One of the problems in the optimization of a fuel cell performance is the operation prediction for short and long-time behaviours. The employ of exact analytical functions for picturing the distribution of potential and current densities in 2D polymer electrolyte membrane fuel cells, generalizes the study and reduces large computational times for each experimental situation. Therefore, we foresee analytical solutions for mass balance equations using the asymptotic velocity equations (normal and tangential coordinates) to obtain a 2D concentration, current and overpotential profiles for smooth platinum catalysts. Dimensionless numbers are deduced, i.e. Wagner, Damkoehler and Graetz to characterize the fuel cell performance, first with a 1D approach and also along 2D coordinates. Besides, the complete polarization curve is predicted comparing the theoretical results with the proper variations of electrochemical magnitudes in a single home-made hydrogen/oxygen 200 cm2 polymer electrolyte membrane fuel cell.