Comparison Between Analytical and Numerical Solutions for Water Transport in the Membrane on a PEMFC Model

Based on the necessity of better understanding the trade-off between the accuracy and computational efficiency of fuel cell models, this work aims to evaluate the impact of a simplifying assumption that permits the analytical description of water transport in the electrolyte. This simplification is the usage of a mean value for the water diffusivity, which is a function of the membrane’s water content. For this test, analytical expressions for the transport are developed for two different electro-osmotic drag models, Springer’s linear description and a piecewise-linear proposal. Those expressions are implemented on a PEMFC model along with the non-simplified description, which is solved numerically. Both submodels have good accuracies on the polarization curve while the water concentration does not reach the region of the peak in diffusivity ( \(\lambda \cong 4\) $\lambda \cong 4$ ), indicating that the underestimation of the back-diffusion caused by the mean can hinder the accuracy. As for computational time, improvements of 49.85 and 23.69% are, respectively, obtained for Springer’s and the piecewise-linear electro-osmotic drag models for a larger interval between the solved current densities. However, the analytical expressions cause a performance loss of 6.80% when a smaller interval is used for the piecewise description. Therefore, the assumption of a mean diffusivity can be beneficial for models if the cell operates under well-humidified conditions and with fewer points in the domain, but it loses some of its benefits with smaller intervals in current density.