A system and method for operating a fuel cell, including reacting a fuel with an oxidant within the fuel cell to produce electricity and reaction products comprising steam. The fuel is fed through the fuel cell, wherein a concentration of the steam increases in the first direction through the fuel cell. The direction of fuel-flow through the fuel cell is altered or reversed upon satisfying a condition, thereby altering the concentration gradient of steam in the fuel cell and providing for removal of carbon deposition with the fuel cell. Such reversal of fuel flow may also provide an exhaust from the fuel cell that can regenerate an external or adjacent hydrocarbon reformer.