Mathematical Modeling And Simulation For The Catalyst Layers Of PEMFC

The proton electrolyte membrane fuel cell(PEMFC) is considered as one of the most promising alternative automotive power sources to compete with internal combustion engines, due to its higher efficiency, lower overall emission and eco-friendliness.Since the attempt to develop a good fuel cell experimentally is expensive and time consuming, mathematical modeling and numerical simulation have become an important tool to explore the relationship between the cell performance and the cell structure parameters and the operation conditions. This paper focuses on the mathematical modeling and simulation of PEMFC' s catalyst layer. First, a brief overview and development perspectives of the fuel cell are given. In addition, PEMFC and cathode catalyst layers of it are also introduced. On the basis of the oxygen balance and the Butler-Volmer equation and the Ohm law, the modeling of the cathode catalyst layers of PEMFC is given in the form of a set of non-linear differential equations: The boundary conditions can be specified as,η_o is taken as an unknown parameter. The callenge comes from the process of solving the equation set due to the feature of the cathode catalyst layers of PEMFC. A cathode catalyst layer, as a key component of PEMFC, is a porous and composite thin-film coating located between a membrane and a cathode gas diffusion layer. The thickness of the catalyst layers and the cross-section of flow channels are in very different size scale. The mesh must be small enough for the sake of chemical reaction, so the numerical approaches such as finite element methods and finite volume methods pose a big challenge.Then this paper transforms the non-linear ordinary differential equations into a third-order nonlinear ordinary differential equations with variable coefficients,(?) (4.3)with the boundary conditions as,η(z= o) =η₀ (4.4)and gives proof of boundedness.Since concentration of oxygen in chemical reactions is very close to its initial concentration, oxygen concentration was taken as constant, giving an exact solution of the simplified modeling of the catalyst layer of PEMFC.This paper also gives a detailed description of power series method. The method has been applied to solve systems of non-linear differential equations. The numerical example has been presented to show that the approach is promising and it is worth continuing the research in this direction. Power series method has been proposed for solving differential equation systems. This method is very simple and effective for most of differential equations systems. So this method is applied to solve the mathematical modeling of the catalyst layer of PEMFC with Maple soft.Finally the solutions from the catalyst layer of PEMFC to the exact solutions of the simplified modeling are compared. The comparison shows that satisfactory accuracy can be reached by the first six terms of the power series. Image display results shows that with the increasing of current density, the oxygen concentration gradient increases; current intensity from the interface of the catalyst layer and diffusion layer to the membrane increases; overpotential along the interface of the catalyst layer and diffusion layer to the membrane increases, and reaches to the maximum at the interface of the catalyst layer and membrane, to the minimum at the interface the catalyst layer and diffusion layer.