Optimization of the cathode geometry in polymer electrolyte membrane (PEM) fuel cells

A nonlinear constrained optimization procedure is used in the cathode design in order to maximize the average current density at a fixed voltage in a polymer electrolyte membrane (PEM) fuel cell with interdigitated fuel/air distributors. The operation of the PEM fuel cell is studied using a steady-state, two-phase, two-dimensional electro-chemical model. The following geometrical parameters of the cathode are considered: the thickness, and length per one shoulder of the interdigitated air distributor and the length of the shoulder. The optimization results obtained show that within manufacturability controlled lower and the space-limitation controlled upper bounds of these parameters, the optimal-cathode design corresponds to the lower bounds in the cathode length per one shoulder of the interdigitated air distributor and the fraction of the length associated with the shoulders and at a low (but larger than the lower bound) value of the cathode thickness. These findings are explained using an analogy with the effect of pipe dimensions on the fluid flow through a pipe and by considering the role of forced convection on the oxygen transport to the membrane/cathode interface.