Analysis of Sutterby multi-diffusive nanoliquid flow over expanding cylinder using an artificial neural networks and numerical simulations in presence of activation energy and oscillating magnetic field

This study presents an analysis of the Sutterby multi-diffusive nanoliquid flow over an expanding cylinder, incorporating an oscillatory magnetic field and activation energy, through the application of numerical simulation and artificial neural networks. Recently, artificial neural networks have attracted considerable interest owing to their applications in diverse fields, such as robotics, image processing, fluid mechanics, and beyond. This research aims to explore the transfer of heat and mass by employing numerical methods and artificial neural networks. The system consists of complex fluid-flow partial differential equations that are converted into ordinary differential equations by utilizing similarity variables. In the present problem, Buongiorno two-phase model is used, in the said model, slip due to nanoparticles at the wall is studied through two major slip mechanisms, namely, thermophoresis and Brownian diffusion. Further, by using MATLAB software, the reference data produced by the artificial neural network, which utilizes a Levenberg–Marquardt intelligent network, is allocated through three distinct characteristics: training, testing, and validation. The study involves calculating the mean squared error, analyzing histograms, and conducting regression analyses to demonstrate and assess the effects of the drag force and Nusselt number. The matrix laboratory function, utilized in addressing a boundary value problem through a 5th order method, enables the simulation of graphs and tables that clearly depict the various physical influences numerically represented in fluid flow profiles and gradients. The periodic magnetic field's intensity diminishes the energy transfer rate, concurrently leading to an elevation in the liquid's temperature, with the periodic characteristics of the magnetic field being distinctly evident. Furthermore, in the neural network simulation, 211 and 619 data points obtained from the numerical solutions of the velocity and temperature equations function as the databases throughout the training phase. In the training phase, the dataset is systematically partitioned into three subsets: 70 % is allocated for training purposes, 15 % is assigned for validation, and the final 15 % is set aside for testing, significantly.