Novel investigation of burger fluid with gyrotactic microorganisms over a sheet using levenberg marquardt back propagations (LMBP)

Abstract

Artificial neural networks are used to solve boundary layer flow over a stretching sheet. The simplified form of governing equations is adopted and extended for supervised machine learning with linear regression technique. The application of similarity variables transforms the governing flow equations into a system of ODEs. The initial numerical results are evaluated with bvp4c. The analysis includes examining various parameters including magneto force, fluid parameter beta 1, Biot number gamma 1and gamma 2, peclet number by using Levenberg Marquart Back Propagations (LMBP) and result in the form of a graph. The ANN model uses the data set with 70 % allocation for training, 15 % for validation, and 15 % for testing. The accuracy and reliability of the solution are evaluated using Mean Squared Error (MSE), while the convergence of the results is examined using the performance graph. Key fluid dynamics parameters, such as skin friction, Nusselt number, Sherwood number, and motile density are considered. The optimal MSE validation is obtained at different epochs in every case with an indication that the graph is converging at that point. In regression analysis where R gets closer to 1 show that the prediction result through ANN is very close to the true data. The energy curve raising with raising the value of Biot number and Brownian motion where boundary layer thickness decreases. The concentration profile increases with an increase in Biot number, and with an increase in Peclet numbers, motile density decreases. Besides, the strength of the magnetic field increases the Cfx and the Nux increase by gamma 1. Also study the isothermal contour plot and stream lines for Nusselt number and Hartmann number. Practical application of these non-Newtonian fluids i.e. Biomedical application, food industry, Pharmaceutical industry, Petroleum and Chemical Industries.

Artificial neural networks are used to solve boundary layer flow over a stretching sheet. The simplified form of governing equations is adopted and extended for supervised machine learning with linear regression technique. The application of similarity variables transforms the governing flow equations into a system of ODEs. The initial numerical results are evaluated with bvp4c. The analysis includes examining various parameters including magneto force, fluid parameter β1, Biot number γ1andγ2, peclet number by using Levenberg Marquart Back Propagations (LMBP) and result in the form of a graph. The ANN model uses the data set with 70 % allocation for training, 15 % for validation, and 15 % for testing. The accuracy and reliability of the solution are evaluated using Mean Squared Error (MSE), while the convergence of the results is examined using the performance graph. Key fluid dynamics parameters, such as skin friction, Nusselt number, Sherwood number, and motile density are considered. The optimal MSE validation is obtained at different epochs in every case with an indication that the graph is converging at that point. In regression analysis where R gets closer to 1 show that the prediction result through ANN is very close to the true data. The energy curve raising with raising the value of Biot number and Brownian motion where boundary layer thickness decreases. The concentration profile increases with an increase in Biot number, and with an increase in Peclet numbers, motile density decreases. Besides, the strength of the magnetic field increases the Cfx and the Nux increase by γ1. Also study the isothermal contour plot and stream lines for Nusselt number and Hartmann number. Practical application of these non-Newtonian fluids i.e. Biomedical application, food industry, Pharmaceutical industry, Petroleum and Chemical Industries.