The tubes in a component-cooling water heat exchanger are frequently affected by shock waves that occur due to fluid flow in a nuclear power plant. Thus, the tubes often wear out. Such a fluid flow may alter the dynamic characteristics of a water heat exchanger and cause instability in it. In this study, the dynamics and instabilities in a component cooling water heat exchanger are examined. Because of the presence of fluid coupling between tubes, periodic tubes were used to realize a periodic coupling system. It is found that each tube is coupled to the adjacent tube through the fluid, and the system is weakly coupled. The dynamic equations of the heat exchanger system with consideration for the effect of fluid flow were derived using Galerkin method. Numerical results revealed that fluctuations in fluid flow may significantly affect the dynamics and instability of a component cooling water heat exchanger.