Two-dimensional approximate analytical solutions for the anode of a direct methanol fuel cell

Abstract

We present the derivation of two-dimensional (2D) approximate analytical solutions for the velocities, pressure, and methanol mass fraction in the anode of a direct methanol fuel cell. These are obtained from a steady-state, liquid-phase model that considers conservation of mass, momentum, and species together with the electrokinetics. A narrow-gap approximation and scaling arguments allow for a significant reduction in the mathematical complexity; that is, the partial differential equations (PDEs) reduce to a set of ordinary differential equations and one parabolic PDE. Integration, Taylor-series expansions, homogenization, and separation of variables then allow for approximate analytical solutions. Two typical types of flow fields are considered: porous (e.g. a metallic mesh) and plain (e.g. parallel or serpentine flow channels). For the porous flow field, the 2D approximate analytical solutions can capture the three-dimensional behavior of the anode, whereas the solutions are less accurate for the latter. The analytical solutions are verified with numerical solutions of the full set of equations and validated with experiments for the porous flow field: Good agreement is found. We further highlight how the solutions can be extended to encompass the whole cell, two-phase transport, and other types of liquid fuel cells such as the direct ethanol fuel cell. © 2009 The Electrochemical Society.