Integrated fuel cell and combustion system

A topping cycle fuel cell unit includes a support plate having internal flow passages that extend to combustion outlets, a first electrode layer, an electrolyte layer, and a second electrode layer. The second electrode layer is configured to be coupled to another support plate of another fuel cell unit. The internal flow passages are configured to receive and direct air across the first electrolyte layer or the second electrolyte layer and to receive and direct fuel across another of the first electrolyte layer or the second electrolyte layer such that the first electrode layer, the electrolyte layer, and the second electrode layer create electric current. The internal flow passages are configured to direct at least some of the air and at least some of the fuel to the combustion outlets where the at least some air and the at least some fuel is combusted.