An analytical study of the PEM fuel cell with axial convection in the gas channel

A quasi two-dimensional mathematical model for a polymer electrolyte membrane (PEM) fuel cell is developed with consideration of axial convection in the gas channel and analytical solutions are obtained. A half-cell model which contains the cathode gas channel, gas diffuser, catalyst layer, and the membrane is investigated. To account for the effect of gas velocity in the gas channel, axial convection is included in the oxygen transport equation of the gas channel. Expressions for the oxygen mass fraction distribution in the gas channel, gas diffuser, and catalyst layer, and the current density and the membrane phase potential in the catalyst layer and membrane are derived. The solutions are presented in the form of infinite series. The polarization curve is also expressed as a function of the surface overpotential. Due to the advantage of the closed-form solutions this model can be easily employed as a diagnostic tool for PEM fuel cell simulations.