The proton exchange membrane (PEM) fuel cell using a polybenzimidazole (PBI) membrane operates between 120 °C and 180 °C, higher than the PEM fuel cell with a Nafion based membrane (lower than 80°C). Few studies have been conducted in the theoretical modeling of the PEM fuel cell with a PBI membrane. Experimental results have shown that the conductivity of a PBI membrane is affected by the phosphoric acid doping level, the cell operating temperature and the relative humidity. The fuel cell performance is thus affected by these parameters as well. The objective of this paper is to develop a three dimensional non-isothermal model to investigate the performance of the fuel cell with a PBI membrane. This new model considers influences of the relative humidity of the inlet air, the phosphoric acid doping level, and the operating temperature on the performance of fuel cells. The model is validated using the experimental data. A high oxygen concentration is found under the flow channel, as well as a high temperature region. The performance of fuel cells increases with the increase of the phosphoric doping level, temperature or relative humidity. The fuel cell performance is found to be more sensitive to the doping level and temperature changes, and less sensitive to the change of relative humidity.

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