The optimization of a fuel cell performance involves the prediction of its operation conditions and electrochemical properties for short and long‐time periods. One of the topics not studied in detail is the influence in the change of surface roughness and morphology of metallic catalytic layers on the fuel cell working conditions. For platinum anodic catalysts a columnar growth was demonstrated after 1 month of hydrogen/oxygen continuous operation at 1 A cm−2. In this sense the mass balance equations was solved to obtain current and overpotential profiles for these columnar electrodes adapting a curvilinear parametric model of periodic columns (trochoid curvilinear contours). Since they acted as a dynamic system, numerical solutions were not useful as they permanently needed parametric profile optimizations. The use of exact analytical functions instead, reduced large computational times and assured this information only knowing the structure morphology. The analytical solutions were compared with those of a smooth surface (early uses of the fuel cell) and with experimental values obtained using a 200 cm2 home‐made hydrogen/oxygen polymeric membrane cell.