Analytical calculation of transfers across a cermet for solid oxide fuel cells and electrolyzers

This work focuses on the calculation of transfers inside a cermet for solid oxide membrane fuel cells and electrolyzers. A differential system of equations presented in a previous work is linearized for low inlet current densities using assumptions that can be checked quantitatively. By integrating the linearized equations, we obtain explicit functions that allow direct calculation of the physical quantities describing the transfers of the process inside the cermet. The functions show good agreement with the values obtained with the non-linearized system. In addition, the model does not require any numerical simulation to be solved and can be implemented in common spread sheets fairly accurately. A remarkable dimensionless number, named A, appears in the demonstration and is used for the calculation of the reaction layer thickness of the cermet, where 99.9% of the charge transfer occurs. This thickness does not depend on inlet current density or on the thickness of the cermet.