Entropy generation and heat transfer in MHD free convection within l-shaped cavities: A computational and AI-based approach

• Optimized thermal transport and entropy generation in an l -shaped cavity using finite element method (FEM) and artificial neural networks (ANN). • Magnetohydrodynamic (MHD) free convection analyzed for varying aspect ratios (height and width) to assess its impact on heat transfer. • Inclined magnetic field effects investigated to understand its role in entropy minimization and flow control. • ANN predictive modeling provides accurate estimations of thermal and entropy behaviors, enhancing computational efficiency. • Findings contribute to thermal management applications, including electronic cooling and energy systems. This study examines entropy generation and heat transfer in an l -shaped enclosure to optimize thermal system design by analyzing step aspect ratios (height vs. width). Governing equations (continuity, momentum, energy) are non-dimensionalized and solved via finite element simulations, with entropy production (thermal, viscous, total) evaluated across varying Rayleigh numbers (Ra), Hartmann number (Ha), aspect ratio (AR=h/w), and irreversibility ratios. Heat flux is predicted by an artificial neural network (ANN) that has been trained on simulation data, improving computing efficiency. As shown by previous research and grid sensitivity testing, the ANN model forecasts heat transport patterns with accuracy. These findings illustrate the usefulness of ANN in speeding up thermal research by elucidating entropy dynamics and optimizing geometric parameters, which are crucial for building energy-efficient devices. The main conclusions show that magnetic entropy generation can account for up to 44.8 % of total entropy generation under strong magnetic fields (Ha≥20). The average Nusselt number rises by 37.6 % as the Rayleigh number rises from 103 to 106, but it decreases slightly (0.25 %) under high Hartmann numbers, indicating MHD trade-offs. Kinetic energy has a 99.8 % increase with Ra, indicating convection dominance in taller geometries (h = 0.75, w = 0.25).