Hybrid Adaptive Computational Framework for MHD Nanofluid Thermal Transport: Machine Learning Integration and Entropy Optimization

This study presents a novel hybrid adaptive computational framework integrating machine learning with modified Runge-Kutta-Fehlberg methods for magnetohydrodynamic (MHD) nanofluid thermal transport analysis. Key innovations include: (i) neural network-assisted shooting parameter optimization reducing computational time (ii) nanoscale corrections incorporating quantum and molecular effects (∆nano), (iii) adaptive mesh refinement with dual error indicators, and (iv) comprehensive thermal efficiency index balancing heat transfer, entropy generation, and irreversibility. The methodology achieve accuracy with enhanced Nusselt number correlations validated against recent experimental studies (mean error 0.23%).