In this paper analysis results for a 2D solid oxide fuel cell model are presented. The model is solved on an unstructured mesh with the finite-volume scheme using an iterative Newton’s method. A cost function is computed on the anode/electrolyte interface proportional to the ratio of the density of hydrogen to water. Sensitivity derivatives of the cost function are obtained with respect to the design variable, Psi, the ratio of porosity to tortuosity in the mean transport pore model with three methods: finite-difference, direct differentiation, and the adjoint technique. The results of the three methods are compared for accuracy. An optimization step is taken using the sensitivity derivative to improve the value of the cost function. The cost function is improved with the design step.