The first two dimensional mathematical model of a complete direct propane fuel cell (DPFC) is described. The governing equations were solved using FreeFem software that uses finite element methods. Robin boundary conditions were used to couple the anode, membrane, and cathode sub-domains successfully. The model showed that a polytetrafluoroethylene membrane having its pores filled with zirconium phosphate (ZrP-PTFE), in a DPFC at 150 degrees C performed much the same as other electrolytes; Nafion, aqueous H3PO4. and H2SO4 doped polybenzimidazole, when they were used in DPFCs. One advantage of a ZrP-PTFE at 150 degrees C is that it operates without liquid phase water. As a result corrosion will be much less severe and it may be possible for non-precious metal catalysts to be used. Computational results showed that the thickness of the catalyst layer could be increased sufficiently so that the pressure drop between the reactant and product channels of the interdigitated flow fields is small. By increasing the width of the land and therefore the reactant's contact time with the catalyst it was possible to approach 100% propane conversion. Therefore fuel cell operation with a minimum concentration of propane in the product stream should be possible. Finally computations of the electrical potential in the ZrP phase, the electron flux in the Pt/C phase, and the overpotential in both the anode and cathode catalyst layers showed that serious errors in the model occurred because proton diffusion, caused by the proton concentration gradient, was neglected in the equation for the conservation of protons. (c) 2010 Elsevier B.V. All rights reserved.