A nuclear reactor cooling system with passive cooling capabilities operable during a loss-of-coolant accident (LOCA) without available electric power. The system includes a reactor vessel with nuclear fuel core located in a reactor well. An in-containment water storage tank is fluidly coupled to the reactor well and holds an inventory of cooling water. During a LOCA event, the tank floods the reactor well with water. Eventually, the water heated by decay heat from the reactor vaporizes producing steam. The steam flows to an in-containment heat exchanger and condenses. The condensate is returned to the reactor well in a closed flow loop system in which flow may circulate solely via gravity from changes in phase and density of the water. In one embodiment, the heat exchanger may be an array of heat dissipater ducts mounted on the wall of the inner containment vessel surrounded by a heat sink.