In the present work, a three dimensional model examining the fluid flow along with the fundamental transport phenomena occurring in a typical polymer electrolyte fuel cell (PEMFC), i.e. heat transfer, mass transport and charge transfer, has been developed. The flow field was simulated according to the well known Navier-Stokes equations, while the heat transfer was described by the typical conduction/convection equation and the mass transport by the convection/diffusion one. Furthermore, reaction kinetics were studied by the Butler-Volmer equation for the heterogeneous reactions occurring at the porous electrodes. The developed model was numerically solved by using the commercially available CFD package CFD-RC©, which is based on the multi-step finite volume method. The fuel cell performance in terms of velocity, temperature, mass fractions of active compounds and electric field has been investigated as well.