Galerkin finite element analysis of double-diffusive magnetohydrodynamic convection in a wavy-walled enclosure containing a hybrid nanofluid

Double-diffusive natural convection, governed by the coupled interplay of thermal and solutal buoyancy forces, is markedly influenced by magnetic damping and geometric confinement, motivating deeper numerical exploration of such complex transport phenomena. This study presents a numerical investigation of magnetohydrodynamic thermo-solutal convection within a wavy-walled enclosure filled with a $$\:Cu-Al₂O$$ ₃/water hybrid nanofluid, embedded with an internally heated circular cylinder, wherein the bottom wall and cylinder are maintained at elevated temperature while the undulating side walls are held at comparatively lower temperature and concentration. The governing conservation equations are solved via the Galerkin Finite Element Method (GFEM), enabling a comprehensive parametric analysis of the Rayleigh number, Hartmann number, hybrid nanoparticle volume fraction, Lewis number, and cylinder position, to elucidate their combined influence on flow structure, heat transfer, and mass transfer characteristics. The results reveal that increasing the Rayleigh number from 10⁴ to 10⁶ substantially intensifies buoyancy-driven circulation by 97.27%, promoting stronger thermal plume development and a corresponding 66.53% enhancement in the local Nusselt number \:NuLocal ; conversely, elevating the Hartmann number to 100 introduces dominant Lorentz forces that suppress velocity gradients, diminishing the ( \:Nuavg , \:Shavg ) by 40.3% and 15.7%, respectively. Increasing the Lewis number from 1 to 10 further reduces thermal diffusion by 48.26% while simultaneously amplifying mass diffusion by 88.5%, and cylinder position significantly affects thermal performance by modifying the flow structure, thermal plumes, and boundary-layer interactions. Collectively, these findings offer valuable insight into optimizing hybrid nanofluid-based thermo-solutal systems for enhanced energy and mass transport efficiency under magnetic field control.