Mathematical modeling of direct liquid fuel cells multidimensional analytical solutions and experimental validation

Mathematical Modeling of Direct Liquid Fuel Cells Multidimensional Analytical Solutions and Experimental Validation EE SHER LIN (B. Eng, Hons.) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF CHEMICAL AND BIOMOLECULAR ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2011 Typeset with AMS-LATEX. Doctor of Philosophy thesis for public evaluation, National University of Singapore, Engineering Drive 4. c Ee Sher Lin 2011 To my loved ones, who always support me, no matter what. The farmer who plants your rice, the parents who sacri…ce, the seas mercilessly rise, and the love we hold alive, we are all connected in this circle of life, yocto, one, yotta, likewise, in here, the yearn to contribute to us, to knowledge and science that always last. v Acknowledgements I would like to thank my supervisor, Dr. Karl Erik Birgersson for his guidance and willingness to share his knowledge. Hi Erik, thank you for imparting a set of wellrounded skills of signi…cant relevance working in this world. I always enjoyed the sharing of ideas, views and insights, and the many open and honest discussions. Thank you for mentoring me through my PhD candidature; for this I will always be grateful. I would also like to thank all of my groupmates Hung, Jundika, Agus, Ashwini, Praveen, and Karthik and my NUS friends for the many fruitful discussions that are both enlightening and motivating. I would also like to thank Chiu Jin Ping and Sadegh for been such a great friend in many ways possible. Sadegh, you have an inspiring character, remain this way and thank you so much for your many sel‡ess acts! Jin Ping, thank you for always supporting my choices in life! Its a great pleasure to have met Prof. Bill William Krantz during my candidature. Thank you Prof. Krantz for been a great teacher. You bring the best out of people. Thanks for the many inspirations and always looking out to maximize the potential in each of us. Thanks for your high regards that help to keep me motivated even till this day. Thank you Assoc. Prof Laksh and Dr. Saif Khan for accepting to be examiners of this thesis. I still remember the questions asked during my PhD qualifying, which I am very thankful of. I would like to thank Prof. Sundmacher for accepting to be the external examiner: Obwohl natürlich Sie Englisch können denke ich, dass es schön ist, wenn ich mich auf Deutsch bei Ihnen bedanke. Ich danke Ihnen sehr für Ihre Bereitschaft, meine Doktorarbeit zu korrigieren und danke Ihnen für Ihr Feedback schon im Voraus. Ich glaube, Ihr Kommentar wird sicherlich sehr hilfreich sein. I would also like to thank the Ministry of Education, Singapore for the scholarship that makes this PhD possible. Special thanks to Prof. Lee Jim Yang for allowing me to use the equipments and vi materials in the lab. vii My loved ones: My family and Rocky, you are my support, joy, and laughter, always believing and always proud of me, especially my mother, Maggie, who support me wholeheartedly through the interesting ups and downs of many aspects in life. My family, the …ve of you, are the peace in my heart, and de…nitely my pride. My best friend, Christiana Shen, without whom I would never have had the opportunity to an overseas degree, not mentioning my PhD. Your unwavering support I will remember my whole life, and should there be eternity, I will make sure my gratefulness are etched on it. Thank you Jie for always sel‡essly support my every paths in life. My husband, Khoo Geek Seng, You have been so understanding and supportive through my PhD, and always want the best for whatever I embark in. Whenever I have an idea or question or thoughts, I know I can count on you for the best discussion. Your insights are always hit-on. Thank you for your love and for believing nothing is too di¢ cult for me. Finally, my loved ones, this thesis is dedicated to you. Contents Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Introduction 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Technical and Implementation Issues with the DLFC . . . . . . . . . . . 1.3 DLFC Modeling and Experimental Validation . . . . . . . . . . . . . . . 1.4 Aim and Structure of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . Literature Review 15 2.1 Simpli…cations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2 Available Analytical Solutions for DLFC models . . . . . . . . . . . . . 25 2.3 Experimental Validation Strategy . . . . . . . . . . . . . . . . . . . . . . 26 2.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Mathematical Formulation 3.1 29 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v 29 vi CONTENTS 3.2 Single phase model (2D and 3D) . . . . . . . . . . . . . . . . . . . . . . 33 3.3 Two phase model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.4 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.5 Constitutive Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.6 Electrokinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.7 Numerics and Symbolic Computations . . . . . . . . . . . . . . . . . . . 47 3.8 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Scale Analysis 51 4.1 Model Reduction based on Scale Analysis . . . . . . . . . . . . . . . . . 51 4.2 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Experimental Setup 57 5.1 Fuel Cell System and Cell Assembly . . . . . . . . . . . . . . . . . . . . 57 5.2 Cell-conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.3 Steady-state Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Two-Dimensional Approximate Analytical Solutions for the Anode 63 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 6.2 Mathematical Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 64 6.3 Reduced Mathematical Formulation . . . . . . . . . . . . . . . . . . . . 66 6.4 Solutions for the Di¤usion Layer . . . . . . . . . . . . . . . . . . . . . . 66 6.5 Solutions for the Porous Flow Field . . . . . . . . . . . . . . . . . . . . . 70 6.6 Solutions for a Flow Channel . . . . . . . . . . . . . . . . . . . . . . . . 74 6.7 Symbolic computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6.8 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6.9 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Two-Dimensional Approximate Analytical Solutions for the Full Cell 83 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 7.2 Mathematical Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 84 7.3 Symbolic computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 7.4 Calibration and Validation . . . . . . . . . . . . . . . . . . . . . . . . . . 85 7.5 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 CONTENTS 7.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Three-Dimensional Approximate Analytical Solutions vii 98 101 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 8.2 Mathematical Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 103 8.3 Numerics and Symbolic Computations . . . . . . . . . . . . . . . . . . . 103 8.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 8.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Experimental Validation with Design of Experiments 119 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 9.2 Mathematical Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 120 9.3 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 9.4 Calibration and Validation . . . . . . . . . . . . . . . . . . . . . . . . . . 123 9.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 10 Conclusions and Outlook 127 10.1 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 10.2 Applications and Future Work . . . . . . . . . . . . . . . . . . . . . . . 129 10.3 Conference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Publications 135 Appendix A 142 Appendix B 143 Bibliography 146 144 Publications and the solution to is derived by expressing Eq. at y = to …nally give the following new expression for ic ic (x) = i(x) + ip (x) = a I X ci e a ix ; (B-5) i=1 where a = Malc =( (l) D (l) zF C ). alc The above simpli…es the expression for ic to be only dependent on the streamwise direction, x: Generalized Fourier coe¢ cients With the method of eigenfunction expansion [211, 230], the generalized Fourier coe¢ cients is given by aj (x) = aj (0) exp( j c (x)x) + exp( j Z x (x)x) fj (x0 ) exp( j c {z |0 aj where fj (x) = R hcfc F (x; y) j (y)dy : R hcfc (y)dy j 0 c (x )x )dx ; (B-6) } (B-7) Here, the generalized Fourier coe¢ cients ,aj (x), comprises of two parts, …rst the initial value of the generalized Fourier coe¢ cient, aj (0), multiplies the homogeneous solution, exp( j c (x)x), plus a particular solution, which is given by aj multiply the homogeneous solution. To obtain for aj (x), aj (0) and aj , have to be derived; the integration of the latter completes the expression for the generalized Fourier coe¢ cients. In the subsequent section, we show how one can derived aj (0) and aj . Derivation of initial values of the generalized Fourier coe¢ cient, aj (0) — In Eq. 7.15, we have expanded the unknown solution W (x; y) in a series of the related homogeneous eigenfunctions. This expansion automatically satis…es the homogeneous boundary conditions in Eq. 7.14b. The initial condition, Eq. 7.14c, is satis…ed if g(y) = J X aj (0) j (y), (B-8) j=0 where g(y) is de…ned in Eq. 7.14e. Here, j (y) is the eigenfunctions. Due to the orthogonality of the eigenfunctions (with weight because of the constant boundary 145 10.3. Conference conditions), we can determine the initial values of the generalized Fourier coe¢ cients as R hcfc aj (0) = For j = 0, the eigenfunction becomes (y) g(y) j (y)dy ; R hcfc (y)dy j (B-9) = cos(0) = 1; (B-10) substituting into Eq. B-9 and integrating, the initial value of the Fourier coe¢ cient at j = is, hcfc a0 (0) = ! in O2 where c MO2 =(4F = (g) (g) in DO2 ) and ic (0) = For j > 0, we integrate Eq. a c ic (0); hP (B-11) I i=1 ci i . B-9 to obtain the initial values of the generalized Fourier coe¢ cients as aj (0) = R hcfc g(y) R hcfc j>0 (y)dy = j>0 (y)dy sin(j ) sin(j ) (j ) 2(j ) 1=2 sin(2j ) + j c ic (0)hcfc + 2! in O2 : (B-12) Derivation of integral, aj — For j = 0, the integration of fj (x0 ) in Eq. B-6 is R hcfc where F (x0 ; y) (y)dy = R hcfc (y)dy 0 dic (x0 ) = dx0 a I X c hcfc dic (x0 ) dx0 a i ci c c ic (x ) hcfc a ix exp ; (B-13) ; (B-14) i=1 and ic (x0 ) is de…ned in Eq. B-5 at x = x0 . Substituting into Eq. B-6, and integrating, we have at j = a0 (x) = Z x R hcfc F (x0 ; y) (y)dy exp R hcfc (y)dy c hcfc ic (x) a I X i=1 0 c (x )x ci ! c dx0 = c hcfc a I X i=1 ci + ci e a i a ix : (B-15) 146 Publications For j > 0, the integration of fj (x0 ) is fj (x0 ) = c c sin(j ) ic (x0 ) (cos(j ) sin(j ) + j ) hcfc (1 sin(j )j =2 sin(j )=j ) + (cos(j ) sin(j ) + j ) j c hcfc dic (x0 ) ; (B-16) dx and substituting backing into aj and integrating, we have the …nal form for aj at j > as aj (x) = I X i=1 a c a hcfc sin(j ) 1=2 sin(2j ) + j e( a i a i + c j )x ci c j c a hcfc i j sin(j )(0:5j j 2 sin(j ) 1) : (B-17) Bibliography [1] J. S. Walker, Three Mile Island: A Nuclear Crisis in Historical Perspective, University of California Press, USA (2004). [2] J. E. Turner, Atoms, Radiation, and Radiation Protection, WILEY-VCH Verlag GmbH and Co, Germany, 3rd edn. (2007). [3] Times, http://www.time.com/time/sponsoredarchive/landing/0,31909,1977537,00.html, last assessed on Jun 2011. [4] X. Ren and S. Gottesfeld, J. Electrochem. Soc., 148, A87 (2001). [5] H. Dohle, J. Mergel, and D. Stolten, J. Power Sources, 111, 268 (2002). [6] M. M. Mench, Fuel Cell Engines, John Wiley, New Jersey, USA (2008). [7] U. B. Demirci, J. Power Sources, 169, 239 (2007). [8] S. Arisetty, U. Krewer, S. G. Advani, and A. K. Prasad, J. Electrochem. Soc., 157, B1443 (2010). [9] J. Nordlund and G. Lindbergh, J. Electrochem. Soc., 151, A1357 (2004). [10] J. Meyers and J. Newman, J. Electrochem. Soc., 149, A710 (2002). 147 148 BIBLIOGRAPHY [11] A. Heinzel and V. M. Barragan, IEEE Trans. Magn., 45, 1570 (2009). [12] V. Neburchilov, J. Martin, H. Wang, and J. Zhang, J. Power Sources, 169, 221 (2007). [13] N. W. DeLuca and Y. A. Elabd, J. Polym. Sci. Part B: Polym. Phys., 44, 2201 (2006). [14] A. Serov and K. Chan, Appl. Catal. B: Env., 90, 313 (2009). [15] V. B. Oliveiraa, C. M. Rangelb, and A. M. F. R. Pinto, Chem. Eng. J., 157, 174 (2009). [16] G. B. Jung, A. Su, C. H. Tu, Y. T. Lin, F. B. Weng, and S. H. Chan, J. Power Sources, 171, 212 (2007). [17] G. B. Jung, C. H. Tu, P. H. Chi, A. Su, F. B. Weng, Y. T. Lin, Y. C. Chiang, C. Y. Lee, and W. M. Yan, J. Solid State Electrochem., 13, 1455 (2007). [18] Q. X. Wu, T. S. Zhao, and W. W. Yang, Int. J. Heat and Mass Transfer, 54, 1132 (2011). [19] A. Casalegno, L. Colombo, S. Galbiati, and R. Marchesi, J. Power Sources, 195, 4143 (2010). [20] W. L. Pberkampfa and T. G. Trucano, Prog. Aerosp. Sci., 38, 209 (2002). [21] I. V. Datskov, G. M. Ostrovsky, L. E. K. Achenie, and Y. M. . Volin, Chem. Eng. Sci., 61, 2379 (2005). [22] P. Alotto, M. Guarnieri, and F. Moro, IEEE Trans. Magn., 45, 1570 (2009). [23] S. Basri, S. K. Kamarudin, W. R. W. Daud, and M. M. Ahmad, Int. J. Hydrogen Energy, 35, 1759 (2010). [24] R. Wang, L. Qi, X. Xie, Q. Ding, C. Li, and C. M. Ma, J. Power Sources, 185, 1201 (2008). [25] W. Wu and Y. T. Lin, Int. J. Hydrogen Energy, 35, 9701 (2010). [26] Y. Wang, G. Au, E. J. Plichta, and J. P. Zheng, J. Power Sources, 175, 851 (2007). BIBLIOGRAPHY 149 [27] M. Shen and K. Scott, J. Power Sources, 148, 24 (2005). [28] J. Cruickshank and K. Scott, J. Power Sources, 70, 40 (1997). [29] K. Scott, W. Taama, and J. Cruickshank, J. Power Sources, 65, 159 (1996). [30] K. Scott, P. Argyropoulos, and K. Sundmacher, J. Electroanal. Chem., 477, 97 (1999). [31] K. Scott, W. M. Taama, P. Argyropoulos, and K. Sundmacher, J. Power Sources, 83, 204 (1999). [32] U. Krewer, M. Christov, T. Vidakovic, and K. Sundmacher, J. Electroanal. Chem., 589, 148 (2006). [33] J. Meyers and J. Newman, J. Electrochem. Soc., 149, A718 (2002). [34] J. Nordlund and G. Lindbergh, J. Electrochem. Soc., 149, A1107 (2002). [35] M. R. Shivhare, C. L. Jackson, K. Scott, and E. B. Martin, J. Power Sources, 173, 240 (2007). [36] J. Ge and H. Liu, J. Power Sources, 160, 413 (2006). [37] M. Vera, J. Power Sources, 171, 763 (2007). [38] V. Saarinen, O. Himanen, T. Kallio, G. Sundholm, and K. Kontturi, J. Power Sources, 172, 805 (2007). [39] V. A. Danilov, J. Lim, I. Moom, and H. Chang, J. Power Sources, 162, 992 (2006). [40] J. Ge and H. Liu, J. Power Sources, 163, 907 (2007). [41] W. Liu and C. Y. Wang, J. Electrochem. Soc., 154, B352 (2007). [42] W. W. Yang, T. S. Zhao, and C. Xu, Electrochim. Acta, 53, 853 (2007). [43] W. Liu and C. Y. Wang, J. Power Sources, 164, 561 (2006). [44] A. A. Kulikovsky, Electrochem. Commun., 6, 1259 (2004). [45] H. Guo and C. F. Ma, Electrochem. Commun., 6, 306 (2004). [46] A. A. Kulikovsky, J. Electrochem. Soc., 152, A1121 (2005). 150 BIBLIOGRAPHY [47] A. Casalegno and R. Marchesi, J. Power Sources, 175, 372 (2007). [48] A. A. Kulikovsky, J. Divisek, and A. A. Kornyshev, J. Electrochem. Soc., 147, 953 (2000). [49] A. A. Kulikovsky, J. Appl. Electrochem., 30, 1005 (2000). [50] J. R. Fan, G. L. Hu, J. Yao, and K. F. Chen, Energy Fuels, 16, 1591 (2008). [51] E. Birgersson, J. Nordlund, H. Ekstrom, M. Vynnyvky, and G. Lindbergh, J. Electrochem. Soc., 150, A1368 (2003). [52] J. Divisek, J. Fuhrmann, K. Gärtner, and R. Jung, J. Electrochem. Soc., 150, A811 (2003). [53] Z. H. Wang and C. Y. Wang, J. Electrochem. Soc., 150, A508 (2003). [54] E. Birgersson, J. Nordlund, M. Vynnyvky, C. Picard, and G. Lindbergh, J. Electrochem. Soc., 151, A2157 (2004). [55] R. Chen, T. S. Zhao, W. W. Yang, and C. Xu, J. Power Sources, 175, 276 (2007). [56] J. Rice and A. Faghri, Int. J. Heat and Mass Transfer, 49, 4804 (2006). [57] W. W. Yang and T. S. Zhao, Electrochim. Acta, 52, 6125 (2007). [58] W. W. Yang and T. S. Zhao, J. Power Sources, 174, 136 (2007). [59] T. Z. Yan and T. C. Jen, Int. J. Heat and Mass Transfer, 51, 1192 (2007). [60] W. W. Yang and T. S. Zhao, J. Power Sources, 185, 1131 (2008). [61] Z. Miao, Y. L. He, X. L. Li, and J. Q. Zou, J. Power Sources, 185, 1233 (2008). [62] B. Xiao and A. Faghri, Int. J. Heat and Mass Transfer, 51, 3127 (2008). [63] S. F. Baxter, V. S. Battaglia, and R. E. White, J. Electrochem. Soc., 146, 437 (1999). [64] K. Scott, W. Taama, and J. Cruickshank, J. Appl. Electrochem., 28, 289 (1998). [65] H. Dohle, J. Divisek, and R. Jung, J. Power Sources, 86, 469 (1999). BIBLIOGRAPHY 151 [66] K. Sundmacher, T. Schultz, S. Zhou, K. Scott, M. Ginkel, and E. D. Gilles, Chem. Eng. Sci., 56, 333 (2001). [67] K. T. Jeng and C. W. Chen, J. Power Sources, 112, 367 (2002). [68] A. K. Shukla, C. L. Jackson, K. Scott, and G. Murgia, J. Power Sources, 111, 43 (2002). [69] C. H. Chen and T. K. Yeh, J. Power Sources, 160, 1131 (2006). [70] G. Murgia, P. Pisani, A. K. Shukla, and K. Scott, J. Electrochem. Soc., 150, A1231 (2003). [71] R. K. Raman, G. Murgia, and A. K. Shukla, J. Appl. Electrochem., 34, 1029 (2004). [72] F. Liu and C. Y. Wang, J. Electrochem. Soc., 154, B514 (2007). [73] A. A. Kulikovsky, Electrochem. Commun., 4, 939 (2002). [74] A. A. Kulikovsky, Electrochem. Commun., 5, 530 (2003). [75] K. Scott and P. Argyropoulos, J. Power Sources, 137, 228 (2004). [76] K. Scott and P. Argyropoulos, J. Electroanal. Chem., 567, 103 (2004). [77] S. Eccarius, B. L. Garcia, C. Hebling, and J. W. Weidner, J. Power Sources, 179, 723 (2007). [78] B. L. Garcia, V. A. Sethuraman, J. W. Weidner, and R. E. White, J. Fuel Cell Sci. Technol., 1, 43 (2004). [79] R. Chen and T. S. Zhao, J. Power Sources, 152, 122 (2005). [80] K. M. Yin, J. Power Sources, 167, 420 (2007). [81] K. M. Yin, J. Power Sources, 179, 700 (2008). [82] M. A. Mosquera and W. H. Lizcano-Valbuena, Electrochim. Acta, 54, 1233 (2009). [83] D. Kareemulla and S. J. Jayanti, J. Power Sources, 188, 367 (2008). [84] A. A. Kulikovsky, Electrochim. Acta, 53, 1353 (2007). 152 BIBLIOGRAPHY [85] V. B. Oliveira, D. S. Falcao, C. M. Rangel, and A. M. F. R. Pinto, Int. J. Heat and Mass Transfer, 33, 3818 (2008). [86] C. Xu, T. S. Zhao, and W. W. Yang, J. Power Sources, 178, 291 (2007). [87] W. W. Yang and T. S. Zhao, J. Power Sources, 188, 433 (2008). [88] D. Ko, M. J. Lee, W. H. Jang, and U. Krewer, J. Power Sources, 180, 71 (2008). [89] S. S. Sandhu, R. O. Crowther, and J. P. Fellner, Electrochim. Acta, 50, 3985 (2005). [90] T. Schultz and K. Sundmacher, J. Membr. Sci., 276, 272 (2005). [91] U. Krewer, H. K. Yoon, and H. T. Kim, J. Power Sources, 175, 760 (2007). [92] P. P. Schonewill and D. T. L. Jr., AIChE. J, 54, 1410 (2008). [93] A. Lam, B. Wetton, and D. P. Wilkinson, J. Electrochem. Soc., 158, B29 (2011). [94] C. Xu, Y. L. He, T. S. Zhao, R. Chen, and Q. Ye, J. Electrochem. Soc., 153, A1358 (2006). [95] H. Dohle and K. Wippermann, J. Power Sources, 135, 152 (2004). [96] H. Tu, Y. Wang, C. Wan, and K. Hsueh, J. Power Sources, 159, 1105 (2006). [97] T. H. Kim and Y. C. Bae, Polymer, 46, 6494 (2005). [98] Y. J. Chiu, Int. J. Hydrogen Energy, 35, 6418 (2010). [99] B. Gurau and E. S. Smotkin, J. Power Sources, 112, 339 (2002). [100] J. S. Cowart, J. Power Sources, 143, 30 (2005). [101] Q. Zhang, X. Wang, L. Zhong, Y. Zhou, X. Qiu, and L. Liu, Sensor Actuat. A-Phys., 154, 247 (2009). [102] C. Xu, A. Faghri, X. Li, and T. Ward, Int. J. Hydrogen Energy, 35, 1769 (2010). [103] F. Barbir, PEM fuel cells: Theory and Practice, Academic Press, USA (2005). [104] S. Srinivasan, Fuel Cells: From Fundamental to Applications, Springer Science +Business Media LLC, USA (2006). BIBLIOGRAPHY 153 [105] H. Yang, T. S. Zhao, and Q. Ye, J. Power Sources, 139, 79 (2005). [106] G. Q. Lu and C. Y. Wang, J. Power Sources, 134, 33 (2004). [107] J. Nordlund, P. C, E. Birgersson, M. Vynnycky, and G. Lindbergh, J. Appl. Electrochem., 34, 763 (2004). [108] S. L. Ee and E. Birgersson, J. Electrochem. Soc., 158, B1224 (2011). [109] S. L. Ee and E. Birgersson, J. Electrochem. Soc., 156, B1329 (2009). [110] C. E. Sha¤er and C. Y. Wang, J. Power Sources, 195, 4185 (2010). [111] S. Celik and M. D. Mat, Int. J. Hydrogen Energy, 35, 2151 (2010). [112] C. E. Sha¤er and C. Y. Wang, Electrochim. Acta, 54, 5761 (2009). [113] Y. Yang and Y. C. Liang, J. Power Sources, 194, 712 (2009). [114] P. Sun, G. Xue, C. Wang, and J. Xu, SIAM J. Appl. Math, 70, 600 (2009). [115] F. Liu and C. Y. Wang, Electrochim. Acta, 53, 5517 (2008). [116] W. Liu and C. Y. Wang, J. Power Sources, 164, 189 (2006). [117] C. Xu and A. Faghri, Int. J. Heat and Mass Transfer, 53, 1951 (2010). [118] Z. Miao, Y. H. He, and J. Q. Zou, J. Power Sources, 195, 3693 (2010). [119] H. Bahrami and A. Faghri, Int. J. Heat and Mass Transfer, 53, 2563 (2010). [120] B. Xiao, H. Bahrami, and A. Faghri, J. Power Sources, 195, 2248 (2009). [121] D. Ye, X. Zhu, Q. Liao, J. Li, and Q. Fu, J. Power Sources, 192, 502 (2009). [122] G. Jewett, A. Faghri, and X. Bin, Int. J. Heat and Mass Transfer, 52, 3564 (2009). [123] Y. L. He, X. L. Li, Z. Miao, and Y. W. Liu, Appl. Therm. Eng., 29, 1998 (2008). [124] J. Rice and A. Faghri, J. Heat Transfer, 130, (2008). [125] J. Rice and A. Faghri, Int. J. Heat and Mass Transfer, 51, 948 (2008). [126] K. Fei, T. S. Chen, and C. W. Hong, J. Power Sources, 195, 1940 (2009). 154 BIBLIOGRAPHY [127] C. Xu and A. Faghri, J. Power Sources, 195, 7011 (2010). [128] M. Kaviany, Principles of Heat Transfer in Porous Media, Springer-Verlag, New York (1995). [129] A. Z. Weber, R. M. Darling, and J. Newman, J. Electrochem. Soc., 151, A1715 (2004). [130] T. V. Nguyen, G. Lin, H. Ohn, and Z. Wang, Electrochem. Solid-State Lett., 11, B127 (2008). [131] J. Ko, P. Chippar, and H. Ju, Energy, 35, 2149 (2010). [132] P. Chippar, J. Ko, and H. Ju, Energy, 35, 2301 (2010). [133] D. Gerteisen, J. Power Sources, 195, 6719 (2010). [134] W. Vielstich, v. A. Paganin, F. H. B. Lima, and E. A. Ticianelli, J. Electrochem. Soc., 148, A502 (2001). [135] V. A. Paganin, E. Sitta, T. Iwasita, and W. Vielstich, J. Appl. Electrochem., 35, 1239 (2005). [136] C. Y. Du, T. S. Zhao, and C. Xu, J. Power Sources, 167, 265 (2007). [137] S. Matar and H. Liu, Electrochim. Acta, 56, 600 (2010). [138] Y. P. Sun, L. Xing, and K. Scott, J. Power Sources, 195, (2009). [139] S. Zhou, T. Schultz, M. Peglow, and K. Sundmacher, Phys. Chem. Chem. Phys., 3, 347 (2000). [140] T. Schultz and K. Sundmacher, J. Power Sources, 145, 435 (2005). [141] C. Xu, P. M. Follmann, L. T. Biegler, and M. S. Jhon, Comput. Chem. Eng., 29, 1849 (2005). [142] U. Krewer and K. Sundmacher, J. Power Sources, 154, 153 (2005). [143] U. Krewer, A. Kamat, and K. Sundmacher, J. Electroanal. Chem., 609, 105 (2007). [144] H. Bahrami and A. Faghri, J. Electrochem. Soc., 157, B1762 (2010). BIBLIOGRAPHY 155 [145] T. K. Yeh and C. H. Chen, J. Power Sources, 175, 353 (2008). [146] J. R. Fan, G. L. Hu, J. Yao, and K. F. Cen, Energy Fuels, 16, 1591 (2002). [147] J. J. Huang, S. D. Wu, L. K. Lai, C. K. Chen, and D. Y. Lai, J. Power Sources, 161, 240 (2005). [148] U. Krewer, Y. Song, K.Sundmacher, V. John, R. Lubke, G. Matthies, and L. Tobiska, Chem. Eng. Sci., 59, 119 (2004). [149] C. Siegel, Energy, 33, 1331 (2008). [150] P. Argyropoulos, K. Scott, and W. M. Taama, Chem. Eng. J., 73, 217 (1999). [151] A. A. Kulikovsky, Electrochim. Acta, 51, 4405 (2006). [152] A. A. Kulikovsky, J. Electrochem. Soc., 155, B509 (2008). [153] J. C. Schlake, C. Preusse, J. Winkelhake, and U. Konigorski, J. Power Sources, 153, 100 (2006). [154] J. Zou, Y. He, Z. Miao, and Z. Li, Int. J. Hydrogen Energy, 35, 7206 (2010). [155] S. Basri, S. K. Kamarudin, W. R. W. Daud, Z. Yaakub, M. M. Ahmad, N. Hashim, and U. A. Hasran, Int. J. Hydrogen Energy, 34, 5759 (2009). [156] R. S. Jr., D. M. dos Anjos, G. Tremiliosi-Filho, E. R. Gonzalez, C. Coutanceau, E. Sibert, J. M. Leger, and K. B. Kokoh, J. Power Sources, 180, 283 (2008). [157] A. Casalegno, R. Marchesi, and D. Parenti, Fuel Cells, 8, 37 (2007). [158] J. Cruickshank and K. Scott, J. Power Sources, 70, 40 (1998). [159] K. Sundmacher and K. Scott, Chem. Eng. Sci., 54, 2927 (1999). [160] M. G. Medeiros, R. R. Bessette, C. M. Deschenes, and D. W. Atwater, J. Power Sources, 96, 236 (2001). [161] W. L. Yu, S. J. Wu, and S. W. Shiah, Int. J. Hydrogen Energy, 33, 2311 (2008). [162] M. Grujicic and K. M. Chittajallu, Appl. Surf. Sci., 227, 56 (2004). 156 BIBLIOGRAPHY [163] H. S. Lee, H. J. Kim, S. G. Kim, and S. H. Ahn, J. Mater. Process Technol., 187 (2007). [164] M. Grujicic and K. M. Chittajallu, Chem. Eng. Sci., 59, 5883 (2004). [165] J. Wu, Q. Liu, and H. Fang, J. Power Sources, 156, 388 (2006). [166] G. H. Guvelioglu and H. G. Stenger, J. Power Sources, 156, 424 (2006). [167] M. Oszcipok, D. Riemann, U. Kronenwett, M. Kreideweis, and M. Zedda, J. Power Sources, 145, 407 (2005). [168] S. J. Wu, S. W. Shiah, and W. L. Yu, 34, 135 (2009). [169] R. C. Dante, J. L. Escamilla, V. Madrigal, T. Thesuss, J. de Dios Caldron, O. Solorza, and R. Rivera, Int. J. Hydrogen Energy, 28, 343 (2003). [170] M. F. Torchio, M. G. Santarelli, and A. Nicali, J. Power Sources, 149, 33 (2005). [171] M. Ordonez, M. T. Iqbal, J. E. Quaicoe, and L. M. Lye, Canadian conference on electrical and computer engineering, 1, 1120 (2006). [172] R. Chandrasekaran, W. Bi, and T. F. Fuller, J. Power Sources, 182, 546 (2008). [173] K. Scott, P. Argyropoulos, P. Yiannopoulos, and W. M. Taama, J. Appl. Electrochem., 31, 823 (2001). [174] A. Kumar and R. G. Reddy, J. New Mater. Electrochem. Syst., 6, 231 (2003). [175] A. Kumar and R. G. Reddy, J. Power Sources, 114, 54 (2003). [176] M. Noponen, E. Birgersson, J. Ihonen, M. Vynnycky, A. Lundblad, and G. Lindbergh, Fuel Cells, 4, 365 (2004). [177] G. M. Andreadis, A. K. M. Podias, and P. E. Tsiakaras, J. Power Sources, 181, 214 (2008). [178] G. M. Andreadis, A. K. M. Podias, and P. E. Tsiakaras, J. Power Sources, 194, 397 (2009). [179] H. Ly, E. Birgersson, M. Vynnycky, and A. P. Sasmito, J. Electrochem. Soc., 156, B1156 (2009). BIBLIOGRAPHY 157 [180] W. Wu and Y. T. Lin, Ind. Eng. Chem. Res., 49, 5725 (2010). [181] V. B. Oliveira, C. M. Rangel, and A. M. F. R. Pinto, Int. J. Hydrogen Energy, 34, 8245 (2009). [182] H. Pramanik and S. Basu, Chem. Eng. Process., Article in press (2009). [183] R. Taylor and R. Krishna, Multicomponent Mass Transfer, John Wiley, New York (1993). [184] D. Gawin, E. Majorana, and B. A. Schre‡er, Mech. Cohesive-Frict Mater., 4, 37 (1999). [185] D. R. Lide, Handbook of Chemistry and Physics, CRC Press/Taylor and Francis, Boca Raton, FL, internet version 89th edn. (2009). [186] J. F. Coulson and J. R. Richardson, Coulson and Richardson’s Chemical Engineering, vol. 1, Pergamon Press, Oxford, UK, 4th edn. (1993). [187] H. Ly, E. Birgersson, and M. Vynnycky, J. Electrochem. Soc., 157, B982 (2010). [188] E. Antolini, J. Power Sources, 170, (2007). [189] C. Lamy, E. M. Belgsir, and J.-M. Leger, J. Appl. Electrochem., 31, 799 (2001). [190] F. Vigier, S. Rousseau, C. Coutanceau, J.-M. Leger, and C. Lamy, Top. Catal., 40, 111 (2006). [191] S. Rousseau, C. Coutanceau, C. Lamy, and J. M. Leger, J. Power Sources, 158, 18 (2005). [192] Q. Wang, G. Q. Sun, L. H. Jiang, Q. Xin, S. G. Sun, Y. X. Jiang, S. P. Chen, Z. Jusys, and R. J. Behm, Phys. Chem. Chem. Phys., 9, 2686 (2007). [193] Q. Wang, G. Q. Sun, L. Cao, L. H. Jiang, G. X. Wang, S. L. Wang, S. H. Yang, and Q. Xin, J. Power Sources, 177, 142 (2008). [194] G. Li and P. G. Pickup, J. Power Sources, 161, 256 (2006). [195] M. Zhu, G. Sun, and Q. Xin, Electrochim. Acta, 54, 1511 (2008). 158 BIBLIOGRAPHY [196] G. A. Camara, R. B. de Lima, and T. Iwasita, J. Electroanal. Chem., 585, 128 (2005). [197] S. Q. Song, W. J. Zhou, Z. H. Zhou, L. H. Jiang, G. Q. Sun, Q. Xin, V. Leontidis, S. Kontou, and P. Tsiakaras, Int. J. Hydrogen Energy, 30, 995 (2005). [198] A. Ghumman and P. G. Pickup, J. Power Sources, 179, 280 (2007). [199] T. V. Nguyen and R. E. White, J. Electrochem. Soc., 140, 2178 (1993). [200] Comsol Multiphysics 4.1, http://www.comsol.com, last assessed Feb 2012. [201] Maple Soft 13, http://www.maplesoft.com, last assessed May 2011. [202] Matlab and Simulink, http://www.mathworks.com, last assessed May 2012. [203] A. Kumar and R. G. Reddy, J. Power Sources, 129, 62 (2004). [204] Scribner Associates Inc., http://www.scribner.com/, last assessed July 2011. [205] BCS Fuel Cells, Inc, http://www.bcsfuelcells.com, last assessed Mar 2012. [206] DuPont, http://www2.dupont.com. [207] Fuel Cell Technologies, E-tek division, http://www.fuelcelltechnologies.com/fuelcell/, last assessed July 2011. [208] W. B. Krantz, Scaling Analysis in Modeling Transport and Reaction Processes, John Wiley, New York (2007). [209] D. W. Trim, Applied Partial Di¤ erential Equations, PWS Publishing Company, Boston, USA (1990). [210] J. Ge and H. Liu, J. Power Sources, 142, 56 (2005). [211] G. Evans, J. Blackledge, and P. Yardley, Analytic Methods for Partial Di¤ erential Equations, Springer-Verlag, London (1999). [212] M. M. Mench and C. Y. Wang, J. Electrochem. Soc., 150, A79 (2002). [213] J. C. Amphlett, B. A. Peppley, E. Halliop, and A. Sadiq, J. Power Sources, 96, 204 (2000). BIBLIOGRAPHY 159 [214] S. H. Seo and S. L. Chang, Energy Fuels, 22, 1212 (2008). [215] A. M. C. Luna, A. Bonesi, W. E. Triaca, A. D. Blasi, A. Stassi, V. Baglio, V. Antonucci, and A. S. Arico, J. Nanopart. Res., 12, 357 (2009). [216] M. M. Mench and C. Y. Wang, J. Electrochem. Soc., 150, A79 (2003). [217] S. K. Lee, K. Ito, T. Ohshima, S. Noda, and K. Sasaki, Electrochem. Solid-State Lett., 12, B126 (2009). [218] M. M. Mench, Q. L. Dong, and C. Y. Wang, J. Power Sources, 124, 90 (2003). [219] Q. Dong, J. Kuli, and M. Mench, J. Power Sources, 139, 106 (2005). [220] D. C. Montgomery, Design and Analysis of Experiments, John Wiley, USA, 6th edn. (2005). [221] M. S. Tavallali, S. L. Ee, E. Birgersson, and I. A. Karimi, in Conference Proceedings of the 14th Asia Paci…c Confederation of Chemical Engineering (2012). [222] A. S. A. Alghamdi, JKAU: Eng. Sci., 21, 73 (2010). [223] D. A. Nield and A. B. A, Convection in Porous Media, Springer-Verlag, USA (1992). [224] H. Wang, Z. Jusys, and R. J. Behm, J. Phys. Chem. B, 108, 19413 (2004). [225] R. C. Reid, J. M. Prausnitz, and B. E. Poling, The Properties of Gases and Liquids, Chemical Engineering Series Inc., Mc Graw-Hill, Singapore, 4th edn. (1988). [226] H. Ju, C. Y. Wang, S. Cleghorn, and U. Beuscher, J. Electrochem. Soc., 152, A1645 (2005). [227] C. H. Ly, E. Birgersson, and M. Vynnycky, Int. J. Hydrogen Energy (2012). [228] Neuro‡ash Pte Ltd, http://www.neuro‡ash.com.sg/, last assessed Dec 2011. [229] R. S. BroKaw, Ind. Eng. Chem. Process Des. Dev, 8, 240 (1969). [230] R. Haberman, Handbook of Chemistry and Physics, Prentice-Hall International, Inc., London (1987). [...]... a sound theoretical framework with mathematical models This way, a detailed prediction of the inner life of the cell according to di¤erent operating conditions and layout thus becomes possible 1.3 DLFC Modeling and Experimental Validation 1.3 7 DLFC Modeling and Experimental Validation Mathematical modelling provides a means to capture knowledge and understanding, and transfer this between the di¤erent... = 0 Comparison between numerical solutions of full set of equations (symbols) and analytical soin lutions of Eq 6.8b (solid lines) for the inlet velocities: Ua = 7.3 10 ( ), 7.3 10 3 (H) and 3 10 2 ms 1 4 ( ); EA = 0:7 V, T = 50 o C, and 1 M inlet methanol concentration 6.4 68 Rate of convergence of analytical solutions as a function of number of eigenvalues (normalized with the... troubleshooting of experiments, designs, and failures In addition, the mathematical process presented are not limited to fuel cell modeling, but can also be extended to any non-homogeneous parabolic 2nd order PDE with non-local convective boundary conditions Key words: Direct Methanol Fuel Cell; Direct Ethanol Fuel Cell; Reduced model; Scale analysis; Analytical Solutions; COMSOL Multiphysics; Mathematical Modeling; ... Design of Experiments List of Tables 1.1 Reactions of popular liquid fuels for the DLFC 5 1.2 Types of scenarios modeling can aid in 8 3.1 Convergence study of the 2D model for the DLFC with channels in Sect 3.2 49 8.1 3D Approximate Analytical Solutions 118 9.1 Variables and levels in the 2¸ factorial experimental. .. parameters for Chap 9 141 ix List of Figures 1.1 Schematic of a typical proton exchange membrane fuel cell 1.2 Schematic of a Direct Liquid Fuel Cell with geometrical dimensions of the Membrane Electrode Assembly (MEA) 2.1 3 6 Typical polarization and power curves of a fuel cell illustrating the regions of performance losses: activation overpotential (I),... cient design of experiments (DoE) This way, we ensure that in each experimental series, the solutions are able to predict all possible combinations of the desired operating conditions On a …nal note, in the context of the DLFC, the derived analytical solutions are fast, reliable and are able predict the mechanistic behavior of the cell, and thus lend themselves well to multi-objective and/ or variable... layers of some popular liquid fuels) As such, methanol still remains the most popular choice now among the candidates of liquid fuel as its electrooxidation only involve one carbon One other aspect associated with fuel cell implementation is the socioeconomic impact on the use of platinum For the DLFC, platinum loading is higher than the hydrogen-counterpart to facilitate the electrooxidation of the liquid. .. solved analytically to give 3D approximate analytical solutions for the DLFC that is able to predict the behavior in a DLFC with ‡ channels, that initially ow was only possible with 3D numerical solutions; albeit there is some loss of information with the analytical solutions due to spatial smoothing A¢ rming the accuracy of the analytical solutions is equally crucial as deriving them; the approximate analytical. .. semi -analytical solution can be secured In general, analytical solutions that capture the salient features of the transport phenomena and electrochemistry can often provide a deeper and ‘ richer’understanding than could be achieved with numerical computations alone, because complex phenomena can often be reduced to simpler processes and leading-order physical phenomena be revealed Further, when analytical. .. hydrogen, to electrical energy directly Hydrogen was the choice of fuel because of its high power energy density, and is an ideal candidate for applications that require high performance The PEMFC technology served as part of NASA’ project Gemini in the early days of the U.S s piloted space program The expensive cost of platinum, which is used for the catalytic activity of hydrogen electrooxidation, . Mathematical Modeling of Direct Liquid Fuel Cells Multidimensional Analytical Solutions and Experimental Validation EE SHER LIN (B. Eng, Hons.) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF. loss of information with the analytical solutions due to spatial smoothing. A¢ rming the accuracy of the analytical solutions is equally crucial as deriving them; the approximate analytical so- lutions,. Schematic of a Direct Liquid Fuel Cell with geometrical dimensions of the Membrane Electrode Assembly (MEA). . . . . . . . . . . . . . . . . 6 2.1 Typical polarization and power curves of a fuel cell