Analysis of a model for a loaded, planar, solid oxide fuel cell

We analyze a model for the combustion of methane in a planar solid oxide fu el cell. The model includes diffusive and advective transport processes, an electrochemical source of oxygen, and the consumption of oxygen and methan e through combustion. The effect of the presence of the reaction products a nd atmospheric nitrogen is also included. Since the combustion takes place in a narrow gap we are able to reduce the problem from three to two dimensi ons. After assuming that the flow is steady and axisymmetric, we use the me thod of matched asymptotic expansions to construct solutions in six asympto tic regions. This allows us to model the voltage-current characteristics fo r a given flowrate of fuel and predict the position of the flame region tha t separates an oxygen-rich region from a fuel-rich region. Comparisons show that the theory is in reasonable agreement with experiments.