Fuel cells are promising for future energy systems, because they are energy efficient and able to use renewable fuels. However, there is still a need for improvement and a fully coupled computational fluid dynamics (CFD) approach based on the finite element method, in three-dimensions, is developed to describe an anode-supported planar solid oxide fuel cell (SOFC). Governing equations are solved for electron, ion, heat, gas-phase species and momentum transport, and implemented and coupled to kinetics describing electrochemical reactions. It is shown that the heat generation due to the electrochemical reactions results in an increased temperature distribution and further current density along the main flow direction. This increase is limited due to the consumption of electrochemical reactants within the cell. For cases with a high current density generation, the resistance to electron transport and the oxygen gas-phase flow is high for positions (within the cathode) under the interconnect ribs, which gives a high current density gradient in the direction normal to the electrode/electrolyte interface. The increase in the current density is accelerated by an increased temperature along the main flow direction, due to the strong coupling between the local current density and the local temperature. It is shown that an increase of the anode active area-to-volume ratio with a factor of two transfers around 20 mV of (activation) polarization from the anode to the cathode side, for the case investigated in this study. (C) 2013 ElSevier Ltd. All rights reserved.