Dynamics of a Heated Flexible Cantilever Plate under Natural Convection in a Square Cavity.*

In this study, we conducted an analysis on the dynamics of a flexible cantilever plate positioned centrally within a square cavity subject to natural convection. The investigation encompasses four distinct boundary condition scenarios, where two opposing walls are subjected to isothermal heating while the remaining two walls are maintained adiabatic. The dynamics of the flexible plate were examined across a range of non-dimensional parameters, including the Cauchy number (Ca), Rayleigh number (Ra), and the mass ratio (M). Computational simulations were 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. Distinct shifts in the dynamic behavior of the plate were observed corresponding to different boundary conditions. In Cases 1 and 4, the plate exhibited no discernible unsteadiness across the considered parameter range, whereas Cases 2 and 3 revealed oscillatory behavior within certain parameter regimes. Notably, the amplitude (A∗) and period of oscillation (T ) of plate oscillations, alongside pertinent heat transfer metrics such as the average Nusselt number (Nu) over the heated flexible plate and the average temperature inside the cavity (Tavg), were meticulously analyzed. The findings of this investigation offer comprehensive insights into the influence of controlling parameters on the dynamic response of the plate. Additionally, bifurcation diagrams were constructed for all cases, illustrating the plate tip displacement against varying Ra values, further elucidating the complex interplay between system parameters and dynamic behavior.