Unsteady free convection in a composite enclosure having flexible wall

Transient free convection in a composite enclosure having a cold flexible plate and a hot rigid plate is simulated numerically. It is assumed that the flexible plate is hyper-elastic. A porous layer with various sizes and permeabilities is attached to the rigid plate. The enclosure is filled with water. Fluid flow in the fluid domain was governed by the Navier-Stokes equations, and the flow within a saturated porous layer was governed by the Brinkman-Forchheimer extended Darcy model. The unsteady continuity, momentum, and energy equations are solved using the Arbitrary-Lagrangian-Eulerian (ALE) approach based on the fluid-structure interaction (FSI). It is found that the development of convective flow goes through initial, transitional, and stationary states. Each state interval is shifted by varying the Darcy number and Rayleigh number. In the transitional state, the deformation of the flexible parts reaches its maximum bending. The profile of the flexible plate at steady state is in a sinusoidal shape for the non-Darcy regime, while it is in an asymmetric parabolic shape for the Darcy regime. The steady state is reached for Da ? 8 , Da = 10( - 3) , and Da = 10 (- 5) before t = 0 . 061 , 0 . 065 , 0 . 091 .