In this study, the flow and heat transfer of a Newtonian power fluid in a cavity square is discussed. The top and bottom walls of the cavity are well insulated. the left vertical wall is at a hot temperature, and the right wall is at a cold temperature. A flexible elastic fin is fixed in the middle of the wall in different positions (left, right). The fluid-structure interaction (FSI) in the cavity and the hot fins and Newtonian fluid are combined. The interaction of the flow with the fin leads to the deformation of the fin and the change of the fin position modifies the flow and the heat transfer. The arbitrary Lagrangian-Eulerian (ALE) method with the moving mesh method is employed to model the deflection of the structure within the fluid domain. The finite element method is adopted to solve the governing equations, the parameters studied are the power law index, the Rayleigh number, the elasticity modulusPrandtl number (10).isotherms and streamlines and the average Nusselt number are studied. Results obtained in this study that increasing the Rayleigh number leads to an increase in the average Nusselt number, which is associated with a higher Rayleigh number. Therefore, it was found that a square cavity can increase the heat transfer rate.