To model solid oxide fuel cells (SOFC) with unresolved electrolyte, you need to perform the following:
Capture the fluid flow, heat transfer, and the mass transfer in the flow channels and in the porous anode and cathode electrodes.
Model the transport of the current and the potential field in the porous electrodes and in the solid conducting regions.
Model the electrochemical reactions that take place at the electrolyte/electrode/gaseous species interface.