MHD Boundary Layer Flow over a Stretching Sheet: A New Stochastic Method

Abstract

In this study, a new computing model is developed using the strength of feed-forward neural networks with the Levenberg–Marquardt scheme-based backpropagation technique (NN-BLMS). It is used to find a solution for the nonlinear system obtained from the governing equations of the magnetohydrodyanmic (MHD) boundary layer flow over a stretching sheet. Moreover, the partial differential equations (PDEs) for the MHD boundary layer flow over a stretching sheet are converting into ordinary differential equations (ODEs) with the help of similarity transformation. A dataset for the proposed NN-BLMM-based model is generated at different scenarios by a variation of various embedding parameters: Deborah number $\left(\beta \right)$ and magnetic parameter (M). The training (TR), testing (TS), and validation (VD) of the NN-BLMS model are evaluated in the generated scenarios to compare the obtained results with the reference results. For the fluidic system convergence analysis, a number of metrics, such as the mean square error (MSE), error histogram (EH), and regression (RG) plots, are utilized for measuring the effectiveness and performance of the NN-BLMS infrastructure model. The experiments showed that comparisons between the results of proposed model and the reference results match in terms of convergence up to E-02 to E-10. This proves the validity of the NN-BLMS model. Furthermore, the results demonstrated that there is a decrease in the thickness of the boundary layer by increasing the Deborah number and magnetic parameter. The importance of the experiment can be seen due to its industrial applications such as MHD power generation, MHD generators, and MHD pumps.