Transient thermal analysis plays the central role in the design and optimization of high temperature solid oxide fuel cells (SOFCs) during startup/shutdown, because of the potential for damaging thermal gradients to develop within the SOFC components. To this end, we consider the SOFC unit cell, which is heated by hot air supplied into the oxidizer channel at a specified, time-dependent inlet temperature. Closed-form analytical solutions are obtained for two simplified 1-D models of the SOFC unit cell: (1) purely convective heating, assuming thermally-thin cell components, and (2) convective-conductive heating, under the assumption of local thermal equilibrium in the direction normal to flow. Given thresholds of maximum allowable temperature gradients, the optimal design is one that minimizes the total time required to reach a prescribed final operating temperature. With appropriate scaling, the models we developed predict the maximum temperature gradients and heating time requirements for various operating conditions, and the results are generalized by presentation in terms of the effective cell Peclet number and inlet temperature function. Finally, these predictions are used to identify favorable trends and design rules for optimizing the transient heating process. The simplicity, computational savings, and ability to capture the essential physics of the transient process demonstrated by application of the analytical models provide compelling justification for their use over more accurate, highly detailed, numerical/CFD schemes.

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