Artificial neural network and Bvp4c approach for mixed convective magnetized Casson nanoliquid flow and heat transportation over a stretchable cylinder under the presence of activation energy and nth order chemical reaction

The goal of the current study is to investigate mixed convection magnetohydrodynamic (MHD) heat transfer in non-Newtonian Casson nanoliquid flowing across a stretching cylinder under the collective effects of thermal radiation, activation energy, and nth order chemical reaction. The present proposed model is applicable to industrial processes involving cooling of cylindrical components and high-temperature manufacturing systems. Convective boundary conditions, Brownian motion, thermophoresis, and mixed-convection effects are included in the mathematical model to capture the transport phenomena adequately. The transformed governing differential equations are then solved numerically using hybrid approach bvp4c and ANN. To improve predictive capability and computational efficiency, a Levenberg-Marquardt-based Artificial Neural Network (ANN) is developed using the numerical dataset generated from the bvp4c solutions. The dataset is subdivided into 70% of training, 15% of validation, and 15% of testing, and the ANN predictions exhibit excellent agreement with the numerical results, demonstrating high accuracy and strong generalization performance. The effects of the governing parameters on the velocity, temperature, and concentration distributions are examined comprehensively. The novel results reveal that increasing the magnetic parameter and Casson fluid parameter suppresses the velocity field, whereas thermal radiation and convective heating significantly enhance the temperature distribution. Moreover, higher activation energy intensifies the concentration profile, while enhancing the order of chemical reaction reduces nanoparticle concentration. The variations in wall friction coefficient, local Nusselt number, and local Sherwood number are also quantified and discussed in detail. Comparison with previously published limiting cases confirms the accuracy and reliability of the proposed numerical methodology. The findings demonstrate that the hybrid bvp4c-ANN framework provides an efficient and reliable computational tool for analyzing complex nonlinear nanofluid transport problems encountered in advanced thermal engineering, energy systems, and industrial heat transfer applications..