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 congruent to 4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda \cong 4$$\end{document}), 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.