Three-dimensional approximate analytical solutions for direct liquid fuel cells

A three-dimensional (3D) isothermal model for a direct liquid fuel cell (DLFC) is introduced and reduced in several steps to finally yield closed-form approximate analytical solutions for the anode and overall cell behavior. The model reductions are verified with numerical solutions of the 3D counterpart and validated with experiments from an in-house DLFC fed with a liquid methanol-water mixture: overall, good agreement is found. The approximate analytical solutions are shown to be able to capture effects such as channel widths in the flow field and variations in the overall path length in the diffusion layer. These solutions lend themselves well to wide-ranging parameter studies and optimization of a DLFC with respect to geometry and operating conditions.