Dynamics of a hot flexible cantilever plate under natural convection heat transfer in a square cavity

This study investigates the fluid-structure interactions of a flapping plate within a square cavity under four distinct boundary conditions, where two opposing walls are heated isothermally, and the others are adiabatic. These configurations are defined as case 1 (cooled side walls), case 2 (cooled top and bottom walls), case 3 (heated bottom and cooled top wall), and case 4 (heated top wall and cooled bottom wall). The effects of non-dimensional parameters, including Rayleigh number (Ra), Cauchy number (Ca), and mass ratio (β) on plate dynamics and convective heat transfer are analyzed. Numerical investigations are executed utilizing the SU2 open-source multi-physics computational fluid dynamics solver, with a fixed Prandtl number (Pr) set at 0.71 and dimensionless temperature difference (ϵ) established at 0.6. The results show that in cases 1 and 4, the plate exhibits no observable unsteadiness, while cases 2 and 3 reveal different oscillatory behavior within certain parameter ranges, including static mode, periodic flapping mode, quasi-periodic flapping mode, and chaotic flapping mode. In particular, the configuration in case 3 possesses higher inherent instability than case 2, causing the earlier onset of Hopf bifurcation. These findings provide valuable insights into the influence of boundary conditions on the behavior of flexible structures in fluid environments, highlighting the critical role of flow instabilities and boundary conditions in determining the dynamic response of the system.