The effect of hydrogen cross-over from anode to cathode through the membrane is modeled by a total leakage current (A). In addition to the source terms expressed by Equation 20–18 through Equation 20–20, the following extra volumetric source terms are added to the corresponding equations:

(20–55)

(20–56)

(20–57)

Here, and are the volumes of the catalytic layers on the anode and cathode sides, and 2 and 4 are the numbers of electrons per mole of reactants and products.

Accordingly, the volumetric leakage current () is subtracted from the cathode transfer current () that is computed by Equation 20–6 and Equation 20–8.