Artificial intelligence approach to magnetohydrodynamic flow of non-Newtonian fluids over a wedge: Thermophoresis and Brownian motion effects

Abstract

The paper deals with the analysis of the laminar incompressible flow of a Carreau-Casson-Williamson fluid having magnetohydrodynamics effects with thermophoresis and Brownian motion effects over a wedge surface. Using similarity variables, a set of coupled ordinary differential equations are formulated for the governing equations of fluid flow. The solution process comprises a two-stage calculation. ODEs are first solved numerically using MATLAB’s bvp4c function, a known solver of boundary value problems known to solve complex ODEs within fluid dynamics very effectively. Further optimization and simplification of the analysis are achieved by using an artificial neural networking base Levenberg Marquardt algorithm (ANN-LMA) model. The derived dataset was divided into three parts: training 70%, validation 15%, and testing 15%. MSE metric between the values of ${10}^{-8}$ and ${10}^{-10}$. MSE values can be used to grade the model’s performance. Increased Weissenberg number increases velocity and elasticity by facilitating flow with the boundary layer. On the other hand, raised Casson, Williamson, and magnetic parameters bring down the velocities as there comes the effect of damping and more resistance. Thermophoresis affects the migration rates of the particles by controlling the thermal and concentration gradient in the boundary layer with Brownian motion influencing its diffusion on the viscosity level and stability of fluid while in motion. In general, there is a fundamental interest in wedge flow because this geometry is present in aerodynamics and hydrodynamics, the study of fluids flowing around shapes like airfoils, nozzles, and underwater vehicles.