This paper develops a mathematical model and a structured procedure to optimize the internal structure (relative sizes, spacings) and external shape (aspect ratios) of a unit PEM fuel cell so that net power is maximized. The optimization of flow geometry is conducted for the smallest (elemental) level of a fuel cell stack, i.e., the unit PEM fuel cell, which is modeled as a unidirectional flow system. The polarization curve, total and net power, and efficiency are obtained as functions of temperature, pressure, geometry and operating parameters. The optimization is subjected to fixed total volume. There are two levels of optimization: (i) the internal structure, which basically accounts for the relative thicknesses of two reaction and diffusion layers and the membrane space, and (ii) the external shape, which accounts for the external aspect ratios of a square section plate that contains all unit PEM fuel cell components. The available volume is distributed optimally through the system so that the net power is maximized. Temperature and pressure gradients play important roles, especially as the fuel and oxidant flow paths increase. Numerical results show that the optimized internal structure is “robust” with respect to changes in external shape. The optimized internal structure and external shape are results of the optimal balance between electrical power output and pumping power required to supply fuel and oxidant to the fuel cell through the gas channels. Directions for future improvements at the PEM fuel cell stack level in constructal geometric optimization are discussed.

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