The present study reviews the relevant research done on the fluid-structure interaction (FSI) in channels and vessels. The cases of FSI in channels with elastic plates, channels with variable geometry, flow airfoils, blood vessels, and heart valves are presented, using data from credible research articles. The review is carried out with a focus on the performance of the FSI method in solving engineering problems in channels, reporting its findings such as the effect of power-law exponent, the Nusselt number in different parts of a fluid, lift, and drag for a rigid cylinder and a plate in Newtonian fluids, the formation of eddy current, and the distribution of velocity and pressure in a fluid and on walls. The review is instrumental for researchers, engineers, and academics in providing comprehensive insight into methodologies and applications of fluid-structure interaction.
