A Study on Water Balance in Stationary Load Proton Exchange Membrane(PEM) Fuel Cell Power Generator

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(1)A St udyonWat erBal ancei nSt at i onar yLoadPr ot onExchangeMembr ane( PEM)FuelCel l PowerGener at or/Agung Bakhtiar 외. [논문] 한국태양에너지학회 논문집 Journal of the Korean Solar Energy Society. Vol. 31, No. 4, 2011 IS S N 1 5 9 8 - 6 4 1 1. A Study on Water Balance in Stationary Load Proton Exchange Membrane(PEM) Fuel Cell Power Generator AgungBak ht i ar * Oh,Hoo-Ky u* * Yoon,J ung-I n* * Ki m,Young-Bok * * * Choi ,Kwang-Hwan* * *Gr aduat eSc hoolofRe f r i ge r at i onandAi rCondi t i oni ngEngi ne e r i ng,PukyongNat i onalUni ve r s i t y, **De pt .ofRe f r i ge r at i onandAi rCondi t i oni ngEngi ne e r i ng,PukyongNat i onalUni ve r s i t y, ***De pt .ofMe c hani c alSys t e m Engi ne e r i ng,PukyongNat i onalUni ve r s i t y( c hoi kh@pknu. ac . kr ). 고정 부하를 갖는 PEM 연료전지 발전기에 있어서의 수분 평형에 관한 연구 아궁 박타아르* ,오후규* * ,윤정인* * ,김영복* * * ,최광환* * *냉동공조공학과 대학원,부경대학교, **냉동공조공학과,공과대학,부경대학교( c hoi kh@pknu. ac . kr ) , ***기계시스템공학과,공과대학,부경대학교. Abst r act 일반적으로 PEM 연료전지에서는 수분 균형이 시스템의 효율에 결정적으로 영향을 미치기 때문에,이에 대한 균형 ( bal anc e ) 을 잡는 것이 매우 중요하다.특히,촉매 층에서 물이 넘치는 익수현상( f l oodi ng) 이나 건조현상( dr yi ng) 이 발 생하게 되면 연료전지의 효율이 급격하게 저하하므로,항상 수분의 균형이 잡히도록 시스템을 제어하는 것이 일반적 이다.이 때,수분의 익수현상이나 건조현상은 PEM 연료전지의 용량과 주위의 환경,즉 온도와 습도에 많은 영향을 받게 된다. 금번 논문에서는 가정용 규모인 3kW급에서 1 0 kW급까지의 PEM 연료전지를 설치하였을 때,주위의 환경( 온도와 습도) 이 수분 이동에 어떠한 영향을 미치는 지를 시간에 따라서 시뮬레이션( s i mul a t i on) 한 결과를 보여주고 있다.결과 에서 유입공기의 온도가 5 0 ℃ 이하일 경우,고정부하가 5 kW급 이하이면 대부분이 건조현상이 발생하였으나,고정부하 가 6 kW급 이상이 되면 익수현상이 운전시간이 20 분 이내에서 발생하였다.또한 고정부하를 최고 10 kW급까지 올린 경우,유입공기의 온도가 5 0℃까지는 익수현상이 발생하였으나 6 0℃ 이상인 경우에는 거의 건조현상이 발생함을 알 수 있었다. Ke ywor ds:연료전지( Fue lc e l l ) ,모델링( Mode l l i ng) ,수분평형( Wat e rbal anc e ) ,상시하중( St at i one r ar yl oad) , 수분포화( Wat e re vapor at i on). 투고일자 :2011년 1월 5일,심사일자 :2011년 1월 8일,게재확정일자 :2011년 8월 24일 교신저자 :최광환( choi kh@pknu. ac. kr ). Journal of the Korean Solar Energy Society Vol. 31, No. 4, 2011. 127.

(2) [ 논문]한국태양에너지학회 논문집. Nomencl at ur e   ρ   s ε μ T δ λ .         W. -1. :Mol arr at e ,[ mol · s] :El e c t r oos mot i cdr agc oe f f i c i e nt :de ns i t y,[ kg· c m-3] :Re l at i vemol e c ul armas s , -1 [ kg· mol] :Pe r me abi l i t y,[ m2] :Li qui ds at ur at i onl e ve l ,[ -] :Por os i t y 2 -1 :Dynami cvi s c os i t y,[ m· s] :Te mpe r at ur e ,[ ℃] :Thi c kne s s ,[ m] :Lat e nthe at ,[ kJ · kg-1] :He att r ans f e rc oe f f i c i e nt , -2 -1 [ W· m · K ] -2 :Cur r e ntde ns i t y,[ A· m ] 2 :Cr os ss e c t i onar e a,[ m] -1 :Far adayc ons t ant ,[ C· mol ] -1 :Humi di t yr at i o,[ g· kg ] :Mas s ,[ kg] 3 -1 :Spe c i f i cvol ume ,[ m· kg ] 3 :Vol ume ,[ m] 3 -1 :Fl ow r at e ,[ m· s] :Powe r ,[ Wat t ]. Subscr i pt   r c t s at l i q vap. :c api l l ar i t y :evapor at i on :r eac t i on :s at ur at ed :l i qui d :vapor. 1.I nt r oduct i on A wa t e rma na ge me nti nPEM f ue lc e l lha s as i gni f i c anti mpac tont heove r al ls ys t e m pe r f or manc e ,t he r e f or ei tbe c ome s one of t hemos tc r i t i c ali s s ue sandwi de l ys t udi e d.. 128. Pr ope rwat e rmanage me nts houl d pr ovi de a na d e q ua t eme mbr a nehyd r a t i o na nda vo i d a nc e ofwa t e rf l oodi ngi nt hec at al ys tl a ye r .Thus wa t e rma na ge me nti sac r i t i c a lc ons i de r a t i o n f orbe t t e rde s i gnofPEM f ue lc e l ls ys t e ms . Theamountofwat e randt hedi s pos i t i onof wat e rwi t hi nt he PEM f ue lc e l ls t r ongl y af f e c t se f f i c i e nc yandr e l i abi l i t y[ 1] . The oxi dat i on r e ac t i on t hat pr oduc e s wat e ri n PEM f ue lc e l loc c ur sac t ual l yi n c a t ho de .Thef l oodi ngi nc a t hoder e duc e st he a c t i ver e a c t i o na r e aa nde ve nt ua l l yde c r e a s e s t he pe r f or manc e[ 2 ] .The f l oodi ng oc c ur s whe nt hewat e rpr oduc t i on r at ei shi ghe r t hani t sr e mova lr at e .Howe ve r ,t hef l oodi ng c a nal s ooc c ure ve na tl ow c ur r e ntde ns i t i e s unde rac e r t ai n ope r at i ng c ondi t i ons ,s uc h asl ow t e mpe r at ur e sandhi ghhumi di t y. Thi s pr e s e nt s t udy pr opos e s a wat e r t r ans por t at i onmode lofPEM f ue lc e l land al s ogi ve sas i mul at i onr e s ul t soc c ur r e di n as t a t i o na r yp o we rge ne r a t i o n.Wi t ht hi smo d e l , f l oodi ngons t at i onar ypowe rge ne r at i onc an bepr e di c t e dandi twi l lbehe l pf ulonwat e r ma na ge me nts ys t e mt oge tt hewa t e rba l a nc e .. 2.Pr oposedmodel Bas e dont hepr i nc i pl e sofwat e rbal anc e , an anal yt i c almode li s de ve l ope di nt hi s s e c t i o nt ode s c r i bePEM f ue lc e l l .Thes pe c i f i c a s s umpt i ons f o rt he pr e s e ntmode l l i ng ar e t hef ol l owi ngs . 1)Thef ue lc e l li st r e at e d asal umpe d s ys t e m wi t hauni f or mt e mpe r at ur e . 2)Thegasmi xt ur ei sani nc ompr e s s i bl e andi de al . 3)Gas di f f us i on l aye r ( GDL) ,CCL,and me mbr a nea r ei s o t r o p i ca ndho mo ge ne o us .. 한국태양에너지학회 논문집 Vol. 31, No. 4, 2011.

(3) A St udyonWat erBal ancei nSt at i onar yLoadPr ot onExchangeMembr ane( PEM)FuelCel l PowerGener at or/Agung Bakhtiar 외. 4) The vol t age l os s due t oe l e c t r oni c r e s i s t anc e si sne gl i gi bl e ..                  . Wat e rbal anc ei nc at hodec at al ys tl aye r ( CCL) s houl d be bas e d on t he di f f e r e nt amountbe t we e nr at e ofwat e ri nputand out putass howni nFi g.1.. . ( 3)  .            ( 5)                   . ( 4). ( 6). Thel i qui ds a t ur a t i onr a t i ooft hewat e ri n CCL i st he ngi ve nbyEq.8.. Fi g.1Sc hemat i cofwat erbal anc ei nCCL. Thewat e rge ne r a t i onr a t ei nt heCCLc a n bes i mpl i f i e dande xpr e s s e dast heamount oft hewat e rpr oduc t i on r at ef r om oxyge n r e duc t i onr e ac t i on( ORR)anddr agge df r om t heanodes i deass howni nEq.1[ 2-5] .            . ( 1). Bas e dont heASHRAE s t andar df or mul a t oc al c ul at et heai rpr ope r t i e s [ 6] ,t hei nput wa t e rf r om humi da i rc a nbet he nc a l c ul at e d by us i ng Eq.2t oEq.6.Whe nt hewat e r addi t i oni sl e s st hant hes at ur at e dc ondi t i on, t heavai l abl emol ars pac ef orwat e raddi t i on i sgi ve nbyEq.4.Thee xc e e dwat e rove r t hes at ur at e damountt ur ne di nt ol i qui d.As l ongast hewa t e ri nputi snots at ur a t e d,t he wat e rout puti nt he vaporphas e wi l lbe gi ve n by Eq.5and al s ot hel i qui d phas e gi ve nbyEq.6..      ∆         . ( 7 ).       ∆    . ( 8 ). Many s t udi e s ar er e l at e dt ot hes t e ady s t at ewat e rt r ans por t at i oni nGDL ofPEM f ue lc e l l[ 2 ,5 ,7 ,8 ] .I nt he i rwo r ks ,i twa ss e e n t hatc api l l ar i t yt r ans por ti st he domi nant t r ans por tpr oc e s st or e move wat e rf r om f l oode dGDLs .Mol arf l ow r at eoft hewat e r t r ans por t e dby c api l l ar i t y pr oc e s si sgi ve n byEq.9 .Fur t he r mor e ,t hel i qui ds at ur at i on c ha ngeb yc a p i l l a r i t yp r o c e s si sgi ve nbyEq .1 0 .             ×.   cos          ( 9 )     ∆       . And t he l i qui ds at ur at i on be c ome st he f ol l owi ng.       ∆      ∆  .         . ( 2). ( 10 ). ( 11 ). Thec ont i nuum mode loft he s at ur at i on. Journal of the Korean Solar Energy Society Vol. 31, No. 4, 2011. 129.

(4) [ 논문]한국태양에너지학회 논문집. us e di nt hi spa pe rc anbede s c r i be da sc ubi c ass howni nFi g.2.Thet ot alvol umeoft he c ubei sx3wi t ht ot als ur f ac ear e aof6x2.I f al i qui d phas ei s pr e s e nt e d wi t hl i qui d s at ur at i onl e ve ls ,t hes ur f ac ear e aofl i qui d be c o me s( 4 s +2 ) x2 .He nc et hewa t e re va p o r a t i o n r a t ec a nbede f i ne da sac e r t a i nr a t i obe t we e n t he he att r ans f e rand t he l at e nthe atas gi ve ni nEq.12[ 9] .. s i mul at i on wi t ht he c ur r e nt mode l .The val ue soft he s epar ame t e r si ss uf f i c i e ntt o pr oduc et hede s i r e dpowe rde mand.Among di f f e r e ntc ondi t i ons ,t hepar t i c ul ari nputai r c ondi t i ons ,s uc h ast e mpe r at ur e ,humi di t y, andf ue lc e l lpowe rl oad,ha vebe e nc hange d f orc ompar i s on wi t ht heamountofwat e r t r ans por t at i on. Tabl e1 .Si mul at i onpar amet er s.                 . ( 1 2). Fi g.2Modelofs at ur at i onc ube. ( 1 3). The f i nall i qui ds at ur at i on c an be al s o e xpr e s s e dasf ol l owi ng.       ∆     ∆     ∆   . ( 14 ). 3.Si mul at i onpar amet er s Ta bl e1s howst hepa r a me t e rus e di nt hi s. 130. Val ue 3 -1 0 . 0 8m s 0. 02m2.   . 3. 10 m. N. 448. -4. . 0. 5. κ ε σ. 1. 810 m 0. 6 0. 0625N/ m. -1 8. 2. . 120. h λ. 105. 28W/ mK 2417. 44kJ / kg. 2. 4.Resul tanddi scussi on. The l i qui ds at ur at i on c hange var i e d by e vapor at i on pr oc e s s wi l lbe de s c r i be d as ne xte quat i on.     ∆       . Par ame t e r Q A. Thepowe rde mandoft hef ue lc e l le f f e c t s t oi t sc ur r e ntde ns i t y.Whe nt hep o we rde ma nd washi gh,t hec ur r e ntde ns i t ybe c amehi gh, t he r e f or et hewat e rge ne r at e d by f ue lc e l l r e ac t i on wasal s ohi gh.Thes i mul at i on i n t hi ss t udywasc onduc t e dbyus i ngdi f f e r e nt var i at i onsofs t at i onar ypowe rde mandand t hel i qui ds at ur at i onl e ve l sar ec ompar e das i t sr e s ul t s .Fi r s t l y,wehaves i mul at e dt he mode l i ngus i ngl ow t e mpe r at ur eai r .Att hi s t i me t he ai rpr ope r t i e s of40 ° C and 3 8% R. H. ( r e l at i vehumi di t y)wasr e c ogni z e d as t her e pr e s e nt at i ve .Ther e s ul t swe r es hown i nFi g.3andt hef l oodi ngoc c ur r e donhi gh powe rde mandc ondi t i on.. 한국태양에너지학회 논문집 Vol. 31, No. 4, 2011.

(5) A St udyonWat erBal ancei nSt at i onar yLoadPr ot onExchangeMembr ane( PEM)FuelCel l PowerGener at or/Agung Bakhtiar 외. Fi g .3Si mu l at i onr e s u l t satl owt empe r at u r ean dl owh u mi di t y. Thee a r l i e s tf l oodi nga mongt hes i mul a t e d hasar ous e datt hepowe rde mandof6 kW. I nc as eof6 kW,i tbe gan t of l oods har pl y wi t hs t ar t i ngandt he nf l oode dal mos twi t h 1, 100s e c onds .Ther e as onf ort hef l oodi ng i s be c aus et he c ur r e nt de ns i t y was t he mos thi gh and s ot he amountofwat e r ge ne r at e dbyf ue lc e l lr e ac t i ongi ve ni nEq. 1wa shi gh.Toavoi dt hef l oodi ng,t hei nput a i rt e mp e r a t ur es ho ul dbei nc r e a s e d .I nc r e a s i ng t het e mpe r at ur ewi t houtaddi ng anywat e r wi l li nc r e a s et hee va p o r a t i o no ft hea c c umul a t e d wat e ri ns i det hegasdi f f us i onl aye r .. Fi g .4Si mu l a t i onr e s u l t sa th i g ht e mp e r a t u r ean dl owh u mi d i t y. The r e f or e ,t he s e c ond s i mul at i on was f oc us e dont hei nf l ue nc eoni nc r e as i ng t he i nputai rt e mpe r at ur ef r om 40 ° Ct o5 0° C wi t houtanyhumi di f yi ngpr oc e s s .Thr ough t hes i mul at i on,i twasc l e art hatt hel i qui d s at ur at i onl e ve lde c r e as e dt hef l oodi ng,but t hi sal s oc aus e dt hedr yi ngi nal lc ondi t i ons ass howni nFi g.4. Ther e a s o nt hi sdr yi ngha ppe ne di sbe c a us e t hewat e rge ne r a t i onandt hewat e rr e moval f a i l e dt os t r i ket heba l a nc e .Thewa t e rr e mo va l c aus e dby e vapor at i on asgi ve ni n Eq.1 2 be c ame hi ghe rt han t he wat e rge ne r at i on pr oduc e dbyf ue lc e l lr e ac t i on.The r e f or e ,i n t hi sc as et het ot alamountofwat e raddi t i on s ho ul dbei nc r e a s e dt oa voi dt hedr yi ng.The i nc r e me nto ft hewa t e ra ddi t i o ni sus ua l l ydo ne bya ddi ngt hewa t e ri nt ot hei np uta i r .Ano t he r s i mul a t i o nwa sp e r f o r me dt oi nve s t i ga t ee f f e c t s o ni nc r e a s i ngt hehumi di t yo ft hei nputa i r . Fi g.5hass hown t hes i mul at e dr e s ul t s af t e ri nc r e as i ngonl yt heai rhumi di t yf r om 22 . 7 %( R. H. )t o5 0 %( R. H. )a tai rt e mpe r a t ur e of50° C.Unde rt hi sc ondi t i on t he dr yi ng a ndt he f l oo di nga ppe a r e da tt hes amet i me . Thepowe rde ma ndof6 kW ha st hef l o odi ng, butbe l ow of6 kW hasr e s ul t e di na l ldr yi ng.. Fi g .5Si mu l a t i o nr e s u l t sa th i g ht e mp e r a t u r ea n dh i g hh u mi d i t y. Journal of the Korean Solar Energy Society Vol. 31, No. 4, 2011. 131.

(6) [ 논문]한국태양에너지학회 논문집. Fr om t he s er e s ul t s ,i twas known t hat t he wat e rbal anc e wi l lbe e xi s t e di nt he r angeoft hepowe rde mandbe t we e n4. 2kW and6 kW.Howe ve r ,t he r ewasl i t t l ec hange s ne art hepowe rde mandof3kW t o4. 2kW. Ont heot he rhand,t he6kW hass howna s t e adyc hangeupt ot hedr yi ng.Soi twas wor t hi nve s t i gat i ng t heaf f e c t st oc l os et o t he r ange of6 kW and mor es i mul at i ons we r ee xe c ut e d by f oc us i ng on t he r ange 5kW t o6kW.Fi g.6s howst her e s ul t sof t hi ss i mul at i on and i t bor ec l e ar l y t he di f f e r e ntf l oodi ngs l ope s .. Fi g.7Si mul at i onr es ul t sat5 k W wi t ht emper at ur ev ar i at i on. Fi g.8Si mul at i onr es ul t sat1 0 k W wi t ht emper at ur ev ar i at i on. Fi g.6 Si mul at i on r es ul t satpowerdemand of5 k W t o 6 k W. On as s umi ng t hatt hewat e rbal anc ei s obt ai ne df r om ar oundt hepowe rde mandof 5. 6kW,weal s ope r f or me dt hes i mul at i on byappl yi ngt hehi ghe rpowe rde mandt han i t s bal anc e d poi nt .I nt hi ss i mul at i on,t he f oc us was on t he var i at i ons wi t h t he t e mpe r at ur ec hange s ,40 ℃ t o60 ℃,ast he powe rde mand and t hehumi di t yr at i oar e f i xe d.Thes i mul at i on r e s ul t swe r es hown i nFi g.7.. 132. The s er e s ul t s ,howe ve r ,haves hownt hat t hef l oodi ng s t i l lar os ef r om t hel ow i nl e t ai rt e mpe r at ur e ,e ve nt hei nl e tai ri shumi d. Thehi ghe ra i rt e mpe r a t ur ei s ,t hes t e e pe rt he dr yi ng s l opei s .Sowene e de dt oanal yz e t hei nf l ue nc es pe c i f i c al l ybe t we e n4 0℃ and 50 ℃ by r ai s i ng t hepowe rde mand up t o 10 kW af t e rf i xi ng t he i nl e tai rpr ope r t i e s s ameast hec as eof5. 5kW.Thes i mul at i on r e s ul t sf ort hi swe r es howni nFi g.8andi t r e ve a l e dt ha t et hef l oo di ngha se ve no c c ur r e d notonl yatt he5 0℃,but40℃.I twasal s o c l e a rt ha tt hedi f f e r e nc eo ft hepo we rde mand. 한국태양에너지학회 논문집 Vol. 31, No. 4, 2011.

(7) A St udyonWat erBal ancei nSt at i onar yLoadPr ot onExchangeMembr ane( PEM)FuelCel l PowerGener at or/Agung Bakhtiar 외. c a nc ha nget hes e ns i t i vi t yo ft het e mpe r a t ur e t ot hel i qui ds at ur at i onl e ve li nFi g.7and Fi g.8.Thi sme anst hes l ope soft hel i qui d s at ur at i on l e ve l wi t h di f f e r e nt i nl e t ai r pr ope r t i e shavenotl i ne arr e l at i ons hi pwi t h di f f e r e nts t at i onar ypowe rde mand. Ont heot he rhand,weal s ohadt ol ook i nt ot he t e nde nc y ofl i qui ds at ur at i on t o pr ovet hi sc onc l us i ver e s ul tbe f or er e ac hi ng f l oodi ngi nFi g.8 .Thus ,Fi g.9s howst he l i qui ds a t ur a t i o nc a us e dbyt hedi f f e r e nti nl e t ai rt e mpe r at ur e .. Thee vapor at i onr at ei nt hel ow i nl e tai r t e mpe r at ur ei s ve r ys mal lc ompar e d wi t h t hehi ghi nl e tai rt e mpe r at ur e ,t he r e f or et he l i qui d wat e rpr oduc t i on i nc r e as e sr api dl y. Thel ar ge re vapor at i on r at ewasac qui r e d f r om hi ghe ri nl e tai rt e mpe r at ur eandt hi s phe nome nawasde s c r i be di nFi g.1 0. I naddi t i on,t hee vapor at i onr at e si nc as e of40 ° C and5 0° C ar eve r ys mal l e r .Thi si s c aus e d notonl y by t he l ow t e mpe r at ur e , butal s ot hehi ghhumi di t yoft hei nl e tai r .. 5.Concl usi on. Fi g.9Si mul at i onr es ul t swi t hc api l l ar i t yt r ans por ti nf l oodi ng. The l i qui d wat e ri n CCL i s pr oduc e d whe nt hewat e rvapori sc onde ns e d af t e r s at ur at i on.I ft he l i qui d wat e rr e movali s l owe rt han l i qui d wat e raddi ng,and t he n l i qui d wat e rwi l lbeac c umul at e di nt ot he por eofCCLa nda l s oi nc a t hodeGDL.Thus , t hel i qui d wat e rac c umul at i on i sa ve c t or t hathasapl usval uewhe nt headdi ngr at e ofl i qui dwat e ri sgr e at e rt hant her e moval r a t eo fl i qui dwa t e r .He nc e ,i ft hea c c umul a t e d wa t e rr at ehasapl usval ueandr e mai nsf or l ongpe r i od,t hi swi l lpr oduc eaf l oodi ng. Thec onc l us i onsoft hes i mul at i onr e s ul t s ar ede s c r i be dast hef ol l owi ng:. Fi g.1 0Si mul at i onr es ul t sofev apor at i onr at e. 1.Thef l oodi ng st i l lcan behappened i n c as eoft hel ow t e mpe r at ur eofi nl e tai r , e ve nt hei nl e tai ri shumi di f i e d. 2.Thes l ope soft hel i qui ds at ur at i onl e ve l wi t h di f f e r e nti nl e tai rpr ope r t i e s have not l i ne ar r e l at i ons hi p wi t h di f f e r e nt s t at i onar ypowe rde mand. 3.Thel ow e vapor at i onr at ei sc aus e dnot onl y by t hel ow t e mpe r at ur eonl y,but. Journal of the Korean Solar Energy Society Vol. 31, No. 4, 2011. 133.

(8) [ 논문]한국태양에너지학회 논문집. al s ot hehi ghhumi di t yoft hei nl e tai r .. Ref er ence 1 .M.G.I z e ns o n,R.W.Hi l l ,Pr o c e e d i ngso ft he I MECE2 0 0 2 ,ASMEI nt e r na t i o na lMe c ha ni c a l Engi ne e r i ng Congr e s s& Expos i t i on,pp. 14 7,200 2 2.UgurPas aogul l ar i ,C.Y.Wang,' Li qui d Wa t e rTr a ns po r ti nGa sDi f f us i o nLa ye ro f Po l y me rEl e c t r o l yt eFu e lCe l l s ' ,J .El e c t r o c h e m. Soc .154 ,pp.A399-A4 06,20 04 3.G.Ho o ge r s ,Fue lCe l lTe c hn o l o gyHa n d b o o k . CRC Pr e s s ,200 3 4.N.Sa mme s ,Fue lCe l lTe c hno l o gyRe a c hi ng To wa r dsCo mme r c i a l i z a t i o n,Spr i nge r ,2 0 0 6 5.Le ngMao,Chao-YangWang," Anal ys i s ofCol dSt ar ti nPol yme rEl e c t r ol yt eFue l Ce l l s , "J .El e c t r oc he m.Soc .15 4,pp.B1 39 -B14 6,200 7 6.ASHRAE,2 001ASHRAE Fundame nt al s Handbook,Ne w Yor k,20 01 7.H.J u,' Anal yz i ngt hee f f e c t sofi mmobi l e l i qui ds at ur at i on and s pat i alwe t t abi l i t y var i at i on on l i qui d wat e rt r ans por ti n di f f us i o nme di aofpo l yme re l e c t r o l yt ef ue l c e l l s( PEFCs ) ' ,J our nalofPowe rSour c e s , vol .185 ,pp.55 -62 ,2 008 8.E.C.Kumbur ,K.V.Shar p,andM.M. Me nc h," Ont hee f f e c t i ve ne s sofLe ve r e t t a ppr oa c hf orde s c r i bi ng, "J o ur na lo fPowe r Sour c e s ,vol .16 8,pp.3 56-3 68,20 07 9 .Y.A.Ce nge l ,He a ta ndMa s sTr a ns f e r ,' A Pr a c t i c a lAp p r o a c h ' ,3 r de d i t i o n ,Mc Gr a w-Hi l l , 20 06. 134. 한국태양에너지학회 논문집 Vol. 31, No. 4, 2011.

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