An Analytical Analysis on the Cross Flow in a PEM Fuel Cell with Serpentine Channel

A serpentine flow channel can be considered as neighboring channels connected in series, and is one of the most common and practical channel layouts for PEM fuel cells since it ensures the removal of liquid water produced in a cell with excellent performance and acceptable parasitic load. During the reactant flows along the flow channel, it can also leak or cross directly to the neighboring channel via the porous gas diffusion layer due to the high pressure gradient caused by the short distance. Such a cross flow leads to a larger effective flow area resulting in a substantially lower amount of pressure drop in an actual PEM fuel cell compared to the case without cross flow. In this work, an analytical solution is obtained for the cross flow in a PEM fuel cell with a serpentine flow channel based on the assumption that the velocity of cross flow is linearly distributed in the gas diffusion layer between two successive U-turns. The analytical solution predicts the amount of pressure drop and the average volume flow rate in the flow channel and the gas diffusion layer. The solution is validated over a wide range of the thickness and permeability of the gas diffusion layer by comparing the results with experimental measurements and 3-D numerical simulation in literature. Excellent agreement is obtained for the permeability less than 10-9 m2, which covers the typical permeability values of the gas diffusion layers in actual PEM fuel cells. The solution presents an accurate and efficient estimation for the cross flow providing a useful tool for the design and optimization of PEM fuel cells with serpentine flow channels.