Document Type : Research Article

**Authors**

**Abstract**

A one dimensional isothermal mathematical modeling of cathode side of a Proton Exchange Membrane (PEM) fuel cell is developed for the water management problem. Water transport is investigated in both cathode Gas Diffusion Layer (GDL) and membrane through solving appropriate equations for fluid flow and mass transport in GDL and water transport within the membrane. The gaseous mixture flowing in cathode GDL consists of three species: oxygen, water vapor and nitrogen. The model considers one phase flow in the gas diffusion layer and then predicts the regions with possible condensation. Homogenous distribution of wet phase (liquid water) is assumed throughout each wet control volume as fog. The model couples all governing equations in both membrane and GDL using an innovative algorithm. A detailed discussion of numerical techniques for the PEMFC model is given with a flow diagram to provide an overview of the solution procedure. Validation for polarization curve is implemented to show agreement between the obtained results and existing results in the literature.

**Keywords**

[1] D. M. Bernardi and M. W. Verbrugge, "Mathematical Model of a Gas Diffusion Electrode Bonded to a Polymer Electrolyte," *AIChE J., 37(9),* pp.1151–1163, 1991.

[2] T. E. Fuller and J. Newman, "Water and Thermal Management in Solid-Polymer-Electrolyte Fuel Cells," *J. Electrochem. Soc., 140,* pp.1218–1225, 1993.

[3] T. E. Springer, T. A. Zawodzinski, and S. Gottefeld, "Polymer Electrolyte Fuel Cell Model," *J. Electrochem. Soc., 138 (8),* pp.2334–2342, 1991*.*

[4] L. You and H. Liu, "A Two-Phase and Transport Model for the Cathode of PEM Fuel Cells," *Int. J. Heat and Mass Transfer, 45 *pp. 2277–2287, 2002.

[5] M. J. Kermani and J. M. Stockie, "Heat and Mass Transfer Modeling of Dry Gases in the Cathode of PEM Fuel Cells," *Int. J. Comp. fluid dyn., 18(2), *pp. 153–164, 2004.

[6] R. E. De la Rue and C. W. Tobias, "On the Conductivity of Dispersions," *J. Electrochem. Soc., 106,* pp. 827–833, 1959.

[7] E. L. Cussler, Diffusion Mass Transfer in Fluid Systems, CambridgeUniversity Press, 1984.

[8] Ugur Pasaogullari, C.Y. Wang and Ken S. Chen. "Two-Phase Transport in Polymer Electrolyte Fuel Cells with Bilayer Cathode Gas Diffusion Media," *J. Electrochem. Soc., 152(8),* pp. 1574–1582, 2005.

[9] S. Motupally, A. J. Becker and J. W. Weidner, "Diffusion of Water in Nafion 115 Membranes," *J. Electrochem. Soc.,* *147(9)*, pp. 3171–3177, 2000.

[10] Weber, A.Z. and Newman, J., "Modeling Transport in Polymer-Electrolyte Fuel Cells", *Chem. Rev*., *104*, pp. 4679–4726, 2004.

[11] J. Larminie, and A. Dicks, Fuel Cell Systems Explained, John Wiley and Sons, 2001.

[12] Ticianelli E.A., Derouin C.R., Redondo A., Srinivasan S., "Methods to Advance Technology of Proton Exchange Membrane Fuel Cells" J*. Electrochem. Soc. 135 *pp*. (1988) 2209*.