Performance Analysis of a Co Flow Planar Anode Supported Solid Oxide Fuel Cell with Internal Reformation

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Roderick Evans
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1 ETM-1 The 1 st Conference of Mechncl Engneerng Network of Thlnd October 007, Chonbur, Thlnd Performnce Anlyss of Co Flow Plnr Anode Supported Sold Oxde Fuel Cell wth Internl Reformton Penyrt Chnd 1*, Wshsnuruk Wechstol 1, Rpeepong Suwnwrngkul, Somch Wongwses 3 nd Jun C. Ordonez 4 1 Automotve nd Alterntve Energy Lb (AAA), eprtment of Mechncl Engneerng, Kng Mongkut s Unversty of Technology Thonbur, Thungkru, Bngkok 10140, Thlnd School of Bo-Chemcl Engneerng nd Technology, Srndhorn Interntonl Insttute of Technology, Thmmsrt Unversty, Rungst, Pthum Thn 111, Thlnd 3 Flud Mechncs, Therml Engneerng nd Multphse Flow Reserch Lb (FUTURE), eprtment of Mechncl Engneerng, Kng Mongkut s Unversty of Technology Thonbur, Thungkru, Bngkok 10140, Thlnd 4 Center of Advnced Power Systems nd eprtment of Mechncl Engneerng, Flord Stte Unversty, Tllhssee, Fl 3310, U.S.A. Abstrct Sold oxde fuel cells (SOFCs) re n lterntve dstrbuted power source due to ther hgh therml cency, low emsson nd multple fuel utlzton. SOFC cn be suppled wth vrous knds of fuels such s nturl gs, crbon monoxde, methnol, ethnol nd hydrocrbon compounds. In ths study, mthemtcl model of co flow plnr node supported sold oxde fuel cell wth nternl reformton of nturl gs hs been developed n MATLAB code. The model solves smultneously mss nd energy trnsport equtons, chemcl s well s electrochemcl rectons. The model cn predct ectvely the temperture nd compound spece dstrbutons s well s the SOFC cell performnce under specfc opertng condtons. The cell performnce s reported for severl opertng temperture nd pressure. The cell performnce s specfed n term of cell voltge nd power densty t ny specfc current densty. The nfluence of electrode mcrostructure on cell performnce ws nvestgted. The smulton results show tht the stedy stte performnce s lmost nsenstve to mcrostructure of cells such s porosty nd tortousty. At stndrd opertng pressure (1 tm) nd 800 ºC wth 41% fuel utlzton, n output cell voltge of 0.73 volt, current densty of 0.38 A/cm wth power densty of W/cm ws predcted. Keywords: Sold Oxde Fuel Cells, Co flow plnr node supported SOFC, Internl reformton, Cell performnce, Electrode mcrostructure 1. Introducton Sold oxde fuel cells (SOFCs) re n energy converson devce tht produces electrcty nd het drectly from gsfed fuels by electrochemcl combnton of fuels nd oxdnts. One cell of SOFCs conssts of nterconnect structures nd three lyer regon composed of two cermc electrodes (node nd cthode) seprted by dense cermc electrolyte. SOFCs operte t hgh temperture round C [1, ] nd ether tmospherc or elevted pressures, whle cn utlze vrety of fuels. Oxygen ons formed t the cthode mgrte through the on conductng electrolyte to the node/electrolyte nterfce where they rect wth the fuel gses producng wter nd crbon doxde whle relesng electrons tht flow v n externl crcut to the cthode/electrolyte nterfce. The flexblty n fuel utlzton s n dvntge of SOFCs over other types of fuel cells. Hydrocrbon fuels cn be suppled drectly to the SOFCs wthout the necessry of pre-reformton process, thus dmnshng the externl reformers [1, ]. In ths work the focus s on the mthemtcl modelng of SOFC behvors wth drect nternl reformton. The plnr SOFC type, whch s the focus of ths work, provdes hgher power densty thn the tubulr type [] due to ts shorter current flow pth nd lower ohmc polrzton loss. Moreover, plnr SOFC s smpler to fbrcte nd cn be mnufctured nto vrous confgurtons [1, ]. The problems ssocted wth the hgh temperture opertng condton of plnr SOFCs re the nternl stress nd selng problem due to non-unform therml expnson cused by non-unform temperture dstrbuton. To overcome such problems, the opertng temperture condton hs been reduced to mmedte rnge (roughly round C). Thnner electrolytes hve been used to reduce the ohmc loss. In ths work node-supported SOFC type ws consdered due to ts sutble confgurton for drect nternl reformton of hydrocrbon fuels. Methne ws used s the suppled fuel n ths study. Reformton process nsde the node s composed of stem-methne reformng recton nd wter gs shft recton [3]. Recently vrous models of gs trnsport nsde the thck porous node hve been proposed by severl reserchers. Ykbe et l. [4] nd Lehnert et l. [5] ppled mss trnsport model smlr to the dusty-gs model (GM) n ther computtonl model. Correspondng *e-ml: penyrt@yhoo.com 157

ETM-1 Suwnwrngkul et l. [6] compred the ccurcy to smulte gs trnsport phenomen nsde node of three dfferent models: Fck s lw model (FM), Stefn Mxwell model (SMM) nd the dusty gs model (GM).

2 ETM-1 Suwnwrngkul et l. [6] compred the ccurcy to smulte gs trnsport phenomen nsde node of three dfferent models: Fck s lw model (FM), Stefn Mxwell model (SMM) nd the dusty gs model (GM). Among the three models, the dusty gs model provded the most ccurcy to predct the gs trnsport behvor nsde node when compred wth the experment on the mss trnsport of H H O-Ar nd CO - CO. Unlke the works by Ykbe et l. nd Lehnert et l., the wter gs shft recton ws omtted n the numercl nlyss by Suwnwrngkul et l. Ackmnn et l. [7] ppled the men trnsport pore model (MTPM) to nlyze the mss trnsport n two dmensonl cell model. They ncluded the ects of chemcl nd electrochemcl rectons on the het trnsfer nd temperture dstrbuton nsde the cell. In ths work, we developed mthemtcl model to predct the cell performnce of co-flow plnr nodesupported sold oxde fuel cells when nturl gs s the suppled fuel. The ects of chemcl nd electrochemcl rectons on the het nd mss trnsports nsde the cell were ncluded n the computtonl nlyss. The concept of optmzed prtl prereformton rto n drect nternl reformton process of nturl gs bsed on the expermentl dt of Meusnger et l. [8] ws ntroduced to prevent excessve temperture grdent cross the cell. The mss trnsport n gs flow chnnels s consdered s mss convecton, whle the mss trnsport nsde the porous electrodes s consdered s mss dffuson. The het trnsfer model s ncluded of convectve het trnsfer between sold nd gs phse s well s conductve het trnsfer n sold cell components. The endothermc het consumed durng the stem - methne reformng nd the exothermc het relesed from the electrochemcl rectons were ncluded s the het sources n the numercl clculton of temperture dstrbuton.. Mthemtcl Modelng The suppled nturl gs to the node ws ssumed to hve the followng compostons: 87% by mole of CH 4, 6% by mole of C H 6 nd % by mole of hgher hydrocrbon wth 30% pre-reformton followng suggeston by Meusnger et l. [8]. Ar suppled to the cthode ws used s the oxdnt. All gses behve s del gses. The electrodes hve homogeneous nd sotropc structures. Mss trnsport n porous electrode s consdered s mss dffuson ccompned by chemcl nd electrochemcl rectons. Stem reformng recton s ssumed to occur t the surfce of node nd wter-gs shfted recton s ssumed to occur nsde the vod volume of node. The electrochemcl recton occurs t the vcnty re of node nd electrolyte nterfce. Fully developed gs flowng through chnnels s consdered s ncompressble n lmnr flow regme due to ts low velocty. Mss trnsport n gs flow chnnels were consdered mnly s pure mss convecton. A schemtc one dmensonl model of co flow plnr node supported sold oxde fuel cell s shown n Fg. 1. Ar nd fuel enter the cell n the sme drecton v the flow chnnels nd dffuse through the porous vod of the electrodes (cthode nd node). The dmenson of cell components nd stndrd prmeters used n clculton re gven n Tble 1. Fgure 1 one dmensonl model of co-flow plnr node-supported SOFC Tble 1 Stndrd prmeters used n ths study Geometrcl prmeters of the cell Anode thckness mm. Anode length 10 cm. Anode porosty (ε) 0 Anode tortuosty (τ).75 Anode pore rdus (r n ) 1 μm. cthode thckness 60 μm. cthode length 10 cm. cthode porosty (ε) 0 cthode tortuosty (τ).75 cthode pore rdus (r c ) 1 μm. electrolyte thckness 60 μm. electrolyte length 10 cm. Chemcl nd electrochemcl prmeters trnsfer cocent (α) 0.5 cthode exchnge current densty (j oc ) 0.1x10 4 [A/m ] node exchnge current densty (j o ) 1x10 4 [A/m ] cthode lmtng current densty (j lm,c ) 1x10 5 [A/m ] electrolyte constnt (A) 9x10 7 [K/ohm*m] electrolyte ctvton energy (G ct ) 100x10 3 [J/mol] frdy constnt (F) C/mole specfc surfce re (A S ) 3x10 6 [m /m 3 ] Therml prmeters node ectve therml conductvty 3 [W m -1 K -1 ] (λ,n ) node convectve het trnsfer 57 [W m - K -1 ] cocent (h n ) cthode ectve therml 3 [W m -1 K -1 ] conductvty (λ,ct ) cthode convectve het trnsfer 49 [W m - K -1 ] cocent (h ct ) electrolyte ectve therml 1 [W m -1 K -1 ] conductvty (λ,elec ) Flow rte of fuel nd r t the nlet fuel flow rte 0.5x10-3 m 3 /mn r flow rte 5x10-3 m 3 /mn Opertng pressure nd temperture of the cell opertng pressure (P) 1 tm opertng temperture (T) 800 ºC 158

3 ETM-1.1 Mss trnsport Mss trnsport n sold oxde fuel cell composed of prts, mss dffuson n porous electrodes nd mss convecton n gs flow chnnels. Snce the cthode s reltvely thn comprble to the node thckness, the mss dffuson n the cthode sde could be omtted n ths computtonl nlyss. Mss blnce n porous node The gs trnsport wthn the node pores, whch s strongly dependent on the node mcrostructure, cn be descrbed by combnng the Stefn Mxwell nd Knudsen dffuson reltons. By ssumng tht the totl pressure s unform throughout the porous node, the mss dffusve flux though the node cn be deduced s n Eq. 1, N yn - yn P dy + = - RT dy (1) n j j k, j= 1,j j where y s the mole frcton, P s pressure nd T s temperture, whle N nd N j re the molr flux of speces nd j, respectvely. k, s the ectve Knudsen dffuson cocent nd j s the ectve dffuson cocent. The ectve dffuson cocent though the porous electrode cn be clculted from, j 1.5 = ψ j or, j ( ε ) = () The Knudsen dffuson cocent ( k, ) nd the ectve Knudsen dffuson ( k, ) cocent for gs spece cn be clculted by Eqs. (3) nd (4), respectvely [9, 10]. k, v 8RT = r 3 π M k, k, j (3) = ψ (4) where ψ s the rto between the porosty nd tortuosty nd M s the moleculr weght of spece. The mss blnce of ll speces n the porous node where both mss dffuson nd chemcl rectons occur s ψ d( y P) RT dt = - N + r (5) Two types of chemcl rectons (methne-stem reformng nd wter-gs shfted rectons) occur t node durng supplyng the fuel cells wth nturl gs. CH 4 + H O CO + 3H (6) CO + H O CO + H (7) The endothermc methne-stem reformng recton occurs t the surfce of node whle the exothermc wter -gs shft recton occurs n the porous vod volume of node. The recton rte of methne-stem reformng recton nd wter-gs shfted recton cn be determned from Arhenus curve fts of the dt reported by Lehnert et l. [5, 11] s n Eqs. (8)-(11), k rf R = k P P - 1 rf CH4 HO ( PH ) 3166 = 395exp - RT K PH P CO R = ksf PH OP CO - K ps k sf 3 pr P CO [mol m -3 s -1 ] (8) [mol m -3 P - s -1 ] (9) [mol m -3 s -1 ] (10) = 171exp - RT [mol m-3 P - s -1 ] (11) where R 1 s the recton rte of methne-stem reformng recton nd R s the recton rte for wter-gs shfted recton, k rf s the forwrd ctlyzed recton rte constnt of the reformng recton nd k sf s the forwrd ctlyzed recton rte constnt of the wter-gs shfted recton. The prmeter R s the unversl gs constnt. K pr s the equlbrum constnt for the stem reformng recton nd K Ps s the equlbrum constnt for the wtergs shfted recton [11]. Both constnts cn be clculted from K pr = 67*10 10 *exp(-0.513z Z Z Z+3.770) P (1) 3 Kps = exp( 0.935Z Z Z ) (13) 1000 Z = 1 T( K) (14) The molr spece formton rte, r n Eq. (5) cn be clculted from Eqs. (15) (19). The mnus sgn refers to the consumng rte of ech speces, whle the plus sgn refers to the producton rte. r CH = -R 4 1 [mol m -3 s -1 ] (15) r HO = -R 1 R [mol m -3 s -1 ] (16) r CO = R 1 R [mol m -3 s -1 ] (17) r H = 3R 1 + R [mol m -3 s -1 ] (18) r = R [mol m -3 s -1 ] (19) CO The current densty from the electrochemcl recton of hydrogen cn be clculted by Frdy s lw. 159

4 ETM-1 N HO N = H j F j = - F (0) (1) Mss blnce n gs flow chnnels The mole frcton of ech gs spece chnges long the flow chnnels length due to the norml molr flux N n y drecton through the porous electrodes. For stedy stte, mss blnce for ech speces cn be deduced s n Eq. (). Note tht the pressure drop long the flow chnnels s ssumed neglgble. df dx = πxυ N(y= 0) () where F s the molr flow rte for speces nd υ s the stochometrc cocent (-1 for rectnt speces nd +1 for product speces).. Het trnsfer wthn the cell The het trnsfer n the porous electrodes nd dense electrolyte s domnted by conducton, T T λ + q 0 + = x y (3) where q s the het source term reflectng both exothermc nd endothermc rectons. The ectve therml conductvty cocent (λ ) conssts of sold conductve cocent (λ S ) nd gs conductve cocent (λ f ), λ = ελ + (1- ε ) λs (4) f The het source term s relted to the chemcl rectons wthn porous node nd the electrochemcl recton t the electrode-electrolyte nterfce. Het consumed durng the methne-stem reformton t the surfce of node s ( ) q = R A Δ H (5) 1 1 S 1 Het relesed durng the wter-gs shfted recton n the vod volume of node s q ( H ) = R ε Δ (6) Het relese from the electrochemcl recton t electrode-electrolyte nterfce s jx ( ) q3( x) = Δ HHO + j(x) V C (7) F where A S s the specfc surfce re (re per volume rto), ε s the porosty nd ΔH s the enthlpy of formton. Het trnsfer t the nterfce between the gs flow chnnels nd the electrode s pure convecton conv, _ q = h (T -T ) (8) where h s the convectve het trnsfer cocent of spece. The temperture term T C, s the verge temperture long the flow chnnels. The temperture T s the surfce temperture of the electrode. All tempertures re ntroduced to the mss blnce models n order to clculte the chemcl knetc constnts..3 Cell electrcl performnce The cell voltge V C s ssumed constnt long the cell length nd cn be clculted by potentl blnce, V C C, = E = - ( η + η + η + η + η ) (9) j 0 ohmc conc, conc,c _ ct, ct, c where E j=0 s the open crcut voltge nd cn be clculted from Nernst s equton, E = p ο ΔG RT H O - ln c 1/ F F p (p ) H O = c p (p ) RT O H ο E + ln 4F (p ) H O (30) where ΔG ο s the net stndrd Gbbs free energy of electrochemcl recton t 1 tm nd 5 ºC, E ο s the stndrd Nernst potentl t 1 tm nd 5 ºC, PH O s the wter prtl pressure, P H s the hydrogen prtl C pressure nd PO s the oxygen prtl pressure. The prmeter η ohmc s ohmc polrzton loss. In SOFCs, ohmc polrzton n node nd cthode s ssumed to be neglgble, hence the ohmc polrzton s only relted to the electrolyte resstnce. η conc s the concentrton polrzton nd η ct s the ctvton polrzton. Therefore the ohmc polrzton bsed the electrolyte resstnce cn be determned from [1] η ohmc t σ E = j(asr ohmc ) = j (31) where t E s the thckness of the electrolyte. The electrolyte conductvty (σ) cn be clculted from, ( - Δ G ct e / (RT) ) A σ = (3) T 160

5 ETM-1 where A s the electrolyte constnt nd ΔG ct s the electrolyte ctvton energy. In cse of SOFCs wth thck node, the nodc concentrton or nodc dffusve polrzton cn be expressed from the Nernst s equton s [13], where η conc, y nd = RT ln F y y y ο H H O ο H y H O (33) 0 y represent the mole frctons t nonzero nd zero current denstes t the node-electrolyte nterfce. The cthodc concentrton polrzton s expressed s [13] η conc, c RT j = ln 1 F j lm, c (34) where j lm,c s the cthode lmtng current densty. The ctvton polrzton terms re relted to the electrochemcl rectons rte. The ctvton polrzton terms locted t the electrode-electrolyte nterfce cn be clculted from the Butler-Vollmer equton [13]. The nodc nd cthodc ctvton polrzton losses re expressed respectvely s, η ct, RT j = rcsn h F j 0, (35) voltge s reported n Fg. 3. The cell opertng pressure s t 1 tm. Fgure shows tht t zero current densty, the open crcut voltge decreses s temperture ncreses; wheres the current densty ncreses, the cell voltge ncreses wth the opertng temperture of the cell. Increse n opertng temperture not only enhnces the rte of electrochemcl recton, but lso ncreses the rte of onc conductvty, whch n turn mnmzes the ohmc contrbuton to the polrzton loss nd thus enhnces the cell voltge nd cell power densty s shown respectvely n Fgs. nd 3. The mthemtcl model predcted tht the mxmum power densty of the cell bout W/cm s gven t the current densty of 0.38 A/cm nd cell voltge of 0.73 volt when the cell s operted t the stndrd pressure of 1 tm nd temperture of 800 ºC. The fuel utlzton s t 41 percent T = 800 o C T = 700 o C T = 650 o C η ct, c RT j = rcsn h F j 0, c (36) where j 0, nd j 0,c re respectvely the nodc nd cthodc current denstes t whch the overvoltge begns to move from zero [1]. The Runge-Kutt method ws used to solve mss dffuson equtons coupled wth the het trnsfer equtons. The molr frcton of spece t y (x, y = 0) s equl to the molr frcton n the gs flow chnnels. At y equl to the node thckness t A, the mss flux N s zero for CH 4, CO nd CO, whle N s gven by the Frdy s lw Eqs. (0) - (1) respectvely for H nd H O. The numercl terton s repeted untl the predcted current densty grees wth the correspondng current densty to the specfed cell voltge (V C ) n Eq. (9). 3. Results nd scusson The developed model cn be used to nvestgte the ect of opertng condtons nd desgn prmeters, especlly the geometry of electrode mcrostructures on the performnce of co flow plnr node supported SOFC. The ect of opertng temperture on the cell current densty nd voltge s reported n Fg.. The ect of temperture on the cell power densty nd Fgure Effect of temperture on cell voltge nd current densty Power densty (W/cm ) T = 800 o C T = 700 o C T = 650 o C Fgure 3 Effect of temperture on cell power densty nd current densty 161

6 ETM-1 Fgures 4 nd 5 show the ects of pressure on the cell voltge nd on power densty t the specfed current densty respectvely. Both cell voltge nd power densty ncrese wth the opertng pressure due to the ncrese n rectnt concentrton. However, ncrese n opertng pressure my result n gs selng problems [1]. In order to study the ects of cell geometry such s porosty, tortuosty, pore-rdus nd electrolyte thckness on the cell performnce, the opertng condton s set t 800 ºC nd 1 tm. The ects of porosty on cell voltge nd on power densty t the specfed current densty re shown respectvely n Fgs. 6 nd 7. The cell voltge nd power densty only ncreses wth the porosty t hgh current densty. Normlly the concentrton polrzton loss decreses, whle the ohmc polrzton loss ncreses s the porosty ncreses. Ths mples tht the concentrton polrzton loss s the domnnt loss t hgh current densty. The ects of tortuosty on the cell performnce re reported n Fgs As the tortuosty ncreses the spece dffuson rte decrese; hence the recton rte decreses cusng the cell voltge nd power densty to decrese. The ects of the pore-rdus on the sngle cell performnce re reported n Fgs As the pore sze ncreses, the spece dffuson resstnce decreses; thus the cell voltge nd the power densty ncrese. Fgures 1-13 show the ects of electrolyte thckness on the cell performnce. The cell voltge nd power densty t specfed current densty ncrese s the electrolyte thckness decreses due to the decrese n ohmc loss. 4. Conclusons A mthemtcl model for predctng the performnce of co flow plnr node supported sold oxde fuel cell wth nternl reformton of nturl gs ws developed n MATLAB code. The model solved smultneously mss nd energy trnsport equtons s well s chemcl nd electrochemcl rectons. The model cn predct the cell performnce t vrous opertng condtons. The model s useful n nlyzng the ects of porosty, tortuosty nd pore rdus on the cell performnce. The performnce of the cell ws reported n terms of cell voltge nd power densty t specfed current denstes for severl opertng temperture nd pressure P = 5 tm P = 3 tm P = 1 tm Power densty (W/cm ) P = 5 tm P = 3 tm P = 1 tm Fgure 4 Effect of pressure on cell voltge Fgure 5 Effect of pressure on cell power densty ε = 0 ε = 0.5 ε = 0 Power densty (W/cm ) ε = 0 ε = 0.5 ε = Fgure 6 Effect of porosty on cell voltge Fgure 7 Effect of porosty on cell power densty 16

7 ETM τ =.50 τ =.75 τ = 3.00 Power densty (W/cm ).5.0 τ =.50 τ =.75 τ = Fgure 8 Effect of tortuosty on cell voltge Fgure 9 Effect of tortuosty on cell power densty R =.00 μm R = 1.50 μm R = 0 μm R = 0.75 μm Power densty (W/cm ) R =.00 μm R = 1.50 μm R = 0 μm R = 0.75 μm Fgure 10 Effect of pore rdus on cell voltge Fgure 11 Effect of pore rdus on cell power densty t e = 0 μm t e = 40 μm t e = 60 μm Power densty (W/cm ) t e = 0 μm. t e = 40 μm. t e = 60 μm Fgure 1 Effect of electrolyte thckness on cell voltge Fgure 13 Effect of electrolyte thckness on cell power densty 163

8 ETM-1 Acknowledgement Authors would lke to cknowledge wth sncere grttude to the Thlnd Reserch Fund nd Offce of the Ntonl Reserch Councl of Thlnd for provdng the fnncl support. References [1] Snghl, S.C., nd Kendll, K., 003. Hgh Temperture Sold Oxde Fuel Cells : Fundmentls esgn nd Applctons. Elsever Ltd, Oxford, U.K. [] Lrmne, J., nd cks, A., 000. Fuel Cell Systems Explned. John Wley nd Sons Ltd, Chchester [3] Agur, P., Adjmn, C.S. nd Brndon, N.P., 004. Anode Supported Intermedte Temperture rect Internl Reformng Sold Oxde Fuel Cell I: model bsed stedy - stte. Journl of Power Sources, Vol. 138, pp [4] Ykbe, H., Hshnum, M. Urtn, M.,.Mtsuzk, Y., nd Ysud, I Evluton nd Modelng of Performnce of Anode Supported Sold Oxde Fuel Cell. Journl of Power Sources, Vol. 86, pp [5] Lehnert, W., Meusnger, J., nd Thom, F., 000. Modelng of Gs Trnsport Phenomen n SOFC Anodes. Journl of Power Sources, Vol. 87, pp [6] Suwnwrngkul, R., Croset, E., Fowler, M.W., ougls, P.L., Entchev, E., nd ougls, M.A., 003. Performnce Comprson of Fck s, usty gs nd Stfn Mxwell Models to Predct the Concentrton Overpotentl of SOFC Anode. Journl of Power Sources, Vol. 1, pp [7] Ackmnn, T., e Hrt, L. G. J., Lehnert, W. nd Stolten,., 003. Modelng of Mss nd Het Trnsport n Plnr substrte Type SOFCs. Journl of the Electrochemcl Socety, Vol. 150(6), pp. A783-A789 [8] Meusnger, J., Rensche, E. nd Stmmng, U., Reformng of Nturl Gs n Sold Oxde Fuel Cell Systems. Journl of Power Sources, Vol. 71, pp [9] Brd, R.B., Stewrt, W.E. nd Lghtfoot, E.N., 001. Trnsport Phenomen., Second edton, John Wley nd Sons, New York, U.S.A. [10] Tod, B., nd Young, J.B., 00., Thermodynmcs nd Trnsport Propertes of Gses for Use n Sold Oxde Fuel Cell Modelng., Journl of Power Sources, Vol. 110, pp [11] Hbermn, B.A., nd Young, J.B., 004., Three mensonl Smulton of Chemclly Rectng Gs Flows n the Porous Support Structure of n Integrted-Plnr Sold Oxde Fuel Cell., Interntonl Journl of Het nd Mss Trnsfer, Vol. 47, pp [1] Hyre, R.O., Won Ch, S., Colell W. nd Prnz, F. B., 006. Fuel Cell Fundmentls., John Wley nd Sons, New York, U.S.A. [13] Morel, B., Lurencn, J., Bultel, Y. nd Lefebvre- Joud, F., 005., Anode Supported SOFC Model Centered on the rect Internl Reformng., Journl of the Electrochemcl Socety, Vol. 15(7), pp. A138-A

MACRO-LEVEL MODELING OF PLANAR DIRECT INTERNAL REFORMING SOLID OXIDE FUEL CELLS CAN OZGUR COLPAN. Carleton University

MACRO-LEVEL MODELING OF PLANAR DIRECT INTERNAL REFORMING SOLID OXIDE FUEL CELLS CAN OZGUR COLPAN. Carleton University MACR-LEVEL MDELIG PLAAR DIRECT ITERAL RERMIG SLID XIDE UEL CELLS CA ZGUR CLPA Crleton Unversty tonl Reserch Councl Cnd-Insttute or Chemcl Process nd Envronmentl Technology June 6, 008 - ttw, Cnd UTLIE