Aimed at improving the maximum available power density in a planar-type solid oxide fuel cell, an analytical model is proposed in this work to find the optimum size of a current collector that collects the current from a specific active area of the electrode-electrolyte layer. Distributed three-dimensional current collectors in gas delivery field are designated to allow a larger area of the electrode-electrolyte layer to be active for electrochemical reaction compared to conventional designs that gas channels are separated by current collectors. It has been found that the optimal operating temperature of a planar-type solid oxide fuel cell might be around $850°C$, if the sizes of the distributed current collectors and their control areas are optimized. Decreasing the size of both the current collector and its control area is advantageous in achieving a higher power density. Studies also show that the optimal sizes of the current collector and the current collection area investigated at $850°C$ and zero concentration polarization are applicable to situations of different operating temperatures, and different concentration polarizations. The optimization results of the sizes of current collectors and their control areas are relatively sensitive to the contact resistance between the current collectors and the electrodes of the fuel cell. Results of great significance are provided in the analysis, which will help designers to account for the variation of contact resistance in optimization designing of a bipolar plate of fuel cells.

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