Multilayer neural networks for studying three-dimensional flow of non-Newtonian fluid flow with the impact of magnetic dipole and gyrotactic microorganisms

Abstract

Abstract The current paper explores the three-dimensional flow of an Oldroyd-B liquid with the impact of a magnetic dipole that occurred by stretching a flat surface placed in the plane with a linear velocity variation in two directions containing motile gyrotactic microorganisms. Using proper similarity transformations, the governing equations are reduced into nonlinear coupled ordinary differential equations (ODEs). The ODEs are then solved using Runge–Kutta-Fehlberg (RKF) method. The training, testing, and validation processes are carried out in parallel to adapt neural networks and calculate an approximate solution for the considered model. This helps to reduce the mean square error (MSE) function by Levenberg–Marquardt backpropagation. The efficiency of the suggested backpropagated neural networks methodology has been demonstrated by utilizing outcomes such as MSE, error histograms, correlation and regression. Results reveal that the heat transport augments for increased Biot number values. The mass transport declines for improved chemical reaction rate parameter values. A higher Peclet number will result in a lower motile diffusivity and result in a decline in the micro-organism’s density profile. For the least value of Mu and gradient, better convergence of the findings can be achieved with better network testing and training.