TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The catalyst materials are comprised of formulations of rhodium, nickel, ruthenium, palladium, platinum, molybdenum, vanadium, or cobalt with ceria, alumina, or zirconia. The fuel delivery element is coated with a passivating material configured to minimize solid carbon nucleation. The passivating material is comprised of formulations of ceria, alumina, or zirconia.    TECHNOLOGY FOCUS - INSTRUMENTATION AND TESTING - Preferred Components: The fuel delivery element: is operative to convert a higher hydrocarbon fuel to a smaller species, and to lower production of solid carbon; includes a reforming section configured to reform a hydrocarbon fuel to a smaller species in the presence of an oxidant, which is comprised of at least one of water, carbon dioxide or oxygen; further includes an anode exhaust gas recirculation device configured to cause recirculation of oxygen-rich anode exhaust gas formed in the anode-side cavity of the fuel cell through a length of the fuel delivery passage of the fuel delivery element; further includes a pre-reforming section disposed upstream of the anode exhaust gas recirculation device; and comprises an anode exhaust gas recirculation device configured to cause recirculation of oxygen-rich anode exhaust gas formed in the anode-side cavity of the fuel cell through a length of the fuel delivery passage of the fuel delivery element. The reforming section is located along the fuel delivery element downstream of the anode exhaust gas recirculation device. The anode exhaust gas recirculation device comprises a constriction in the walls forming the fuel passage of the fuel delivery element and at least one suction bore downstream of the constriction, where the suction bores open to the anode-side cavity of the fuel cell, thus anode exhaust gas is drawn into the fuel delivery device through the suction bores by suction and fuel is reformed in the presence of the anode exhaust gas within the fuel delivery device. In the reactor system, a partition is disposed across the fuel passage in the fuel delivery element, and the constriction comprises an orifice in a partition. The constriction comprises a Venturi shape formed in the walls of the fuel delivery element. The portion of the fuel delivery element comprises an ejector configured to eject fuel into the cavity. The ejector is disposed adjacent the fuel outlet. The reforming section comprises: a material to reform a hydrocarbon fuel to a smaller species in the presence of an oxidant; and at least one catalyst material coated on interior and exterior surfaces of the walls of the fuel delivery element. The fuel delivery element comprises an anode exhaust gas recirculation device configured to cause circulation of oxygen-rich anode exhaust gas formed in the anode-side cavity of the fuel cell within a section of the cavity of the fuel cell. The fuel delivery element comprises a Venturi or an orifice located along a portion of the fuel passage. The Venturi or the orifice is disposed adjacent the fuel outlet of the fuel delivery device. The walls of the fuel delivery element: are comprised of a ceramic or a metallic material; and have a thickness selected to provide a predetermined rate of heat transfer through them. The fuel cell is: a solid oxide fuel cell; tubular; and is closed at one end and open at an opposite end, where the open end comprises an anode exhaust port. The reactor system is supported by a tube sheet that forms a wall of a coolant chamber. The tube sheet further includes a block of insulation to aid in controlling the temperature of the coolant chamber or the temperature of the reactor system within the fuel cell. In the fuel cell system, a downstream section of the reactor system is in thermal communication with the fuel cell, and an upstream section of the reactor system extends outside of the fuel cell and is in thermal communication with a chamber external of the fuel cell. The external chamber comprises an anode exhaust chamber or a coolant chamber supplied with a coolant fluid. The coolant fluid comprises air or a fuel. The fuel cell system is configured to have a temperature gradient along the fuel cell. The fuel cell system further includes: a supplemental oxidant feed into the fuel inlet; an oxygen partial pressure sensor disposed within the fuel cell; many additional fuel cells arranged in a stack and fused to a tube sheet that forms a part of a fuel plenum; an insulating material (106) disposed between the fuel plenum and the fuel cells, where the reactor systems extend through the insulating material, thus the fuel cell system is divided into zones having different operating temperature ranges; a plenum thermally insulated from the fuel cell to maintain a lower temperature in the plenum than in the cavity of the fuel cell, where the reactor system extends from the plenum into the fuel cell; and a fuel source in fluid communication with the fuel inlet of the fuel delivery element. The reactor system is disposed in each of the additional fuel cells. The reactor system is in fluid communication with a fuel source under pressure, where the recirculation is induced within the cavity by a motive force due to the pressurization of the fuel. The reactor system is disposed to eject fuel into the cavity at an entrance to the cavity. The fuel source is comprised of a hydrocarbon fuel, methane, biogas or a liquid fuel. The fuel source is comprised of a fuel mixture which, when at thermodynamic equilibrium at an operating temperature of the fuel cell lowers a partial pressure of oxygen below that of oxygen on a cathode side of the fuel cell. Preferred Method: The method further comprises reforming the fuel within the cavity of the fuel cell to smaller hydrocarbon species, preferably hydrogen and carbon monoxide; reforming the hydrocarbon fuel through reaction with at least one catalyst material within the cavity; reforming the hydrocarbon fuel in a fuel delivery tube disposed internally within the cavity, where the fuel delivery tube has an inlet in fluid communication with a fuel source and an outlet within the cavity; introducing the fuel under pressure into the cavity; and controlling the temperature of the fuel introduced into the cavity and the temperature of reactions within the cavity.