Heat and Mass Transfer Under MHD Mixed Convection in an Adjacent Two‐Sided Lid‐Driven Square Cavity

This study presents a numerical investigation of magnetohydrodynamic mixed convection flow of a binary gas mixture in an adjacent two‐sided lid‐driven square cavity. The top and left walls of the cavity move horizontally and vertically, respectively, generating complex flow interactions. The governing equations, based on the Boussinesq approximation, are reformulated using the stream function and vorticity , and solved using the Alternating–Direction–Implicit finite‐difference method. Simulations are conducted with our own MATLAB code across a broad range of nondimensional parameters: buoyancy ratio , Richardson number , Hartmann number , and heat generation/absorption coefficient , while keeping Prandtl number , Schmidt number , and Reynolds number fixed. The accuracy of the numerical model is validated through quantitative and graphical comparisons with benchmark results from established studies in the literature. Flow and thermal characteristics are analyzed via streamline, isotherm, and concentration contours, along with average Nusselt and Sherwood numbers on the vertical walls. The results indicate that increasing the buoyancy ratio enhances thermal transport and alters velocity profiles, while reducing concentration at the cavity center. The magnetic field induces flow retardation, alters heat transfer direction, and reduces the average Nusselt number, highlighting its critical role in controlling convective behavior.