A component cooling water system for a nuclear power plant. In one embodiment, the system includes an inner containment vessel housing a nuclear reactor and an outer containment enclosure structure. An annular water reservoir is formed between the containment vessel and containment enclosure structure which provides a heat sink for dissipating thermal energy. A shell-less heat exchanger is provided having an exposed tube bundle immersed in water held within the annular water reservoir. Component cooling water from the plant flows through the tube bundle and is cooled by transferring heat to the annular water reservoir. In one non-limiting embodiment, the tube bundle may be U-shaped.