A machine learning analysis for hybrid nanofluid flow between two co-axial cylinders

This study investigates steady, incompressible, heat transfer and axisymmetric flow in a hybrid nanofluid, magnetite and multi-walled carbon nanotubes dispersed in water, confined in the annular space between two coaxial cylinders (outer radius normalized to 1, inner radius one quarter of outer). The outer cylinder rotates while a constant radial magnetic field is applied, and the hybrid mixture's effective thermophysical properties are evaluated using a two-step Hamilton-Crosser mixing model. The governing boundary-value problem is solved numerically with MATLAB's bvp4c solver, and a Levenberg-Marquardt trained artificial neural network is developed for rapid prediction and validation. A dataset of [Formula: see text] radial sample points (range [Formula: see text], step [Formula: see text]) is used, with [Formula: see text] for training, remainder split equally for validation and testing. Results show that increasing magnetic strength suppresses velocity while raising the temperature through enhanced viscous and Joule heating; increasing the Brinkman number likewise increases temperature, and higher Reynolds number raises the pressure gradient. The hybrid nanofluid yields larger wall shear stress and, on average, about 7.09% higher heat transfer compared with the single-particle nanofluid. The neural network reproduces bvp4c solutions with excellent fidelity (validation mean squared errors down to the 10^-10-10^-11 range and near-unity correlation), demonstrating that the combined bvp4c plus Levenberg-Marquardt framework enables accurate, computationally efficient parametric studies of magnetohydrodynamic thermal systems.