Proton-conductive Ceramic Fuel Cells (PCFCs) have potential to achieve higher energy efficiency compared with conventional SOFCs, since protons react with oxygen to generate water at cathode side and the fuel at anode side does not diluted. However, some part of generated electrons reacts with transferred electron holes, and the total numbers of electrons in external circuit decrease. The generation and extinction of holes result in loss of energy and excessive heat generation. Then, the hole current should be carefully examined and controlled.

The conductivity of holes strongly depending on local temperature, thickness of electrolyte, partial pressure of oxygen etc.. Therefore, for optimizing the performances of a given PCFCs, coupled analysis considering local temperature, partial pressures, ionic current density is mandatory. Especially, the temperature is one of the strongest factors of the conductivity. Then, the temperature distribution was discussed with results from coupled numerical model considering local temperature distributions, partial pressures, geometries of a cell, and overpotentials.