Local sensitivity and deep learning analysis of heat transfer in an arc-shaped lid-driven cavity using hybrid nanofluids in dihydrogen monoxide under quadratic magnetoconvection

This study investigates fluid flow and heat transfer in an arc-shaped lid-driven cavity filled with Cu–Al₂O₃/water nanofluid under quadratic magnetoconvection. The coupled Navier–Stokes and energy equations are solved using the finite element method with the Newton–Pardiso solver. Two objectives are addressed: (i) sensitivity analysis of six governing parameters on the average Nusselt number using response surface methodology (central composite design and analysis of variance in MINITAB 21) and (ii) prediction of the Nusselt number using a Levenberg–Marquardt artificial neural network trained in MATLAB 21. Results show that the Richardson number exerts the strongest influence on heat transfer. Quadratic magnetoconvection enhances circulation and lowers average temperature, with greater impact on streamlines and isotherms than linear convection. The Eckert number further intensifies flow and thermal fields. Overall, the arc-shaped cavity achieves an 8.48 % higher heat transfer rate compared to a flat-wall cavity, underscoring its superior thermal performance.