Solid oxide fuel cell (SOFC) is a complicated system with heat and mass transfer as well as electrochemical reactions. The flow configuration has great impact on the system performance. Based on the established one dimensional direct internal reforming SOFC mathematical model, with the consideration of the flow, thermal and electrical characteristic, this paper developed the two dimensional mathematical model for both counter-flow and cross-flow types. Plus, the comparison and analysis of the steady distribution are performed. The results reveal that on the geometry parameters and inlet conditions, the outlet temperatures of counter-flow SOFC are lower than that of cross-flow. However, the average temperature of PEN plate is higher than cross-flow, and both the operating voltage and electric efficiency are also higher than that of cross-flow. This will be beneficial for the structure design of SOFC.

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