Dynamics of a heated elastic cantilever plate under shear-driven mixed convection flow in a confined cavity

This study investigates the fluid–structure interaction (FSI) of a heated, flexible cantilever plate inside a square cavity subjected to mixed convection. The cavity consists of a stationary hot bottom wall, a cold moving top wall, and adiabatic vertical sidewalls, establishing Rayleigh–Bénard convection with an additional instability introduced by the shear forces induced by the moving top wall. Numerical simulations are carried out using the open-source Stanford University Unstructured (SU2) multiphysics solver. The effects of Rayleigh number (Ra), Reynolds number (Re), and Cauchy number (Ca) on the flow field and plate dynamics are examined at fixed Prandtl number (Pr) and temperature difference. A bifurcation analysis is conducted to capture transitions in the plate's dynamic behavior. Various dynamic regimes are identified, including static mode, periodic flapping, period-doubled flapping, quasi-periodic, and chaotic flapping modes. The results reveal that increasing Re enhances flow asymmetry due to stronger top-wall shear, promoting period-doubling and earlier onset of chaos. Higher Ca reduces plate stiffness, amplifies oscillation amplitude, and leads to more complex, nonlinear flapping dynamics dominated by inertial forces. The vertical position of the plate also strongly influences its response: proximity to the hot bottom wall triggers earlier chaotic transitions, while placement near the cold top wall yields larger oscillation amplitudes but delayed instability. Overall, this work provides new insights into the coupled effects of thermal convection and structural flexibility in confined domains, offering a foundation for future studies in thermal–fluid–structure interactions relevant to advanced engineering applications.