Levenberg-marquardt based ANN solution for MHD nanofluid flow and heat transportation over a thin needle with...

Artificial neural network (ANN) techniques have emerged as powerful data-driven tools for their effectiveness in analysis, modeling, and simulation. These supervised learning approaches are designed to reduce the error between predicted and observed data, providing accurate approximations of complex physical systems. To improve training performance, the Levenberg-Marquardt algorithm (LMA) is widely adopted due to its fast convergence and suitability for nonlinear problems. The objective of this study is to develop an ANN-based computational framework using the LMA to accurately predict the flow and heat transfer characteristics of an MHD nanofluid over a thin needle based on Buongiorno's model. The novelty of the present work lies in applying an ANN-based predictive framework to the Buongiorno nanofluid model over a moving thin needle, which has received limited attention in the existing literature. The impacts of transverse magnetic field, Brownian motion, and thermophoresis are contained in the mathematical model. The governing equations for fluid flow are converted to ordinary differential equations (ODEs) and numerically solved. The results are also predicted by using Artificial Neural Networks (ANNs) techniques. The effect of physical parameters like magnetic parameter ( $M$ ), Prandtl number ( $\mathrm{Pr}$ ), thermophoresis parameter ( $\mathrm{Nt}$ ), Brownian motion parameter ( $\mathrm{Nb}$ ), and Schmidt number ( $\mathrm{Sc}$ ) on velocity, temperature and concentration profiles are explored. The outcomes indicate that the velocity of the fluid decreases with the upsurge of the magnetic parameter while the temperature increases. Higher values of $\mathrm{Pr}$ and $\mathrm{Sc}$ reduce the temperature and concentration profiles, correspondingly. The Brownian motion parameter boosts the temperature but lowers the concentration, while the thermophoresis parameter rises both temperature and concentration. It is also observed that the magnetic field increases the skin friction coefficient but decreases the heat and mass transfer rates. The ANN results are very close to the numerical results, showing that ANN is an accurate and reliable method for predicting complex nanofluid flow problems.