Fuel cells are a clean and efficient alternative to existing methods of energy production. Solid oxide fuel cells produce electricity directly from the combustion of methane or other hydrocarbons. We present a mathematical model for a tubular solid oxide fuel cell, which includes consideration of advection, diffusion and electrochemical activity. The chemical reaction scheme includes both steam reforming and partial oxidation of methane, as well as carbon deposition on the anode surface. In the steady state, an asymptotic analysis is performed to find the composition of the exhaust gas. The results are compared with experimental data and good agreement is obtained.