A comprehensive, consistent and systematic mathematical model of PEM fuel cells

This paper presents a comprehensive, consistent and systematic mathematical model for PEM fuel cells that can be used as the general formulation for the simulation and analysis of PEM fuel cells. As an illustration, the model is applied to an isothermal, steady state, two-dimensional PEM fuel cell. Water is assumed to be in either the gas phase or as a liquid phase in the pores of the polymer electrolyte. The model includes the transport of gas in the gas flow channels, electrode backing and catalyst layers; the transport of water and hydronium in the polymer electrolyte of the catalyst and polymer electrolyte layers; and the transport of electrical current in the solid phase. Water and ion transport in the polymer electrolyte was modeled using the generalized Stefan–Maxwell equations, based on non-equilibrium thermodynamics. Model simulations show that the bulk, convective gas velocity facilitates hydrogen transport from the gas flow channels to the anode catalyst layers, but inhibits oxygen transport. While some of the water required by the anode is supplied by the water produced in the cathode, the majority of water must be supplied by the anode gas phase, making operation with fully humidified reactants necessary. The length of the gas flow channel has a significant effect on the current production of the PEM fuel cell, with a longer channel length having a lower performance relative to a shorter channel length. This lower performance is caused by a greater variation in water content within the longer channel length.