Thermosolutal convection and entropy generation in hybrid nanofluids: FEM and ANN analysis of a magnetized wavy enclosure

• Innovative Integration: First-ever combined analysis of hybrid nanofluids (Al 2 O 3 -Cu/water), a star-shaped cylinder, and magnetohydrodynamics (MHD) in a wavy enclosure, revealing unique flow dynamics and thermal performance unaddressed in prior studies. • Dual FEM-ANN Approach: Achieved exceptional accuracy (R = 1, MSE = 2.47 × 10 −9 ) in predicting Nusselt numbers via an Artificial Neural Network (ANN), reducing computational costs while validating Finite Element Method (FEM) simulations. • Parameter-Driven Enhancements: Quantified 16.27% rise in heat transfer (Nu Avg ) and 93.53% surge in entropy generation (E Total ) with increasing Rayleigh number from 10 3 to 10 5 , alongside 6.63% thermal gain using hybrid nanoparticles (2% volume fraction). • MHD Control: Demonstrated that strong magnetic fields (Ha = 50) suppress convection, reducing Nu Avg and Sh Avg by 18.03 % and 10.83 %, respectively, but elevate E Total by 80.83 % due to Lorentz forces, critical for energy-efficient system design. • Practical Optimization: Highlighted 41.60 % and 32.90 % improvements in mass transfer (Sh Avg ) at high Lewis number (Le = 10) and buoyancy ratio (N = 10), offering actionable insights for thermal management, energy storage, and electronic cooling applications. This study investigates the thermosolutal convection and entropy generation in a magnetohydrodynamic (MHD) hybrid nanofluid-filled enclosure featuring wavy vertical walls and a centrally placed star-shaped cylinder. The problem addresses the critical need to optimize heat and mass transfer in engineering systems, such as thermal management, energy storage, and electronic cooling. A hybrid nanofluid composed of alumina ( A l 2 O 3 ) and copper ( C u ) nanoparticles in water is analyzed using the Finite Element Method (FEM) via COMSOL Multiphysics, complemented by an Artificial Neural Network (ANN) model to predict the Nusselt number and validate results. Key findings reveal that increasing the Rayleigh number (Ra) from 10 3 to 10 5 enhances the average Nusselt number (Nu Avg ) by 16.27 % and total entropy generation (E Total ) by 93.53 %, driven by intensified buoyancy-driven convection. Conversely, a stronger magnetic field (Ha = 50) suppresses fluid motion, reducing (Nu Avg ) by 18.03 % and Sherwood number (Sh Avg ) by 10.83 %, while increasing E Total by 80.83 % due to Lorentz forces. Hybrid nanoparticles (2 % volume fraction) improve (Nu Avg ) by 6.63 % compared to pure fluid, demonstrating their thermal enhancement potential. The Lewis number (Le) and buoyancy ratio (N) significantly influence mass transfer, with (Sh Avg ) rising by 41.60 % at (Le = 10) and 32.90 % at (N = 10). The ANN model achieves exceptional accuracy (R = 1, MSE = 2.47 × 10 −9 ) in predicting thermal behavior, reducing computational effort. Novelty lies in the combined analysis of hybrid nanofluids, star-shaped geometry, and MHD effects using FEM-ANN integration a configuration unexplored in prior literature. This work provides actionable insights for designing energy-efficient systems with optimized entropy generation and enhanced thermal performance.