Analysis and design of flow fields for proton exchange membrane fuel cell (PEMFC) require coupled solution of the flow fields, gas transport and electrochemical reaction kinetics in the anode and the cathode. Computational cost prohibits the widespread use of three-dimensional models of the anode and cathode flow fields, gas diffusion layers (GDL), catalyst layers (CL) and the membrane for fluid flow and mass transport. On the other-hand, detailed cross-sectional two-dimensional models cannot resolve the effects of the anode and cathode flow field designs. Here, a two-dimensional in-plane model is developed for the resolution of the effects of anode and cathode flow channels and GDLs, catalyst layers are treated as thin-layers of reaction interfaces and the membrane is considered as a thin-layer that resist the transfer of species and the ionic current. Brinkman equations are used to model the in-plane flow distribution in the channels and the GDLs to account for the momentum transport in the channels and the porous GDLs. Fick's law equations are used to model transport of gas species in the channels and GDLs by advection and diffusion mechanisms, and electrochemical reactions in the CL interfaces are modeled by Butler-Volmer equations. Complete features of the flow in the channels and inlet and outlet manifolds are included in the model using resistance relationships in the through-plane direction. The model is applied to a small cell having an active area of 1.3 cm~2 and consisting of 8 parallel channels in the anode and a double serpentine in the cathode. Effects of the anode and cathode stoichiometric ratios on the cell performance and hydrogen utilization are investigated. Results demonstrate that for a sufficiently high cathode stoichiometric ratio enough, anode stoichiometric ratio can be lowered to unity to obtain very high hydrogen utilization and output power.
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