Computational Analysis of MHD Mixed Convection and Fluid–Structure Interaction of Non-Newtonian Fluids in a Vented Cavity with a Flexible Wall

The present study explores the complex phenomena of fluid-structure interaction (FSI) during magnetohydrodynamic conjugate mixed convective heat transfer of non-Newtonian fluid flow in a vented differentially heated cavity. A solid conducting block is fitted with the left heated wall, and one more conducting block cum divider is located at the middle position of the bottom wall. The non-Newtonian fluid is entering into the cavity through a small port on the left-bottom wall and exits through a second port on the top of the right vertical wall. The presence of the flexible wall at the top of the cavity significantly alters the thermo-fluid structure within the cavity and further, it is affected by the presence of the bottom conducting block. Evolved transport equations governing the unsteady thermo-fluid phenomena are solved numerically using the Galerkin Finite Element Method. The study is carried out for a wide range of pertinent parameters affecting the thermal convection like Reynolds number (Re = 100–500), Richardson number (Ri = 0.1–100), Hartmann number (Ha = 0–60), power-law index ( n  = 0.4–1.4), and the flexible wall elastic modulus ( E  = 10 ⁴ –10 ⁹ ). The result shows that the elasticity modulus of the flexible wall dictates the thermo-fluid phenomena within the cavity and its lower value corresponds to the higher heat transfer rate. Furthermore, the setting of the convection mode (combination of Ri and Re) plays a significant role in the magnitude of the heat transfer characteristics. Intensifying the magnetic field strength, fluid flow dampens as well as heat transfer rate deteriorates markedly.