Volumetric source terms (kg/m³-s) for H₂, O₂, and the dissolved water content in the triple-phase boundaries (catalyst layers) due to electrochemical reactions are:

(20–18)

(20–19)

(20–20)

In the above equations, , , and are the molecular mass of water, oxygen and hydrogen, respectively, is the Faraday constant, and 2 and 4 are the numbers of electrons per mole of reactants and products.

Since the total electrical current produced in the cathode and the anode catalyst layer, respectively, is the same, we have the following equation for current conservation:

(20–21)

The performance and efficiency of the PEM fuel cell may be affected by the nitrogen (N₂) crossover through the membrane. N₂ is transported from the cathode to anode side due to the crossover effect, where the driving force is the concentration gradient across the membrane. The N₂ concentration gradient can be expressed through the N₂ partial pressures in the cathode and anode catalyst layers. The nitrogen flux is calculated based on the difference of the partial pressures:

(20–22)

where

and = N2 partial pressures in the cathode and anode catalyst layers, respectively (Pa)

= membrane thickness (m)

= crossover coefficient (kmol/(s m Pa))

is calculated based on an empirical formulation [537]:

(20–23)

where

= N2 crossover scaling factor

= activation energy for N2 equal to 24 kJ/mol

= reference temperature equal to 303 K

= volumetric ratio of water in the membrane given by Equation 20–24

(20–24)

where is the water content, and and are the molar volumes of the dry membrane and liquid water, respectively.

In the Ansys Fluent PEMFC model, the N₂ crossover flux is treated as a source term in the first layer of mesh cells near the interface between the catalyst layers and membrane.