MHD nanofluid flow and heat transfer over a porous stretching sheet under an inclined Hartmann field: Numerical analysis and artificial neural network modeling

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This study investigates unsteady magnetohydrodynamic (MHD) boundary-layer flow and heat transfer of four water-based nanofluids (Cu/water, CuO/water, Al2​O3​/water, and TiO2​/water) over a porous stretching sheet subjected to an inclined magnetic field. The formulation incorporates magnetic-field inclination, thermal radiation, viscous dissipation, heat generation, unsteadiness, and nanoparticle effects within a unified framework. Similarity transformations reduce the governing partial differential equations to nonlinear ordinary differential equations, which are solved using the MATLAB BVP4C collocation solver. The numerical implementation is validated against published benchmark data, with the corrected comparison showing relative discrepancies generally below approximately 0.003% for the tabulated wall quantities. An LMBP-based artificial neural network framework is additionally employed to approximate the BVP4C-generated velocity and temperature profiles for the prescribed parametric cases. The results show that the higher the Hartmann number the lower the velocity of the fluid due to the increased Lorentz force on the fluid. In contrast, increase of the heat generation causes the increase of the fluid temperature and thickness of the thermal boundary layer. Among the four nanofluids considered, Cu/water exhibits the strongest heat-transfer response, consistent with its substantially higher thermal conductivity. The ANN approximations closely reproduce the corresponding BVP4C profiles within the investigated cases, as indicated by the low prediction errors and regression analysis. The combined numerical and data-driven analysis provides insight into controlling momentum and thermal transport in magnetically influenced nanofluid systems relevant to thermal management, heat-exchange, and solar-thermal applications.