Mathematical Modeling of Solid Oxide Fuel Cells: a review
https://doi.org/10.1016/J.RSER.2010.12.011Abstract
This paper presents a review of studies on mathematical modeling of solid oxide fuel cells (SOFCs) with respect to the tubular and planar configurations. In this work, both configurations are divided into five subsystems and the factors such as mass/energy/momentum transfer, diffusion through porous media, electrochemical reactions with and without CO oxidation, shift and reforming reactions, and polarization losses inside the subsystems are discussed. Using variety of fuels fed to SOFCs is issued and their effect on the system is compared briefly. A short review of solid oxide fuel cell configurations and different flow manifolding are also presented in this study. Novel models based on statistical data-driven approach existing in the literatures are considered shortly. Although many studies on solid oxide fuel cells modeling have been done, still more research needs to be done to improve the models in order to predict the fuel cell behaviors more accurately. At the end of this pap...
Key takeaways
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AI
- Mathematical modeling of SOFCs enhances understanding of performance under various conditions, focusing on five subsystems.
- SOFCs operate at 800-1000°C, providing high efficiency (50-60%) and internal reforming capabilities for fuel variety.
- Different configurations (tubular vs planar) impact performance and efficiency, with tubular designs having higher ohmic losses.
- Novel data-driven models, including neural networks and Hammerstein models, show promise for predicting SOFC behavior.
- Further research is needed on CO oxidation effects, microstructure influences, and comprehensive heat transfer modeling.
References (198)
- Sopian K, Wan Daud WR. Challenges and future developments in pro- ton exchange membrane fuel cells. Renewable and Sustainable Energy 2006;31:719-27.
- Sopian K, Shamsuddin AH, Nejat Veziroglu T. Solar hydrogen energy option for Malaysia. In: Proceeding of the international conference on advances in strategic technology. 1995. p. 209-29.
- Ramakumar R, Chiradeja P. Distributed generation and renewable energy sys- tems. In: Proceedings of the 37th intersociety energy conversion engineering conference. 2002. p. 716-24.
- Caisheng W, Hashem N. Distributed generation applications of fuel cells. In: Power systems conference: advanced metering, protection, control commu- nication and distributed resources. 2006. p. 244-8.
- Boudghene S, Traversa E. An alternative to standard sources of energy. Renew- able and Sustainable Energy Reviews 2002:297-306.
- Stambouli AB, Traversa E. Solid oxide fuel cells (SOFCs): a review of an envi- ronmentally clean and efficient source of energy. Renewable and Sustainable Energy Reviews 2002;6:433-55.
- Julian M. A distributed power generation communication system. In: Proceed- ings of the IEEE Canadian conference on electronic computer engineering. 2003. p. 483-539.
- Badwal SPS, Foger K. Solid oxide electrolyte fuel cell review. Ceramics Inter- national 1996;22:257-65.
- Zhu WZ, Deevi Sc. A review on the status of anode materials for solid oxide fuel cells. Materials Science and Engineering A 2003;362:228-39.
- Qiu-An Huang RH, Bingwen Wang, Jiujun Zhang. A review of AC impedance modeling and validation in SOFC diagnosis. Electrochimica Acta 2007;52:8144-64.
- Zhang X, Chan SH, Li G, Ho HK, Li J, Feng Z. A review of integration strategies for solid oxide fuel cells. Journal of Power Sources 2010;195:685-702.
- Bhattacharyya D, Rengaswamy R. A review of solid oxide fuel cell (SOFC) dynamic models. Industrial & Engineering Chemistry 2009;48:6068-86.
- Kakac ¸S, Pramuanjaroenkij A, Zhou XY. A review of numerical model- ing of solid oxide fuel cells. International Journal of Hydrogen Energy 2007;32:761-86.
- Lawlor V, Griesser S, Buchinger G, Olabi AG, Cordiner S, Meissner D. Review of the micro-tubular solid oxide fuel cell: Part I. Stack design issues and research activities. Journal of Power Sources 2009;193:387-99.
- Lawlor V, Griesser S, Buchinger G, Olabi AG, Cordiner S, Meissner D. Review of the micro-tubular solid oxide fuel cell: Part I. Stack design issues and research activities. Journal of Power Sources 2009;195:936-1036.
- Andersson M, Yuan J, Sundén B. Review on modeling development for mul- tiscale chemical reactions coupled transport phenomena in solid oxide fuel cells. Applied Energy 2010;87:1461-76.
- Bavarian M, Soroush M, Kevrekidis IG, Benziger JB. Mathematical model- ing, steady-state and dynamic behavior, and control of fuel cells: a review. Industrial & Engineering Chemistry Research 2010.
- O'hayre RBDM, Prinz FB. The triple phase boundary a mathematical model and experimental investigations for fuel cells. Electrochemistry 2005;152:439-44.
- Farooque M, Maru H. Fuel cells-the clean and efficient power generators. IEEE Proceedings 2001;89:1819-29.
- Swider-Lyons Ke CR, Rosenfeld RL, Nowak RJ. Technical issues and oppor- tunities for fuel cell development for autonomous underwater vehicles. In: Proceedings of workshop on autonomous underwater vehicle. 2002. p. 61-4.
- Yakabe H, Sakuri T, Sobue T, Yamashita S, Hase K. Solid oxide fuel cells as promising candidates for distributed generators. IEEE International Confer- ence on Industrial Information 2006:369-74.
- Hajimolana S Ahmad, Soroush M. Dynamics and control of a tubular solid-oxide fuel cell. Industrial & Engineering Chemistry 2009;48:6112- 25.
- Holtappels P, De Haart L, Stimming U, Vinke I, Mogensen M. Reaction of CO/CO2 gas mixtures on Ni-YSZ cermet electrodes. Applied Electrochemistry 1999;29:561-8.
- Matzusaki Y, Hishinuma M, Yasuda I. Proceedings of solid oxide fuel cell. The Electrochemical Society Proceedings Series 1999;5:560-6.
- Mahcene H, Moussa HB, Bouguettaia H, Bechki D, Babay S, Meftah Ms. Study of species, temperature distributions and the solid oxide fuel cells performance in a 2-D model. International Journal of Hydrogen Energy, in press.
- Costamagna P, Costa P, Antonucci V. Micro-modelling of solid oxide fuel cell electrodes. Electrochimica Acta 1998;43:375-94.
- Burt AC, Celik IB, Gemmen RS, Smirnov AV. A numerical study of cell- to-cell variations in a SOFC stack. Journal of Power Sources 2004;126:76- 87.
- Stiller C, Thorud B, Seljebø S, Mathisen Ø, Karoliussen H, Bolland O. Finite- volume modeling and hybrid-cycle performance of planar and tubular solid oxide fuel cells. Journal of Power Sources 2005;141:227-40.
- Ji Y, Yuan K, Chung JN, Chen Y-C. Effects of transport scale on heat/mass trans- fer and performance optimization for solid oxide fuel cells. Journal of Power Sources 2006;161:380-91.
- Chan SH, Khor KA, Xia Zt. A complete polarization model of a solid oxide fuel cell and its sensitivity to the change of cell component thickness. Journal of Power Sources 2001;93:130-40.
- Yakabe H, Ogiwara T, Hishinuma M, Yasuda I. 3-D model calculation for planar Sofc. Journal of Power Sources 2001;102:144-54.
- Bove R, Ubertini S. Modeling solid oxide fuel cell operation: approaches, tech- niques and results. Journal of Power Sources 2006;159:543-59.
- Ho TX, Kosinski P, Hoffmann AC, Vik A. Modeling of transport, chemical and electrochemical phenomena in a cathode-supported SOFC. Chemical Engi- neering Science 2009;64:3000-9.
- Qi Y, Huang B, Chuang Kt. Dynamic modeling of solid oxide fuel cell: the effect of diffusion and inherent impedance. Journal of Power Sources 2005;150:32-47.
- Autissier N, Larrain D, Van Herle J, Favrat D. CFD simulation tool for solid oxide fuel cells. Journal of Power Sources 2004;131:313-9.
- Hussain MM, Li X, Dincer I. A numerical investigation of modeling an SOFC electrode as two finite layers. International Journal of Hydrogen Energy 2009;34:3134-44.
- Hussain MM, Li X, Dincer I. A general electrolyte-electrode-assembly model for the performance characteristics of planar anode-supported solid oxide fuel cells. Journal of Power Sources 2009;189:916-28.
- Izzo Jr JR, Peracchio AA, Chiu WKS. Modeling of gas transport through a tubular solid oxide fuel cell and the porous anode layer. Journal of Power Sources 2008;176:200-6.
- Chaisantikulwat A, Diaz-Goano C, Meadows ES. Dynamic modelling and con- trol of planar anode-supported solid oxide fuel cell. Computers & Chemical Engineering 2008;32:2365-81.
- Cayan FN, Pakalapati SR, Elizalde-Blancas F, Celik I. On modeling multi- component diffusion inside the porous anode of solid oxide fuel cells using Fick's model. Journal of Power Sources 2009;192:467-74.
- Ni M, Leung Dyc, Leung Mkh. Electrochemical modeling and parametric study of methane fed solid oxide fuel cells. Energy Conversion and Management 2009;50:268-78.
- Yakabe H, Hishinuma M, Uratani M, Matsuzaki Y, Yasuda I. Evaluation and modeling of performance of anode-supported solid oxide fuel cell. Journal of Power Sources 2000;86:423-31.
- Qi Y, Huang B, Luo J. Dynamic modeling of a finite volume of solid oxide fuel cell: the effect of transport dynamics. Chemical Engineering Science 2006;61:6057-76.
- Nagata S, Momma A, Kato T, Kasuga Y. Numerical analysis of output char- acteristics of tubular SOFC with internal reformer. Journal of Power Sources 2001;101:60-71.
- Ho TX, Kosinski P, Hoffmann AC, Vik A. Numerical modeling of solid oxide fuel cells. Chemical Engineering Science 2008;63:5356-65.
- Ho TX, Kosinski P, Hoffmann AC, Vik A. Numerical analysis of a planar anode- supported SOFC with composite electrodes. International Journal of Hydrogen Energy 2009;34:3488-99.
- Ni M, Leung DYC, Leung MKH. Importance of pressure gradient in solid oxide fuel cell electrodes for modeling study. Journal of Power Sources 2008;183:668-73.
- Nikooyeh K, Jeje AA, Hill JM. 3D modeling of anode-supported pla- nar SOFC with internal reforming of methane. Journal of Power Sources 2007;171:601-9.
- Morel B, Laurencin J, Bultel Y, Lefebvre-Joud F. Anode-supported sofc model centered on the direct internal reforming. Journal of the Electrochemical Soci- ety 2005;152:1382-9.
- Ferguson JR, Fiard JM, Herbin R. Three-dimensional numerical simulation for various geometries of solid oxide fuel cells. Journal of Power Sources 1996;58:109-22.
- Suwanwarangkul R, Croiset E, Pritzker MD, Fowler MW, Douglas PL, Entchev E. Modelling of a cathode-supported tubular solid oxide fuel cell operating with biomass-derived synthesis gas. Journal of Power Sources 2007;166:386-99.
- Suwanwarangkul R, Croiset E, Fowler MW, Douglas PL, Entchev E, Douglas MA. Performance comparison of Fick's, dusty-gas and Stefan-Maxwell models to predict the concentration overpotential of a SOFC anode. Journal of Power Sources 2003;122:9-18.
- Karcz M. From 0D to 1D modeling of tubular solid oxide fuel cell. Energy Conversion and Management 2009;50:2307-15.
- Bhattacharyya D, Rengaswamy R, Finnerty C. Isothermal models for anode- supported tubular solid oxide fuel cells. Chemical Engineering Science 2007;62:4250-67.
- Virkar AV. Low-temperature anode-supported high power density solid oxide fuel cells with nano-structured electrodes. University of Utah; 2000.
- Kim JW, Virkar AV, Fung KZ, Mentha K, Singhal SC. Polarization effects in inter- mediate temperature, anode-supported solid oxide fuel cells. Electrochemical Society 1999;146:69-78.
- Bove R, Lunghi P, Sammes NM. SOFC mathematic model for systems simulations. Part one: from a micro-detailed to macro-black-box model. International Journal of Hydrogen Energy 2005;30:181-7.
- Sánchez D, Mu ñoz A, Sánchez T. An assessment on convective and radiative heat transfer modelling in tubular solid oxide fuel cells. Journal of Power Sources 2007;169:25-34.
- Sánchez D, Chacartegui R, Mu ñoz A, Sánchez T. On the effect of methane internal reforming modelling in solid oxide fuel cells. International Journal of Hydrogen Energy 2008;33:1834-44.
- Jin X, Xue X. Mathematical modeling analysis of regenerative solid oxide fuel cells in switching mode conditions. Journal of Power Sources 2010;195:6652-8.
- Suwanwarangkul R, Croiset E, Pritzker MD, Fowler MW, Douglas PL, Entchev E. Mechanistic modelling of a cathode-supported tubular solid oxide fuel cell. Journal of Power Sources 2006;154:74-85.
- Zhu H, Kee Rj. A general mathematical model for analyzing the perfor- mance of fuel-cell membrane-electrode assemblies. Journal of Power Sources 2003;117:61-74.
- Jeon DH. A comprehensive CFD model of anode-supported solid oxide fuel cells. Electrochimica Acta 2009;54:2727-36.
- Nam JH, Jeon DH. A comprehensive micro-scale model for transport and reac- tion in intermediate temperature solid oxide fuel cells. Electrochimica Acta 2006;51:3446-60.
- Lehnert W, Meusinger J, Thom F. Modelling of gas transport phenomena in SOFC anodes. Journal of Power Sources 2000;87:57-63.
- Ni M, Leung DYC, Leung MKH. Mathematical modeling of ammonia-fed solid oxide fuel cells with different electrolytes. International Journal of Hydrogen Energy 2008;33:5765-72.
- Janardhanan VM, Deutschmann O. Numerical study of mass and heat trans- port in solid-oxide fuel cells running on humidified methane. Chemical Engineering Science 2007;62:5473-86.
- Suwanwarangkul R, Croiset E, Entchev E, et al. Experimental and modeling study of solid oxide fuel cell operating with syngas fuel. Journal of Power Sources 2006;161:308-22.
- Aloui T, Halouani K. Analytical modeling of polarizations in a solid oxide fuel cell using biomass syngas product as fuel. Applied Thermal Engineering 2007;27:731-7.
- Chen D, Bi W, Kong W, Lin Z. Combined micro-scale and macro-scale modeling of the composite electrode of a solid oxide fuel cell. Journal of Power Sources 2010;195:6598-610.
- Tsai C-L, Schmidt VH. Tortuosity in anode-supported proton conductive solid oxide fuel cell found from current flow rates and dusty-gas model. Journal of Power Sources 2011;196:692-9.
- Tseronis K, Kookos IK, Theodoropoulos C. Modelling mass transport in solid oxide fuel cell anodes: a case for a multidimensional dusty gas-based model. Chemical Engineering Science 2008;63:5626-38.
- Geankoplis CJ. Mass transport phenomena. New York: Holt, Rinehart & Win- ston; 1972.
- Arpino F, Massarotti N. Numerical simulation of mass and energy transport phenomena in solid oxide fuel cells. Energy 2009;34:2033-41.
- Nehter P. Two-dimensional transient model of a cascaded micro-tubular solid oxide fuel cell fed with methane. Journal of Power Sources 2006;157:325-34.
- Bhattacharyya D, Rengaswamy R, Finnerty C. Dynamic modeling and valida- tion studies of a tubular solid oxide fuel cell. Chemical Engineering Science 2009;64:2158-72.
- Dokamaingam P, Assabumrungrat S, Soottitantawat A, Laosiripojana N. Effect of operating conditions and gas flow patterns on the system performances of IIR-SOFC fueled by methanol. International Journal of Hydrogen Energy 2009;34:6415-24.
- Dokamaingam P, Assabumrungrat S, Soottitantawat A, Sramala I, Laosiripo- jana N. Modeling of SOFC with indirect internal reforming operation: comparison of conventional packed-bed and catalytic coated-wall internal reformer. International Journal of Hydrogen Energy 2009;34:410-21.
- Qu Z, Aravind PV, Dekker NJJ, Janssen AHH, Woudstra N, Verkooijen AHM. Three-dimensional thermo-fluid and electrochemical modeling of anode-supported planar solid oxide fuel cell. Journal of Power Sources 2003;195:7787-95.
- Welty Jrw, Wilson CE, Rorrer Re. Fundamentals of momentum, heat, and mass transfer. 4th Edition. New York: Wiley; 2000.
- Perry RGD, Maloney J. Perry's chemical engineers' handbook. 7th ed. McGraw- Hill; 1997.
- El C. Diffusion mass transfer in fluid systems. Cambridge University Press; 1997.
- Xue X, Tang J, Sammes N, Du Y. Dynamic modeling of single tubular SOFC combining heat/mass transfer and electrochemical reaction effects. Journal of Power Sources 2005;142:211-22.
- Monder DS, Nandakumar K, Chuang KT. Model development for a SOFC button cell using H2S as fuel. Journal of Power Sources 2006;162:400-14.
- Shi Y, Cai N, Li C, Bao C, Croiset E. Modeling of an anode-supported Ni-YSZ|Ni-ScSZ|ScSZ|LSM-ScSZ multiple layers SOFC cell Part I. Exper- iments, model development and validation. Journal of Power Sources 2007;172:235-45.
- Xie Y, Xue X. Transient modeling of anode-supported solid oxide fuel cells. International Journal of Hydrogen Energy 2009;34:6882-91.
- Martinez AS, Brouwer J. Modeling and comparison to literature data of composite solid oxide fuel cell electrode-electrolyte interface conductivity. Journal of Power Sources 195; 7268-77.
- Hayes RE, Kolaczkowski ST. Introduction to catalytic combustion. Amster- dam: Gordon and Breach Science Publishers; 1997.
- Damm DL, Fedorov AG. Reduced-order transient thermal modeling for SOFC heating and cooling. Journal of Power Sources 2006;159:956-67.
- Klein JM, Bultel Y, Georges S, Pons M. Modeling of a SOFC fuelled by methane: from direct internal reforming to gradual internal reforming. Chemical Engi- neering Science 2007;62:1636-49.
- Iora P, Aguiar P, Adjimanb CS, Brandon NP. Comparison of two IT DIR-SOFC models: impact of variable thermodynamic, physical, and flow proper- ties. Steady-state and dynamic analysis. Chemical Engineering Science 2005;60:2963-75.
- Colclasure AM, Sanandaji BM, Vincent TL, Kee Rj. Modeling and control of tubular solid-oxide fuel cell systems. I: Physical models and linear model reduction. Journal of Power Sources 2010;196:196-207.
- Modest MF. Radiative heat transfer. 2nd ed. New York: Academic Press; 2003.
- Mauri R. A new application of the reciprocity relations to the study of fluid flows through fixed beds. Engineering Mathematics 1998;33:103-12.
- Song TW, Sohn JL, Kim JH, Kim TS, Ro ST, Suzuki K. Performance analysis of a tubular solid oxide fuel cell/micro gas turbine hybrid power system based on a quasi-two dimensional model. Journal of Power Sources 2005;142: 30-42.
- Kandepu R, Imsland L, Foss BA, Stiller C, Thorud B, Bolland O. Model- ing and control of a SOFC-GT-based autonomous power system. Energy 2007;32:406-17.
- Kang Y, Li J, Cao G, Tu H, Li J, Yang J. One-dimensional dynamic modeling and simulation of a planar direct internal reforming solid oxide fuel cell. Chinese Journal of Chemical Engineering 2009;17:304-17.
- Wang L, Zhang H, Weng S. Modeling and simulation of solid oxide fuel cell based on the volume-resistance characteristic modeling technique. Journal of Power Sources 2008;177:579-89.
- Danilov VA, Tade MO. A CFD-based model of a planar SOFC for anode flow field design. International Journal of Hydrogen Energy 2009;34:8998-9006.
- Li PW, Chyu MK. Simulation of the chemical/electrochemical reactions and heat/mass transfer for a tubular SOFC in a stack. Journal of Power Sources 2003;124:487-98.
- Cui D, Liu L, Dong Y, Cheng M. Comparison of different current collecting modes of anode supported micro-tubular SOFC through mathematical mod- eling. Journal of Power Sources 2007;174:246-54.
- Haberman BA, Young JB. Three-dimensional simulation of chemically reacting gas flows in the porous support structure of an integrated-planar solid oxide fuel cell. International Journal of Heat and Mass Transfer 2004;47:3617-29.
- Ni M. 2D thermal-fluid modeling and parametric analysis of a planar solid oxide fuel cell. Energy Conversion and Management 2010;51:714-21.
- Young DF, Munson BR, Okiishi TH. A brief introduction to fluid mechanics. New York, Chichester, Brisbane, Toronto, Singapore, Weinheim: Wiley; 1996.
- Tien HC, Chiang KC. Non-Darcy flow and heat transfer in a porous insula- tion with infiltration and natural convection. Marine Science & Technology 1999;7:125-31.
- Doraswami U, Droushiotis N, Kelsall GH. Modelling effects of current distri- butions on performance of micro-tubular hollow fibre solid oxide fuel cells. Electrochimica Acta 2010;55:3766-78.
- Vogler M, Horiuchi M, Bessler WG. Modeling, simulation and optimization of a no-chamber solid oxide fuel cell operated with a flat-flame burner. Journal of Power Sources 195:7067-77.
- Aguiar P, Chadwick D, Kershenbaum L. Modelling of an indirect inter- nal reforming solid oxide fuel cell. Chemical Engineering Science 2002;57:1665-77.
- Aguiar P, Adjiman CS, Brandon NP. Anode-supported intermediate- temperature direct internal reforming solid oxide fuel cell: II. Model- based dynamic performance and control. Journal of Power Sources 2005;147:136-47.
- Aguiar P, Adjiman CS, Brandon NP. Anode-supported intermediate tem- perature direct internal reforming solid oxide fuel cell. I: model-based steady-state performance. Journal of Power Sources 2004;138:120-36.
- Murshed AM, Huang B, Nandakumar K. Control relevant modeling of planer solid oxide fuel cell system. Journal of Power Sources 2007;163: 830-45.
- Nagel FP, Schildhauer TJ, Biollaz Sma, Stucki S. Charge, mass and heat trans- fer interactions in solid oxide fuel cells operated with different fuel gases-a sensitivity analysis. Journal of Power Sources 2008;184:129-42.
- Nagel FP, Schildhauer TJ, Biollaz Sma, Wokaun A. Performance comparison of planar, tubular and Delta8 solid oxide fuel cells using a generalized finite volume model. Journal of Power Sources 2008;184:143-64.
- Cheddie DF, Munroe NDH. A dynamic 1D model of a solid oxide fuel cell for real time simulation. Journal of Power Sources 2007;171:634-43.
- Jia J, Abudula A, Wei L, Jiang R, Shen S. A mathematical model of a tubular solid oxide fuel cell with specified combustion zone. Journal of Power Sources 2007;171:696-705.
- Achenbach E. Three-dimensional and time-dependent simulation of a planar solid oxide fuel cell stack. Journal of Power Sources 1994;49:333-48.
- Bessette NF, Wepfer WJ. Prediction of on-design and off-design performance for a solid oxide fuel cell power module. Energy Conversion and Management 1996;37:281-93.
- Costamagna P, Selimovic A, Del Borghi M, Agnew G. Electrochemical model of the integrated planar solid oxide fuel cell (IP-SOFC). Chemical Engineering Journal 2004;102:61-9.
- Achenbach E, Riensche E. Methane/steam reforming kinetics for solid oxide fuel cells. Journal of Power Sources 1994;52:283-8.
- Salogni A. P. C. Modeling of solid oxide fuel cells for dynamic simulations of integrated systems. Applied Thermal Engineering 2009;30:464-77.
- Brus G, Szmyd JS. Numerical modelling of radiative heat transfer in an internal indirect reforming-type SOFC. Journal of Power Sources 2008;181: 8-16.
- Calise F, Dentice D'accadia M, Restuccia G. Simulation of a tubular solid oxide fuel cell through finite volume analysis: Effects of the radiative heat transfer and exergy analysis. International Journal of Hydrogen Energy 2007;32:4575-90.
- Haynes C. Simulating process settings for unslaved SOFC response to increases in load demand. Journal of Power Sources 2002;109:365-76.
- Ma Z. A combined differential and integral model for high temperature fuel cells. PhD Thesis. Georgia: Georgia Institute of Technology; 2000.
- Iwai H, Yamamoto Y, Saito M, Yoshida H. Numerical simulation of intermediate-temperature direct-internal-reforming planar solid oxide fuel cell. Energy 2010:1-10.
- Wang G, Yang Y, Zhang H, Xia W. 3-D model of thermo-fluid and electrochem- ical for planar Sofc. Journal of Power Sources 2007;167:398-405.
- Campanari S. Thermodynamic model and parametric analysis of a tubular SOFC module. Journal of Power Sources 2001;92:26-34.
- Colclasure AM, Sanandaji BM, Vincent TL, Kee Rj. Modeling and control of tubular solid-oxide fuel cell systems. I: Physical models and linear model reduction. Journal of Power Sources 2010;196:196-207.
- Andreassi L, Rubeo G, Ubertini S, Lunghi P, Bove R. Experimental and numer- ical analysis of a radial flow solid oxide fuel cell. International Journal of Hydrogen Energy 2007;32:4559-74.
- Hofmann P, Panopoulos KD, Fryda LE, Kakaras E. Comparison between two methane reforming models applied to a quasi-two-dimensional planar solid oxide fuel cell model. Energy 2009;34:2151-7.
- Li P, Chyu M. Electrochemical and transport phenomena in solid oxide fuel cells. Heat Transfer Transactions ASME 2005;127:1344-62.
- Ho TX, Kosinski P, Hoffmann AC, Vik A. Effects of heat sources on the per- formance of a planar solid oxide fuel cell. International Journal of Hydrogen Energy 2010;35:4276-84.
- Khaleel MA, Lin Z, Singh P, Surdoval W, Collin D. A finite element analysis modeling tool for solid oxide fuel cell development: coupled electrochem- istry, thermal and flow analysis in MARC®. Journal of Power Sources 2004;130:136-48.
- Ni M. Modeling of a solid oxide electrolysis cell for carbon dioxide electrolysis. Chemical Engineering Journal 2010;164:246-54.
- Tang Y, Liu J. Effect of anode and Boudouard reaction catalysts on the per- formance of direct carbon solid oxide fuel cells. International Journal of Hydrogen Energy 2010;35:11188-93.
- Hussain MM, Li X, Dincer I. Mathematical modeling of planar solid oxide fuel cells. Journal of Power Sources 2006;161:1012-22.
- Recknagle KP, Ryan EM, Koeppel BJ, Mahoney LA, Khaleel MA. Modeling of electrochemistry and steam-methane reforming performance for sim- ulating pressurized solid oxide fuel cell stacks. Journal of Power Sources 2010;195:6637-44.
- Akhtar N, Decent SP, Kendall K. Numerical modelling of methane-powered micro-tubular, single-chamber solid oxide fuel cell. Journal of Power Sources 2010;195:7796-807.
- Fuel Cell Handbook. EG&G Services, Parsons, Inc, Sciences Applications Inter- national Corporation; October 2000.
- Petruzzi L, Cocchi S, Fineschi F. A global thermo-electrochemical model for SOFC systems design and engineering. Journal of Power Sources 2003;118:96-107.
- Minh NQ, Takahashi T. Science and technology of ceramic fuel cells. Amster- dam: Elsevier; 1995.
- Neophytides SG. The reversed flow operation of a crossflow solid oxide fuel cell monolith. Chemical Engineering Science 1999;54:4603-13.
- Lazzaretto A, Toffolo A. Energy, economy and environment as objec- tives in multi-criterion optimization of thermal systems design. Energy 2004;29:1139-57.
- Larminie J, Dicks A. Fuel cell systems explained. 3rd ed. Chichester, West Sussex: John Wiley & Sons Inc.; 2003.
- Sleiti AK. Performance of tubular Solid Oxide Fuel Cell at reduced temperature and cathode porosity. Journal of Power Sources 2010;195:5719-25.
- Hirano A, Suzuki M, Ippommatsu M. Evaluation of a new solid oxide fuel cell system by nonisothermal modelling. Journal of Electrochemical Society 1992;139:2744-51.
- Kapadia S, Anderson WK. Sensitivity analysis for solid oxide fuel cells using a three-dimensional numerical model. Journal of Power Sources 2009;189:1074-82.
- Jiang W, Fang R, Khan JA, Dougal RA. Parameter setting and analysis of a dynamic tubular SOFC model. Journal of Power Sources 2006;162: 316-26.
- Jurado F. A method for the identification of solid oxide fuel cells using a Hammerstein model. Journal of Power Sources 2006;154:145-52.
- Sánchez D, Chacartegui R, Mu ñoz A, Sánchez T. Thermal and electrochemi- cal model of internal reforming solid oxide fuel cells with tubular geometry. Journal of Power Sources 2006;160:1074-87.
- Murshed AM, Huang B, Nandakumar K. Estimation and control of solid oxide fuel cell system. Computers & Chemical Engineering 2010;34:96-111.
- Tanaka T, Inui Y, Urata A, Kanno T. Three dimensional analysis of planar solid oxide fuel cell stack considering radiation. Energy Conversion and Manage- ment 2007;48:1491-8.
- Padullés J, Ault GW, Mcdonald JR. An integrated SOFC plant dynamic model for power systems simulation. Journal of Power Sources 2000;86: 495-500.
- Tanner CW, Virkar AV. A simple model for interconnect design of planar solid oxide fuel cells. Journal of Power Sources 2003;113:44-56.
- Daun KJ, Beale SB, Liu F, Smallwood GJ. Radiation heat transfer in planar SOFC electrolytes. Journal of Power Sources 2006;157:302-10.
- Zhang X, Li G, Li J, Feng Z. Numerical study on electric characteristics of solid oxide fuel cells. Energy Conversion and Management 2007;48:977-89.
- Janardhanan VM, Deutschmann O. CFD analysis of a solid oxide fuel cell with internal reforming: coupled interactions of transport, heteroge- neous catalysis and electrochemical processes. Journal of Power Sources 2006;162:1192-202.
- Fardadi M, Mueller F, Jabbari F. Feedback control of solid oxide fuel cell spatial temperature variation. Journal of Power Sources 2010;195:4222-33.
- Damm DL, Fedorov AG. Spectral radiative heat transfer analysis of the planar SOFC. Fuel Cell Science and Technology 2005;2:258-62.
- Ho TX, Kosinski P, Hoffmann AC, Vik A. Transport, chemical and electrochem- ical processes in a planar solid oxide fuel cell: Detailed three-dimensional modeling. Journal of Power Sources 2010;195:6764-73.
- Ahmed K, Foger K. Kinetics of internal steam reforming of methane on Ni/YSZ- based anodes for solid oxide fuel cells. Catalysis Today 2000;63:479-87.
- Vernoux P, Guillodo M, Fouletier J, Hammou A. Alternative anode material for gradual methane reforming in solid oxide fuel cells. Solid State Ionics 2000;135:425-31.
- Liu M, Wei G, Luo J, Sanger AR, Chuang KT. Use of metal sulfides as anode cat- alysts in H2S.air SOFCs. Journal of Electrochemical Society 2003;150:1025-9.
- Slavov SV, Chuang KT, Sanger AR, Donini JC, Kot J, Petrovic S. A proton- conducting solid state H2S-O2 fuel cell. 1. Anode catalysts, and operation at atmospheric pressure and 20-90 • C. International Journal of Hydrogen Energy 1998;23:1203-12.
- Hadvig S. Gas emissivity and absorptivity-a thermodynamic study. Journal of the Institute of Fuel 1970;53:129-35.
- Incropera F, Dewitt D. Fundamentals of heat and mass transfer. 4th ed. New York: Wiley; 1996.
- Ota T, Koyama M, Wen C-J, Yamada K, Takahashi H. Object-based modeling of SOFC system: dynamic behavior of micro-tube SOFC. Journal of Power Sources 2003;118:430-9.
- Yuan J, Rokni M, Sundén B. Three-dimensional computational analysis of gas and heat transport phenomena in ducts relevant for anode-supported solid oxide fuel cells. International Journal of Heat and Mass Transfer 2003;46:809-21.
- Fryda L, Panopoulos KD, Kakaras E. Integrated CHP with autothermal biomass gasification and SOFC-MGT. Energy Conversion and Management 2008;49:281-90.
- Colpan CO, Dincer I, Hamdullahpur F. Thermodynamic modeling of direct internal reforming solid oxide fuel cells operating with syngas. International Journal of Hydrogen Energy 2007;32:787-95.
- Omosun AO, Bauen A, Brandon NP, Adjiman CS, Hart D. Modelling system efficiencies and costs of two biomass-fuelled SOFC systems. Journal of Power Sources 2004;131:96-106.
- Panopoulos KD, Fryda LE, Karl J, Poulou S, Kakaras E. High temperature solid oxide fuel cell integrated with novel allothermal biomass gasification: Part I: Modelling and feasibility study. Journal of Power Sources 2006;159:570-85.
- Cordiner S, Feola M, Mulone V, Romanelli F. Analysis of a SOFC energy gener- ation system fuelled with biomass reformate. Applied Thermal Engineering 2007;27:738-47.
- Van Herle J, Maréchal F, Leuenberger S, Membrez Y, Bucheli O, Favrat D. Pro- cess flow model of solid oxide fuel cell system supplied with sewage biogas. Journal of Power Sources 2004;131:127-41.
- Van Herle J, Maréchal F, Leuenberger S, Favrat D. Energy balance model of a SOFC cogenerator operated with biogas. Journal of Power Sources 2003;118:375-83.
- Vasileiadis S, Ziaka-Vasileiadou Z. Biomass reforming process for inte- grated solid oxide-fuel cell power generation. Chemical Engineering Science 2004;59:4853-9.
- Baron S, Brandon N, Atkinson A, Steele B, Rudkin R. The impact of wood- derived gasification gases on Ni-CGO anodes in intermediate temperature solid oxide fuel cells. Journal of Power Sources 2004;126:58-66.
- Kaneko T, Brouwer J, Samuelsen GS. Power and temperature control of fluc- tuating biomass gas fueled solid oxide fuel cell and micro gas turbine hybrid system. Journal of Power Sources 2006;160:316-25.
- Staniforth J, Kendall K. Biogas powering a small tubular solid oxide fuel cell. Journal of Power Sources 1998;71:275-7.
- Pujare NU, Semkow KW, Sammells AF. A direct H2S/air solid oxide fuel cell. Electrochemical Society 1987;134:2639-40.
- Aguilar L, Zha S, Cheng Z, Winnick J, Liu M. A solid oxide fuel cell operating on hydrogen sulfide (H2S) and sulfur-containing fuels. Journal of Power Sources 2004;135:17-24.
- Wei G-L, Luo J-L, Sanger AR, Chuang KT, Zhong L. Li2SO4-based proton- conducting membrane for H2S-air fuel cell. Journal of Power Sources 2005;145:1-9.
- Yates C, Winnick J. Anode materials for a hydrogen sulfide solid oxide fuel cell. Journal of Electrochemical Society 1999;146:2841-4.
- Liu M, He P, Luo JL, Sanger AR, Chuang KT. Performance of a solid oxide fuel cell utilizing hydrogen sulfide as fuel. Journal of Power Sources 2001;94: 20-5.
- Chuang KT, Sanger AR, Slavov SV, Donini JC. A proton-conducting solid state H2S-O2 fuel cell. 3. Operation using H2S-hydrocarbon mixtures as anode feed. International Journal of Hydrogen Energy 2001;26:103-8.
- Ni M. Computational fluid dynamics modeling of a solid oxide electrolyzer cell for hydrogen production. International Journal of Hydrogen Energy 2009;34:7795-806.
- Brett DJL, et al. Concept and system design for a ZEBRA battery-intermediate temperature solid oxide fuel cell hybrid vehicle. Journal of Power Sources 2006;157:782-98.
- Arpornwichanop A, Chalermpanchai N, Patcharavorachot Y, Assabumrun- grat S, Tade M. Performance of an anode-supported solid oxide fuel cell with direct-internal reforming of ethanol. International Journal of Hydrogen Energy 2009;34:7780-8.
- Entchev E, Yang L. Application of adaptive neuro-fuzzy inference system techniques and artificial neural networks to predict solid oxide fuel cell performance in residential microgeneration installation. Journal of Power Sources 2007;170:122-9.
- Milewski J, Swirski K. Modelling the SOFC behaviours by artificial neural net- work. International Journal of Hydrogen Energy 2009;34:5546-53.
- Huo H-B, Zhong Z-D, Zhu X-J, Tu H-Y. Nonlinear dynamic modeling for a SOFC stack by using a Hammerstein model. Journal of Power Sources 2008;175:441-6.
- Wu X-J, Zhu X-J, Cao G-Y, Tu H-Y. Modeling a SOFC stack based on GA-RBF neural networks identification. Journal of Power Sources 2007;167:145-50.
- Wu X-J, Zhu X-J, Cao G-Y, Tu H-Y. Nonlinear modeling of a SOFC stack based on ANFIS identification. Simulation Modelling Practice and Theory 2008;16:399-409.
- Wu X-J, Zhu X-J, Cao G-Y, Tu H-Y. Dynamic modeling of SOFC based on a T-S fuzzy model. Simulation Modelling Practice and Theory 2008;16:494-504.
- Arriagada J, Olausson P, Selimovic A. Artificial neural network simulator for SOFC performance prediction. Journal of Power Sources 2002;112:54-60.
- Yang J, Li X, Mou H-G, Jian L. Control-oriented thermal management of solid oxide fuel cells based on a modified Takagi-Sugeno fuzzy model. Journal of Power Sources 2009;188:475-82.
- Wu X-J, Zhu X-J, Cao G-Y, Tu H-Y. Nonlinear modelling of a SOFC stack by improved neural networks identification. Journal of Zhejiang University 2007;8:1505-9.
- Huo H-B, Zhu X-J, Cao G-Y. Nonlinear modeling of a SOFC stack based on a least squares support vector machine. Journal of Power Sources 2006;162:1220-5.