The source terms of energy equation

The source terms of energy equation is divided into two terms. In one hand, the heat source is generated by electrochemical reactions inside the membrane which is a function of current density. In the other hand, heat source is produced by the ohmic resistance mainly caused by the proton transfer. Both ways of heat generation affect the temperature distributions along the PEM fuel cell. And then Ohmic resistance depends on the water content. If the membrane was completely humidified, the limit current would appear from insufficient oxygen transport along the electrode and thus increasing the concentration losses. The humidification variation of the electrolyte is due to diffusion and electro-osmotic transfer of water between the electrode and the membrane. Source terms in the above governing equations are presented in Table 1 for different zones of cathode side. Both initial and boundary conditions are necessary to close the system of equations including conservation equations of continuity, momentum, energy and species. For the initial conditions, we assume that all parameters are initialized to the ambient conditions except to the membrane which it is initially hydrated. With the single-domain approach, no internal boundary conditions need to be defined and the boundary conditions are only at external surfaces of the complete computational domain.