Summary The main objective of this paper is to develop an analytical solution based on the perturbation method to solve the continuity and momentum equations governing the flow in gas channels of a PEMFC having circular and elliptical cross sections. The equations are solved in both the anode and cathode gas channels with appropriately defined perturbation parameters to obtain the velocity profile in these channels. It was observed that by changing the circular cross section to an elliptical one (ie, increasing the value of perturbation parameter), the axial velocity increases. As a result, the penetration of species into the reaction areas decreases. Then, the effect of species penetration speed on the performance of PEMFC is discussed. Increasing the penetration speed (ie, radial velocity) of the reactant gases causes the maximum value of the gas velocity in the channel to decrease. This would imply that the diffusion rate of the reactant species to the reaction areas, and thereby the cell performance would be optimized. Apart from the analytical solution, 3‐D numerical solution of the governing equations using collocated finite volume method along with the SIMPLE algorithm is also performed. The results are validated against the available published data. The numerical results confirm that by converting the circular cross section to the elliptical one, while other conditions are fixed, the PEMFC produces less current density.

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A three-dimensional numerical model has been developed to simulate a proton exchange membrane fuel cell. The governing equations were discretised and solved using a finite-volume technique and the numerical results were verified by empirical test results. In the numerical procedure, the species, temperature and protonic conductivity distribution in various voltages were modelled with great accuracy. The results have shown that by lowering the cell voltage, the maximum temperature at the cathode catalyst–membrane interface will increase. The effects of semi-circular and semi-elliptical gas channel cross-sections on cell performance were studied and compared with base model results. This showed that the elliptical model generates more current density at the same voltage. On the other hand, oxygen distribution is more uniform in geometries in which the value of cathode overpotential has a direct link with oxygen magnitude. Cathode overpotential is also sensitive to shoulder width and oxygen distribution; so the elliptical model presents better performance than the other models. Ultimately, all the numerical and experimental results are compared with published experimental data by Wang et al., which demonstrate desirable agreement.