Mathematical Modelling and Numerical Simulation

  • Alhussein Albarbar
  • Mohmad Alrweq


In this chapter, analytical models and effects of operation parameters on the performance of PEM fuel cells are presented. This was carried out taking account of semi-empirical, one-, two- and three-dimensional modelling methods. Critical analysis of the performance of each modelling methods is included, and the effectiveness of those algorithms is experimentally verified using scaled PEM fuel cell experimental set-up.


PEM fuel cell model PEM fuel cells analytical models Semi-empirical modelling One-dimensional models Two-dimensional cell models Three-dimensional cell models 


  1. 1.
    Mazumder, S., & Cole, J. V. (2003). Rigorous 3-D mathematical modelling of PEM fuel cells II. Model predictions with liquid water transport. Journal of the Electrochemical Society, 150(11), A1510–A1517.CrossRefGoogle Scholar
  2. 2.
    Pasaogullari, U., & Wang, C. Y. (2005). Two-phase modelling and flooding prediction of polymer electrolyte fuel cells. Journal of the Electrochemical Society, 152(2), A380–A390.CrossRefGoogle Scholar
  3. 3.
    Spiegel, C. (2011). PEM fuel cell modeling and simulation using MATLAB. Burlington USA: Academic press. ISBN: 978-0-12-374259-9.Google Scholar
  4. 4.
    Alrweq, M., Albarbar, A. (2016). Investigation into the characteristics of proton exchange membrane fuel cell-based power system IET science, measurement & technology. doi:, Online ISSN 1751–8830.
  5. 5.
    Milewski, J., Świrski, K., Santarelli, M. and Leone, P., 2011. Advanced methods of solid oxide fuel cell modeling. Springer Science & Business Media.CrossRefGoogle Scholar
  6. 6.
    Al-Baghdadi, M. A. (2010). CFD modeling and analysis of different novel designs of air-breathing PEM fuel cells. New York: Nova Science Publishers.Google Scholar
  7. 7.
    Bavarian, M., Soroush, M., Kevrekidis, I. G., & Benziger, J. B. (2010). Mathematical modelling, steady-state and dynamic behaviour, and control of fuel cells: A review†. Industrial & Engineering Chemistry Research, 49(17), 7922–7950.CrossRefGoogle Scholar
  8. 8.
    Andersson, M., Yuan, J., & Sundén, B. (2010). Review on modelling development for multiscale chemical reactions coupled transport phenomena in solid oxide fuel cells. Applied Energy, 87(5), 1461–1476.CrossRefGoogle Scholar
  9. 9.
    Vasile, N. S., Doherty, R., Videla, A. H. M., & Specchia, S. (2016). 3D multi-physics modeling of a gas diffusion electrode for oxygen reduction reaction for electrochemical energy conversion in PEM fuel cells. Applied Energy, 175, 435–450.CrossRefGoogle Scholar
  10. 10.
    Al-Masri, A., Peksen, M., Blum, L., & Stolten, D. (2014). A 3D CFD model for predicting the temperature distribution in a full scale APU SOFC short stack under transient operating conditions. Applied Energy, 135, 539–547.CrossRefGoogle Scholar
  11. 11.
    Abdollahzadeh, M., Pascoa, J. C., Ranjbar, A. A., & Esmaili, Q. (2014). Analysis of PEM (polymer electrolyte membrane) fuel cell cathode two-dimensional modeling. Energy, 68, 478–494.CrossRefGoogle Scholar
  12. 12.
    Siegel, C. (2008). Review of computational heat and mass transfer modelling in polymer-electrolyte-membrane (PEM) fuel cells. Energy, 33(9), 1331–1352.CrossRefGoogle Scholar
  13. 13.
    Liu, Y., Lehnert, W., Janßen, H., Samsun, R. C., & Stolten, D. (2016). A review of high-temperature polymer electrolyte membrane fuel-cell (HT-PEM FUEL CELL)-based auxiliary power units for diesel-powered road vehicles. Journal of Power Sources, 311, 91–102.CrossRefGoogle Scholar
  14. 14.
    Hutzenlaub, T., Becker, J., Zengerle, R., & Thiele, S. (2013). Modelling the water distribution within a hydrophilic and hydrophobic 3D reconstructed cathode catalyst layer of a proton exchange membrane fuel cell. Journal of Power Sources, 227, 260–266.CrossRefGoogle Scholar
  15. 15.
    Carton, J. G., Lawlor, V., Olabi, A. G., Hochenauer, C., & Zauner, G. (2012). Water droplet accumulation and motion in PEM (proton exchange membrane) fuel cell mini-channels. Energy, 39(1), 63–73.CrossRefGoogle Scholar
  16. 16.
    Wang, X., & Van Nguyen, T. (2010). Modelling the effects of the microporous layer on the net water transport rate across the membrane in a PEM fuel cell. Journal of the Electrochemical Society, 157(4), B496–B505.CrossRefGoogle Scholar
  17. 17.
    Liu, F., Lu, G., & Wang, C. Y. (2007). Water transport coefficient distribution through the membrane in a polymer electrolyte fuel cell. Journal of Membrane Science, 287(1), 126–131.CrossRefGoogle Scholar
  18. 18.
    Das, P. K., Li, X., & Liu, Z. S. (2010). Analysis of liquid water transport in cathode catalyst layer of PEM fuel cells. International Journal of Hydrogen Energy, 35(6), 2403–2416.CrossRefGoogle Scholar
  19. 19.
    Lu, Z., Rath, C., Zhang, G., & Kandlikar, S. G. (2011). Water management studies in PEM fuel cells, part IV: Effects of channel surface wettability, geometry and orientation on the two-phase flow in parallel gas channels. International Journal of Hydrogen Energy, 36(16), 9864–9875.CrossRefGoogle Scholar
  20. 20.
    Grimm, M., See, E. J., & Kandlikar, S. G. (2012). Modelling gas flow in PEM FUEL CELL channels: Part I–flow pattern transitions and pressure drop in a simulated ex situ channel with uniform water injection through the GDL. International Journal of Hydrogen Energy, 37(17), 12489–12503.CrossRefGoogle Scholar
  21. 21.
    Gao, F., Blunier, B., Simoes, M. G., & Miraoui, A. (2011). PEM fuel cell stack modelling for real-time emulation in hardware-in-the-loop applications. IEEE Transactions on Energy Conversion, 26(1), 184–194.CrossRefGoogle Scholar
  22. 22.
    Wang, Y., Chen, K. S., Mishler, J., Cho, S. C., & Adroher, X. C. (2011). A review of polymer electrolyte membrane fuel cells: Technology, applications, and needs on fundamental research. Applied Energy, 88(4), 981–1007.CrossRefGoogle Scholar
  23. 23.
    Lobato, J., Cañizares, P., Rodrigo, M. A., Pinar, F. J., Mena, E., & Úbeda, D. (2010). Three-dimensional model of a 50 cm 2 high temperature PEM fuel cell. Study of the flow channel geometry influence. International Journal of Hydrogen Energy, 35(11), 5510–5520.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Alhussein Albarbar
    • 1
  • Mohmad Alrweq
    • 1
  1. 1.School of EngineeringThe Manchester Metropolitan UniversityManchesterUK

Personalised recommendations