Artificial Intelligence-Powered Magnetorheological Dynamics of a Dusty Nanofluid: Employing Artificial Neural Network and Hybrid Fourth-Order Numerical Methods

The present analysis tackles the problem of an unsteady, magnetized Jeffrey nanofluid flow containing dusty particles within a nonlinear stretching regime, considering the effects of viscous dissipation. The governing equations at the plate are formulated using partial differential equations (PDEs) with boundary-layer approximations. These PDEs are then converted to a dimensionless form using similarity transformations, resulting in a system of nonlinear ordinary differential equations (ODEs). This dimensionless system is numerically solved using the Newton-Raphson shooting approach in combination with the fourth-order Runge-Kutta code. The study evaluates flow characteristics and heat transfer behavior across various parameter values. It is found that the thickness of the velocity and momentum boundary layers for both nanofluid and dusty phases decreases as the ratio of relaxation to retardation times increases. Temperature variations in the nanofluid phase of the dusty phase intensify with increasing Jeffrey parameters. The analysis provides valuable insights into the behavior of complex fluid systems in stretching regimes, with applications in various advanced industrial technologies. Additionally, an artificial neural network (ANN) is employed to accurately predict velocity values, demonstrating high accuracy in the ANN model's predictive capabilities. Furthermore, the application of artificial intelligence (AI) in this study extends its utility to optimizing industrial processes, particularly in systems involving dusty nanofluids, such as cooling mechanisms and material processing. Additionally, the AI-driven methods can be applied to enhance the performance of biomedical devices, environmental filtration systems, and energy-efficient heat exchangers involving dusty nanofluids.