Analytical solutions of an isothermal two-dimensional model of a cathode flow channel in a proton exchange membrane fuel cell - Thosar, Aniket U.; Lele, Ashish K. (Chemical Engineering Science, 2018)
Two key assumptions are usually made while deriving analytical solutions of coupled kinetics and transport equations in a single channel on the cathode plate of a proton exchange membrane fuel cell (PEMFC). These are: plug flow and uniform oxygen concentration along the depth of the channel. However these assumptions are not always valid under typical operating conditions of a PEMFC, and particularly so at high current density. In this article we relax these two assumptions and present approximate analytical solutions of the governing equations using the methodology of separation of variables followed by power series solution. Spatial profiles of oxygen concentration and current density were derived, which led to the final derivation of a comprehensive current-potential relationship (polarization curve) in the reaction-controlled regime of an operational PEMFC. We compare polarization curves predicted by the present model with predictions of the earlier analytical model and also with a complete 3D-simulation of the same flow geometry and operation conditions. The local profiles of oxygen concentration and the polarization curve predicted by the present model compare far better with the 3D simulations than the earlier analytical model. While this comparison highlights the importance of the effects of finite oxygen diffusion rate and velocity profile in the channel on the polarization curves, it also points to other important factors that affect the current-potential relation.