A Neural Network Modeling for MHD–Radiative Natural Convection Williamson Fluid Between Concentric Cylinders

Abstract

This study investigates the natural convection flow of Williamson fluid between two concentric cylinders while affected by the radiation effect and magnetic field. The inner cylinder remains fixed while the outer cylinder rotates. Additionally, magnetic field is oriented radially, which influences the flow of the fluid. Applying a proper transformation, one transform the non-linear partial differential equations of the Williamson fluid model into ordinary differential equations. Artificial neural networks (ANN) facilitate the computation of solutions to these nonlinear ordinary differential equations. Trial functions employ a multilayer perceptron neural network with tunable parameters, including weights and biases. The governing equations are satisfied by determining the trial solution’s changeable parameters by applying the Adam (adaptive moment estimation algorithm) optimization technique. Compared to the analytical solutions, the ANN’s result demonstrates good accuracy. Moreover, graphs show how pertinent parameters affect the velocity and temperature profiles. The temperature and velocity profiles get smaller as the magnetic parameter value increases. Furthermore, the temperature and velocity profiles increase as the Hall parameter value rises.