Effective thermal management in geometrically irregular enclosures is crucial for optimizing performance in electronics cooling, renewable energy, and thermal engineering systems. This numerical study investigates conjugate magnetohydrodynamic (MHD) free convection heat transfer in a Cu-H？O nanofluid-filled trapezoidal cavity with a wavy (corrugated) top boundary and embedded internally heat-generating star-shaped copper obstacles. The cavity base angle(？) is fixed at 15？, and the simulation employs the Galerkin finite element method to solve coupled solid-fluid heat transfer equations under varying Rayleigh numbers (Ra = 103 - 106), Hartmann numbers (Ha = 15, 50), and nanoparticle volume fractions (？ = 0.01 - 0.03). The Galerkin finite element method (FEM) is employed due to its robustness in handling irregular geometries and complex boundary conditions. This method ensures accurate resolution of coupled thermal and fluid fields within the wavy trapezoidal cavity and around embedded star-shaped heat sources. Results reveal that both the shape and placement of star-shaped heaters strongly influence heat flow, enhancing convective mixing and thermal dispersion through vortex structures. The corrugated top wall further improves vertical heat transport. Increasing the nanoparticle concentration from 0.01 to 0.03 led to a significant enhancement in average Nusselt number and a reduction in average fluid temperature, demonstrating the superior heat transfer capability of nanofluids. At higher Rayleigh numbers, the dominance of buoyancy-induced flow over magnetic damping further amplified convective efficiency. The findings underscore the potential of integrating nanofluid technologies with complex geometry and internal heating to optimize thermal control in passive cooling applications and high-efficiency heat exchangers.
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