A fuel cell is an electrochemical device that converts chemical energy into electrical energy. The essential difference between a fuel cell and a battery is that the fuel and oxidant are continually supplied to a fuel cell whereas a battery has a finite amount of fuel stored within it which eventually becomes exhausted, after which the battery has to be recharged or replaced. We consider here a tubular cell which is run on methane. A mathematical model for the reaction and transport processes in the cell is presented. This takes into account diffusion, advection and reaction as well as the electrochemical flow of oxygen. When the device is running steadily, we perform an analysis, using the method of matched asymptotic expansions to find the flow field, the mass fractions of each chemical species and the electrical power output. These results are confirmed by a numerical technique and compared with experimental results.