Analysis of a Model for Multicomponent Mass Transfer in the Cathode of a Polymer Electrolyte Fuel Cell

Abstract

A chief factor that is thought to limit the performance of polymer electrolyte fuel cells (PEFCs) is the hydrodynamics associated with the cathode. In this paper, a two-dimensional model for three-component (oxygen, nitrogen, water) gaseous flow in a PEFC cathode is derived, nondimensionalized, and analyzed. The fact that the geometry is slender allows the use of a narrow-gap approximation leading to a simplified formulation. In spite of the highly nonlinear coupling between the velocity variables and the mole fractions, an asymptotic treatment of the problem indicates that oxygen consumption and water production can be described rather simply in the classical lubrication theory limit with the reduced Reynolds number as a small parameter. In general, however, the reduced Reynolds number is O(1), requiring a numerical treatment; this is done using the Keller--Box discretization scheme. The analytical and numerical results are compared in the limit mentioned above, and further results are generated for varying inlet velocity and gas composition, channel width and porous backing thickness, pressure and current density. Also, a novel, compact way to present fuel cell performance, which takes into account geometrical, hydrodynamical, and electrochemical features, is introduced.