid using analytical solutions for simplifid cass vn though lctric and tmpratur filds ar multidimnsional in TEs. Sinc hat flux and currnt dnsity ar not in paralll, th thr-dimnsional (3 thrmolctric phnomnon substantially ffcts th ovrall TE prformanc. In th articls [9 ], it has bn shown that 3 simulations ar mor accurat in ral systm dsign and optimization of TEs. Harris t al. [9] using finit volum basd cod invstigatd th dvic prformanc with th prsnc of inrt gas and insulating matrial considring both thrmal and lctrical contact rsistancs at th intrfacs. Hu [0] numrically studid th charactristics of two compact gas-phas hat xchangrs placd at hot and cold sids of th TE to nhanc a hat transfr and fluid flow whil minimizing thrmal strsss. hn t al. [] rcntly implmntd a 3 numrical modl for thrmolctric gnrators in FLUENT- US nvironmnt taking tmpratur-dpndnt thrmolctric proprtis and non-linar fluid-thrmal-lctric multi physics coupld ffcts. WIT Transactions on Enginring Scincs, Vol 75, 0 WIT Prss ISSN (on-lin

3 Advancd omputational thods and Exprimnts in Hat Transfr XII 7 For th systms such as automobil xhaust gass, powr plants and industrial procsss whr larg amounts of wast hat ar availabl, th high convrsion fficincy of th TE alon is not sufficint; th dvic should also b capabl of xtracting mor of th availabl wast hat. A potntial and promising approach is novl composit TE (TE dsign. TEs ar similar to convntional TEs in that thy us p- and n-typ smiconducting matrials, but diffr in that a highly conducting mtal is laminatd btwn th smiconducting matrials. Th bnfit of this dsign rsids in dcras in total intrnal lctrical rsistivity; us substantially lss rar-arth matrials to achiv narly sam prformanc as convntional TEs. To furthr incras th prformanc of TE, an intgratd TE (ite is fabricatd by bonding a conducting mtal with flow channls btwn both p-typ and n-typ thrmolctric matrials. This in-flow dsign capitalizs on rducd lmntal rsistancs, th nd for auxiliary cramic plats, gras and xtrnal hat xchangrs as in convntional dsigns and thus incrasd systm rliability. Thrfor, in this papr, kping ths salint points in mind, initially th prformanc of TEs using both analytical and numrical mthods and thn followd by thrmolctric charactristics of ite applid to wast hat rcovry with numrical solutions hav bn invstigatd for various load rsistancs, hot surfac tmpraturs, smiconductor slic sizs and fluid flow configurations. Analytical solutions for composit thrmolctric dvic onsidr a thrmolcric lmntal lngth dy with a constant cross-sctional ara A (W as shown in Fig. a. This lmnt is xprincing a tmpratur gradint (-dt/dy and carrying an lctric currnt I. Th lmnt sid walls ar kpt adiabatic. Th on-dimnsional govrning quation for hat transport along an lmnt subjctd to assumptions: thrmolctrical proprtis ar tratd as constants, th matrial is homognous and isotropic, is writtn as d T I I dt 0 ( dy ka ka dy In qn (, th scond and third on th lft hand sid rprsnt th Joul hating and Thomson ffcts, rspctivly. A composit thrmolctric lmnt consists of two n-typs bulk crystallin smiconductors connctd in sris via conductor as shown in Fig. b. Th govrning quation for hat transport in th intr-connctor has bn takn from qn ( by dropping th Thomson ffct trm. Using qn ( and th associatd boundary conditions: top and lowr connctors ar subjctd to tmpraturs T h and T c, rspctivly; at th intrfac btwn th smiconductor and conductor matrials, th continuity of currnt dnsity, tmpratur and hat flux conditions ar imposd; th tmpratur distribution in composit lmnt (Fig. b, th intrfac tmpraturs and th hot sid hat transfr rat valuatd using th analytical solutions ar writtn as: For th top smiconductor slic: Y ( Y ( WIT Transactions on Enginring Scincs, Vol 75, 0 WIT Prss ISSN (on-lin

4 Figur : Schmatics of (a convnctional (b composit and (c intgratd TEs. whr, L y Y, c h c T T T T, ka IL, ( T h T c ka L I, s, s,, and L d. For th intr-connctor: ( Y Y Y c (3 In qn (3, ( ( c and c. For th bottom smiconductor slic: ( Y Y (4 Hr, ( (, (,, s s Th intrfac tmpraturs θ and θ, rspctivly ar ] [ ( ( ] ( ( [ k k k k c s c s (5 8 Advancd omputational thods and Exprimnts in Hat Transfr XII ISSN (on-lin WIT Transactions on Enginring Scincs, Vol 75, 0 WIT Prss

5 Advancd omputational thods and Exprimnts in Hat Transfr XII 9 and ks ks A [ ] [ ( ] ks kc ks k s [ ( ] ( ks kc (6 ( kc whr, ( [ ] [ ] ( A c. ks Th hat transfr rat at th hot surfac is writtn as ks A( Th Tc ( Qh sith [ ] L (7 Th powr gnration from th composit TE is valuatd as P0 I RL (8 whr, I is gnratd lctric currnt I ( ( T T ( T T /( R R. i s h s c i L whr, R is th intrnal rsistanc R ( d ( L d d /. i s c s A 3 Numrical solutions for thrmolctric dvics In this sction, th fluid-thrmo-lctric coupld fild thr-dimnsional (3 numrical mthods for thrmolctric dvics (TE considrring Joul hating, Pltir and Thomson ffcts, along with th tmpratur dpndnt thrmolctric proprty variations, hav bn implmntd. 3. Gomtry, govrning quations and boundary conditions Th 3 schmatics of composit TE (TE and intgratd TE (ite bing invstigatd ar shown in Figs. (b and (c, rspctivly. Th top surfac of TE uppr connctor is subjctd to a hot tmpratur T h whil th bottom surfac of TE lowr connctor and top and bottom surfacs of ite ar st at a cold tmpratur T c. Th othr surfacs as shown in Fig. ar kpt adiabatic. In th ite, a hot fluid with tmpratur T in and uniform vlocity U ntrs th inlt and flows through intr-connctor channl and lavs at th xit of th domain (Fig. c. Th intr-connctor innr walls and lft and right sid surfacs ar alon rsponsibl for hat transfr from th hot fluid to thrmolctric lmnts. Th nd surfacs of connctors act as trminals for load rsistanc R L. Th mass, momntum and hat transport in th fluid flow domain ar govrn by th 3 formulation of consrvation quations subjctd to th following assumptions. Th flow is stady, laminar and incomprssibl. Th thrmophysical proprtis of fluid (air ar kpt constant. Similarly, th currnt flow and hat transport in th thrmolctric matrial ar govrn by th continuity of currnt dnsity and th nrgy quations subjctd to crtain assumptions. Th matrials ar htrognous, isotropic and th thrmolctric proprtis ar spcifid as polynomial functions of tmpratur []. WIT Transactions on Enginring Scincs, Vol 75, 0 WIT Prss ISSN (on-lin

6 0 Advancd omputational thods and Exprimnts in Hat Transfr XII Th st of quations govrning th fluid flow and hat transport in th fluid domain and th thrmo-lctric phnomnon in th conductor and smiconductor matrials undr stady-stat conditions ar writtn as: ontinuity quation: Fluid rgion:.v 0 (9 onductor and smiconductor []:.J 0 (0 omntum quation:.( vv P v ( f Enrgy quation: Fluid rgion: ( c ( vt.( k T ( P Smiconductor []: ( kt J TJ.[( T ( T ] 0 (3 T Th scond and third trms in qn (3 rprsnt th Joul hating, Pltir and Thomson ffcts rspctivly. In th conductor matrial, th third trm in th lft hand sid of qn (3 will b omittd. Using th non-ohmic currnt-voltag rlation, th total lctric potntial is th summation of lctrostatic and Sbck potntials and is calculatd as V V V J T (4 OV With rspct to th gomtry shown in Fig., th associatd thrmal and lctrical boundary conditions ar: th out trminal subjctd to zro potntial whil th in trminal kpt at constant currnt dnsity and is valuatd as I V0 T J and 0 (5 A A ( Ri RL whr, R i th total intrnal rsistanc du to smiconductor slics, connctors and intr-connctors matrials and R L is th xtrnal load rsistanc. V 0 is th total built-in opn circuit voltag at no-load condition known as Sbck voltag. ξ dnots th dirction normal to th corrsponding surfac. For th up and down strams of th ite, sufficint buffr lngths 5W and 0W ar providd rspctivly to achiv no thrmal back diffusion at th inlt and outflow condition at th xit of th flow domain. At th intrfac btwn th smiconductor and connctor or intr-connctor matrials, th continuity of tmpratur, currnt dnsity and th hat flux conditions ar imposd. Th TEs powr output P 0, hat input Q h and fficincy η ar valuatd as: T ka TE P0 P0 I RL, Qh T, and (6 k Q f dasi ite h As i As i, i f SV f WIT Transactions on Enginring Scincs, Vol 75, 0 WIT Prss ISSN (on-lin

7 Advancd omputational thods and Exprimnts in Hat Transfr XII 3. Numrical solution procdur Th numrical simulations ar prformd using th finit volum formulation of qns (9 to (3 and th associatd constitutiv rlation qn (4 along with associatd boundary conditions as shown in Fig. and qn (5 in ANSYS-FLUENT US (Usr find Scalar nvironmnt. Th prssur-vlocity coupling is handld using SIPLE algorithm [3]. Th spatial dscrtisation of th convctiv and diffusion trms with powr law schm and prssur trm with standard schm ar don, rspctivly. Th gomtric modls and msh ar gnratd in Gambit.4. Th Sbck potntial and Ohmic lctric potntial distributions (qn (4, continuity of currnt dnsity (qn (0 and th Pltir trm (qn (3 ar calculatd using US filds. Th Ohmic hating, Pltir and Thomson ffcts ar modld as sourc trms (qn (3. Th lctric currnt is valuatd basd on th opn-circuit Sbck voltag producd at th givn load rsistanc R L (qn (5. Th furthr dscription on numrical implmntation of th TE in th FLUENT has bn givn in []. Th convrgnc critria for mass, momntum, nrgy, currnt dnsity, Sbck and Ohmic lctric potntials ar st as 0-5, 0-5, 0-5, 0-0, 0-0 and 0-0, rspctivly. Suitabl grid sizs wr chosn for furthr numrical simulations on both TEs aftr prforming grid indpndnc study. Grid sizs with 0000 and clls ar usd for TE and ite rspctivly to gnrat furthr rsults. Th orthogonal and nonuniform grids ar usd. Th 3 thrmolctric modl has bn validatd with publishd rsults of a thrmolctric gnrator for th cass of (a constant proprtis [] and (b tmpratur-dpndnt proprtis [4] and ar givn in Tabl. Tabl : omparison of thrmolctric gnrator paramtrs at T h 47 o and T c 7 o. Quantity Analytical ANSYS ANSYS Prsnt Prsnt [] (a [4] (b [4] (a (b Q h,w P 0,W η(p 0 /Q h,% I, A Rsults and discussion In this sction, th thrmolctric prformanc of convntional, composit and intgratd thrmolctric dvics (TEs using both analytical and numrical solutions hav bn invstigatd. For th analytical rsults th thrmolctric proprtis ar valuatd at avragd tmpratur of hot and cold surfacs, whr as in th cas of numrical solutions th proprtis ar varid with tmpratur. Th bulk crystallin n-typ (75% Bi T 3 5% Bi S 3 and p-typ (5% Bi T 3 75% Sb T 3,.75% xcss S smiconductors and coppr as a connctor and intr-connctor matrials ar usd to analyz various TEs prformanc. WIT Transactions on Enginring Scincs, Vol 75, 0 WIT Prss ISSN (on-lin

8 Advancd omputational thods and Exprimnts in Hat Transfr XII 4. omposit Thrmolctric vic (TE As shown in Fig. (b, th connctor siz (W 0 mm, 5 mm and L 0.5mm, th distanc btwn th connctors (L 8 mm, th cross-sctional ara of th lmnt (5 5 mm and th cold wall tmpratur (T c 300K ar fixd for furthr TE simulatd rsults. Th influnc of hot wall tmpratur 350 T h (K 550, th load circuitry rsistanc 0-4 R L (Ohms 0 - and th siz of n-typ matrial 0.5 d(mm 3 on th thrmolctric prformanc of TE has bn analysd and compard with gomtrically quivalnt convnctional TE in trms of th powr output P 0, hat input Q h, convrsion fficincy η, producd lctrical currnt I and th Ohmic and Sbck voltags V. For fixd d mm, Figs. (a-( show th variation of P 0, Q h, η, I and Ohmic V with R L for two hot wall tmpraturs T h. In ths Figurs, th solid lins with filld circls and mpty circls rprsnt th numrical and analytical rsults of TE rspctivly, whil th solid lins with filld squars dscribs convctional TE numrical rsults. In Fig. a and c, it is shown that thr xists a maximum powr output P 0 at R L R i and optimum η at a particular rsistanc R L known as optimum load rsistanc R optml for a givn hot wall tmpratur T h, rspctivly. Th R optml incrass with an incras in T h valus whil all othr paramtrs ar kpt constant. Th sam bhaviour is obsrvd in both th TE and convntional TEs. Howvr, mor P 0 and lss R optml valus ar prdictd whn compard to convntional TEs. It is also obsrvd that th optimum η valu of TEs ar % and 9% lssr than convntional TEs at T h 550 K and 350 K, rspctivly. This is du to th mutual intrplay of P 0 and Q h. At a givn T h valu, Q h dcrass with R L and also Q h dcrass with dcrasing T h valus. Th TE xhibitd narly four tims th valu of Q h as compard to th convntional TE as shown Fig. b. Th numrical rsults ar showd minor diffrnc from analytical prdictions and it is du to inclusion of tmpratur dpndnt proprtis variation and nd connctors in th numrical analysis. From Fig. d and, it is obsrvd that for a givn R L valu, an incras in T h rsults in an incras in both I and V valus. Howvr, at a givn T h with an incras in R L lads to a dcras in both I and V valus and vntually approachs zro valus at largr R L valu. Th sam bhaviour is also obsrvd in th convntional TE. orovr, th I valu in th TE is highr whn compard to th convntional TE and th opposit rspons is obsrvd in V. This is du to th total intrnal rsistanc (R i R c +R n of TE bing lss compard to th convntional TE. It is also obsrvd that th diffrnc btwn th ordinat valus of th TE and th convntional TE dcrass with R L in cas of I, whras th sam trnd has not bn shown for V. Th rason is th intrplay btwn th R i and R L valus. Th influnc of smiconductor slic siz d at R otml valus on thrmolctric prformanc of TEs is shown in Fig. 3. Th P 0, Q h and I show xponntial dcay with an incras in d. onvrsly, η shows an xponntial incras trnd. Whil th tmpratur diffrntial T h -T c and lmnt hight L ar maintaind invariant th incrmnt in d rsults th prformanc paramtrs valus of th TE approach th convntional TE valus. For brvity, undr th similar WIT Transactions on Enginring Scincs, Vol 75, 0 WIT Prss ISSN (on-lin

9 Advancd omputational thods and Exprimnts in Hat Transfr XII 3 conditions, th convntional TE dsign prformanc valus ar mntiond in th rspctiv figurs. It is obsrvd that d has a significant ffct on th thrmolctric prformanc of th TE whn d< mm. Howvr, whn >3mm, it shows minimal chang in P 0, Q h, η and I prdictions. This is du to th substantial chang in th TE total R i valu. Figur : Effct of load rsistanc R L on (a powr output (b hat input (c fficincy (d lctrical currnt and ( voltag for various T h valus [d mm]. WIT Transactions on Enginring Scincs, Vol 75, 0 WIT Prss ISSN (on-lin

10 4 Advancd omputational thods and Exprimnts in Hat Transfr XII Figur 3: Th variation of (a hat input, powr output and fficincy and (b lctric currnt and voltag for diffrnt smiconductor sizs d [T h 450 K]. 4. Intgratd Thrmolctric vic (ite Th ite paramtrs: hot fluid inlt tmpratur T in 550K; smiconductor (ntyp and p-typ lmnt siz d 5mm; th hight of modul H 0mm; connctor thicknss t.5mm; th smiconductor and intr-connctor dpth 5 mm and width W 5mm; th distanc btwn lgs L3 0mm; th bottom connctors lngth 0 mm and th top connctor lngth 0 mm ar kpt constant. Figur 4: Effct of R on (a hat input and load rsistanc (b powr output and fficincy and (c lctric currnt and voltag [T in 550 K, d5mm, R L R i ]. WIT Transactions on Enginring Scincs, Vol 75, 0 WIT Prss ISSN (on-lin

11 Advancd omputational thods and Exprimnts in Hat Transfr XII 5 Th ffcts of svral flow rats 50 R(ρU h /µ 500 on ite prformanc in trms of thrmolctric charactristics (P 0, Q h, η, I and V hav bn shown in Fig. 4(a-(c. Th chang in total intrnal rsistanc R i and th prssur drop ΔP/L with R is also dpictd in fig. 4(a and (b, rspctivly. Hr, in fig. 4(a, Q h and Q h rprsnt th total hat transfrrd to th lft and right lgs of th ite modul, rspctivly. For a givn T in 550K, an incras in R shows an nhancmnt in Q h and hnc, rsultd highr T h -T c valus. This incras in T h - T c valu hlps to achiv largr built-in Sbck voltag and which in turn rsults highr powr output P 0. At R 500, fiv-tims in P 0 and two-fold in η ar obtaind compard to th valus at.r 00 Th lctrical charactristics I and V hav shown similar bhaviour with R. It is also noticd that at givn R, th Ohmic voltag drop is highr than th Sbck voltag drop valu. Furthr, th flow rat in th spcifid rang has minimal ffct on R i prdictions and it is shown narly 7% variation. This chang alon is du to th variation in lctrical rsistivity valu with tmpratur. Th ΔP/L shows a non-linar bhaviour with R and it is du to th inclusion of additional prssur drop for th rcirculation zons formation in th main flow channl. 5 onclusions Using analytical and numrical solutions, th prformanc of convntional, composit and intgratd thrmolctric dvics (TEs considring Joul hating, Pltir and Thomson ffcts, along with th tmpratur dpndnt thrmolctric proprty variations, hav bn invtsigatd. Th influncs of hot surfac tmpratur T h, th smiconductor slic siz d and th hot fluid flow rat R on th thrmo-hydraulic-lctrical charactristics i.. powr output P 0, hat input Q h, convrsion fficincy η, prssur drop ΔP/L, producd lctric currnt I, Ohmic and Sbck voltags V of various TE dsigns hav bn studid. Th diffrnc in P 0 s of TE and convntional TE is dcrasd with an incras in load rsistanc R L. It is showd that P 0 rachs a maximum valu whn th intrnal rsistanc R i quals R L. For th TE, th R optml is lowr than convntional TE valu. For both TEs, an incrmnt in th T h showd a marginal incrmnt in R optml. It is also obsrvd that for th TE with d mm cas is % and 9% lowr in maximum η and narly four tims highr in Q h compard to convntional TE valus at T h 550 K and 350 K, rspctivly. Th P 0, Q h and I valus showd an xponntial dcay rspons with an incras in d, howvr, an xponntial rais in η with d is obsrvd. In th limit, d half of th convntional TE lmnt siz, th prformanc of th TE rachs convntional TE valus. Whn d<mm, it is sn that th siz of slic has significant ffct on th prformanc of th TE dsign. For th ite configuration, as R incrass, thr is an nhancmnt in Q h. This highr Q h hlps to achiv a largr Sbck voltag through tmpratur diffrntial T h -T c and which in turn producs highr P 0 valu. At a givn R, th Ohmic voltag drop is highr than th Sbck voltag drop valu. Th ΔP/L shows a non-linar bhaviour with R and it is du to an additional prssur drop occuranc for th rcirculation zons formd in th main channl flow. WIT Transactions on Enginring Scincs, Vol 75, 0 WIT Prss ISSN (on-lin

12 6 Advancd omputational thods and Exprimnts in Hat Transfr XII Th novl TE and ites hlp xtract largr amounts of wast hat, rduc thrmal strsss and minimiz rar-arth matrial usag as compard to convntional TEs, without compromising thir fficincis and prformanc. Rfrncs [] Row,.., (d. Thrmolctrics Handbook acro to Nano. R Prss, Taylor & Francis Group, Boca Raton, 006. [] Snydr, G.J. and S.Tobrr, E., omplx thrmolctric matrials. Natur atrials, 7, pp. 05-4, 008. [3] Tritt, T.., Thrmolctric phnomna, matrials, and applications. Th Annual Rviw of atrials Rsarch, 4, pp , 0. [4] Kaib, H., Aoyama, I., ukoujima,., Kanda, T., Fujimoto, S., Kurosawa, T., Ishimabushi, H., Ishida, K., Rauschr, L., Hata, Y. and Sijirou, vlopmnt of thrmolctric gnrating stackd moduls aiming for 5% of convrsion fficincy. Int. onfrnc on Thrmolctrics, IEEE, pp. 7-3, 005. [5] Liang, G., Zhou, J. and Huang, X., Analytical modl of paralll thrmolctric gnrator. Applid Enrgy, 88, pp , 0. [6] ran,.t., Kossakovski,. and Bll, L.E., odling th building blocks of a 0% _cint sgmntd thrmolctric powr gnrator. Journal of Elctronic atrails, 38(7, pp , 009. [7] El-Gnk,.S., Sabr, H.H. and aillat, T., Efficint sgmntd thrmolctric unicoupls for spac powr applications, Enrgy onvrsion and anagmnt, pp , 003. [8] ran,.t. and Lagrandur, J., Progrss Rport on BSST-Ld US partmnt of Enrgy Automotiv Wast Hat Rcovry Program, Journal of Elctronic atrials, 39 (9, pp. 4-48, 00. [9] Harris, R., Hogan, T., Schock, H.J. and Shih, T., Hat transfr and lctric currnt flow in a thrmolctric coupl. 44th Arospac Scincs ting and Exhibition, AIAA: Rno, Nvada, 575, 006. [0] Hu, K.S.Y., Hat transfr nhancmnt in thrmolctric powr gnration..s, Iowa Stat Univrsity, 009. [] hn,., Rosndahl, L.A. and ondra, T., A thr-dimnsional numrical modl of thrmolctric gnrators in fluid powr systms. Int. J. Hat and ass Transfr, 54, pp , 0. [] Angrist, S.W., irct Enrgy onvrsion. Allyn and Bacon Inc. (Boston, 4th dition, 98. [3] Patankar, S., Numrical Hat Transfr and Fluid Flow. Taylor and Francis,980. [4] Antonova, E.E. and Looman,.., Finit lmnts for thrmolctric dvic analysis in ansys. IEEE Int. onfrnc on Thrmolctrics, pp , 005. WIT Transactions on Enginring Scincs, Vol 75, 0 WIT Prss ISSN (on-lin