Asymptotic reduction for numerical modeling of polymer electrolyte fuel cells

Most existing three-dimensional (3D) models for the polymer electrolyte fuel cell (PEFC), as well as other types of fuel cells, are fully numerical and computationally expensive. While such models are undoubtedly useful, they cannot provide the qualitative understanding that comes from a complete prior nondimensional analysis of the problem. Here, earlier ideas for the derivation of a two-dimensional (2D) asymptotically reduced model to describe steady isothermal gas-phase flow in the cathode of a PEFC are extended to a 3D nonisothermal model for a whole PEFC with straight channel flow distributors. As well as providing characteristic current density and temperature difference scales for the whole cell, it is also possible to extract potential drops over individual cell components. The analysis indicates that, for realistic operating ranges, the PEFC is sufficiently isothermal with respect to the mass, momentum, and charge transport to enable the thermal problem to be decoupled from the rest, a simplification not noted previously. After the relevant nondimensional parameters have been identified, a reduced model is proposed and some preliminary numerical results comparing the polarization curves obtained from the reduced and 3D models are presented. Good agreement is found; most significantly, the reduced model is found to require between one and two orders of CPU time less than the full 3D model.