Computational Analysis of MHD Mixed Convection in a Heated Lid-Driven Cavity with Fins

A numerical investigation of magnetohydrodynamic (MHD) mixed convection in a lid-driven square cavity with internal heat generation is presented. The cavity is filled with an electrically conducting fluid, and the top wall moves at a constant velocity while the remaining walls are stationary. A uniform magnetic field is applied parallel to the lid motion. The governing continuity, momentum, and energy equations are solved using the Galerkin weighted residual method, finite element method under the Boussinesq approximation. The effects of the Richardson number, Hartmann number, Prandtl number, and internal heat generation parameter on flow and heat transfer characteristics are examined. Results are provided in terms of streamlines, isotherms, the average Nusselt number within the cavity, and the local Nusselt number along the horizontal line of the cavity, depending on the various combinations of the dimensionless governing parameters. The results indicate that increasing Ha suppresses fluid motion and reduces convective heat transfer, whereas higher Ri enhances buoyancy-driven flow. Internal heat generation elevates temperature levels and reduces the overall heat transfer rate. The study highlights the competing roles of magnetic damping and buoyancy forces in controlling thermal performance.