Explicit solution for the cathode catalyst layers of PEM fuel cells

In this paper, the differential equations governing the mass transport and the electrochemical reaction in a cathode catalyst layer of polymer electrolyte membrane fuel cells are solved based on the polynomial series expansion method. Explicit expressions for the polarization curve as well as for the distributions of oxygen, current density and overpotential are obtained when a quadratic, cubic or quartic polynomial is employed to approximate the oxygen concentration distribution. These kinds of explicit solutions are desirable for MEA design and diagnosis purposes. The comparison between the conventional numerical approach and the explicit solution approach proposed here shows that satisfactory accuracy can be reached by the first four terms of the polynomial series. The effect of the catalyst layer thickness on the accuracy of the obtained explicit polynomial solutions is also discussed.