A catalytic firebox reactor employing an exothermic catalytic reaction channel and multiple cooling conduits for creating a partially reacted fuel/oxidant mixture. An oxidation catalyst is deposited on the walls forming the boundary between the multiple cooling conduits and the exothermic catalytic reaction channel, on the side of the walls facing the exothermic catalytic reaction channel. This configuration allows the oxidation catalyst to be backside cooled by any fluid passing through the cooling conduits. The heat of reaction is added to both the fluid in the exothermic catalytic reaction channel and the fluid passing through the cooling conduits. After discharge of the fluids from the exothermic catalytic reaction channel, the fluids mix to create a single combined flow. A further innovation in the reactor incorporates geometric changes in the exothermic catalytic reaction channel to provide streamwise variation of the velocity of the fluids in the reactor.