Electrochemical heating

Heating sources for the energy solution are comprised of enthalpy of reactions (assumed to occur on the electrolyte/fuel interface), enthalpy changes of gaseous species from reference to ambient temperature, and resistive heating. It is assumed that there is no reaction on the air side. The volumetric source terms are ascribed to the electrolyte region.

Enthalpy of formation and enthalpy changes, normalized by number of contributing electrons, are calaculated by specie, accumulating products and reactants separately for each of air and fuel. The separate (normalized) enthalpy accumulations are then combined according to

\[{{h}_{src}}=\left( {{h}_{form}}+{{h}_{P,fuel}}-{{h}_{R,fuel}}+{{h}_{P,air}}-{{h}_{R,air}} \right)\frac{i}{F{{l}_{e}}}\]
where i is current density, F is Faraday’s constant, l_e is the electrolyte thickness, h_form is accumulated enthalpy of formation, h_P,fuel is accumulated enthalpy change of products on the fuel side, h_R,fuel is accumulated enthalpy change of reactants on the fuel side, and similarly for the air side. The final source for the energy equation then becomes

$${{S}_{\text{energy}}}=-{{h}_{\text{src}}}-\frac{iV}{{{l}_{e}}}$$