Numerical and artificial neural network prediction of double-stratified magnetized nanofluid flow and heat transfer over a stretchable cylinder with Brownian motion and thermal slip

The current study aims to investigate the effects of double stratification on magneto-hydrodynamic (MHD) nanofluid flow over a stretching cylinder in the presence of thermal radiation. The model incorporates Brownian motion, thermophoresis, and velocity, thermal, and concentration slip conditions to provide a realistic description of the transport phenomena. The problem is formulated in the form of PDEs are converted to ODEs by applying suitable similarity variables. The transformed system is solved numerically using bvp4c solver in MATLAB. A Levenberg–Marquardt Algorithm (LMA) based Artificial Neural Network (ANN) is developed to validate and improve the predictive capability of the numerical results. The ANN trained using the numerical dataset generated by bvp4c solution, with the dataset 70% for training, 15% for validation, and 15% for testing. The suggested hybrid numerical-ANN framework delivers an efficient and accurate predictive model that reveals excellent agreement with the numerical solutions. The ANN model demonstrates excellent predictive accuracy and computational efficiency, showing close agreement with the numerical results. The influences of various physical parameters on temperature, velocity, and concentration distributions are analyzed graphically. It is pragmatic that the velocity profile decreases with an increasing velocity slip parameter, whereas thermal stratification reduces the temperature field and thermophoresis enhances the concentration distribution. Numerical outcomes of friction factor, heat transfer rate, and Sherwood number are premeditated and discussed in detail. Comparison with previously published results in limiting cases endorsements the accuracy and validity of the current methodology. The findings highlight the effectiveness of the hybrid bvp4c–ANN framework for analyzing complex nanofluid transport problems arising in engineering and industrial applications.