Fractional Analysis of MHD Boundary Layer Flow over a Stretching Sheet in Porous Medium: A New Stochastic Method

Imran Khan,Saeed Islam,Abdu Gumaei,Mehreen Fiza,Hakeem Ullah,Farkhanda Ikhlaq,Muhammad Shoaib,Muhammad Asif Zahoor Raja,Hussain Alsalman,Nehad Ali Shah

doi:10.1155/2021/5844741

Abstract

In this article, an effective computing approach is presented by exploiting the power of Levenberg-Marquardt scheme (LMS) in a backpropagation learning task of artificial neural network (ANN). It is proposed for solving the magnetohydrodynamics (MHD) fractional flow of boundary layer over a porous stretching sheet (MHDFF BLPSS) problem. A dataset obtained by the fractional optimal homotopy asymptotic (FOHA) method is created as a simulated data simple for training (TR), validation (VD), and testing (TS) the proposed approach. The experiments are conducted by computing the results of mean-square-error (MSE), regression analysis (RA), absolute error (AE), and histogram error (HE) measures on the created dataset of FOHA solution. During the learning task, the parameters of trained model are adjusted by the efficacy of ANN backpropagation with the LMS (ANN-BLMS) approach. The ANN-BLMS performance of the modeled problem is verified by attaining the best convergence and attractive numerical results of evaluation measures. The experimental results show that the approach is effective for finding a solution of MHDFF BLPSS problem.

Highlights

In many engineering and industrial processes, an incompressible flow liquid of boundary layer is common to be used over stretching sheet
The performance results are about 10-04 to 10-07, 10-8 to 10-10, and 10-06 to 10-08 for all the scenarios with cases 1 and 3 of MHDFF BLPSS. These results demonstrate that the performance of artificial neural network (ANN)-BLMS is stable for every case of model for the MHDFF BLPSS
It is applied for solving the magnetohydrodynamics (MHD) fractional flow of boundary layer over a porous stretching sheet (MHDFF BLPSS) problem

Summary

Introduction

In many engineering and industrial processes, an incompressible flow liquid of boundary layer is common to be used over stretching sheet. This field has been paid attention by researchers in the last few decades. Sakiadis [4, 5] investigated this area with the new work, and several researchers have explored the boundary flow layer into ongoing stretching sheet in increasing with increasing the speed. (i) An effective application of artificial intelligencebased computing is introduced by means of artificial neural network backpropagation with the Levenberg-Marquardt scheme (ANN-BLMS) for achieving a solution to MHDFF BLPSS at different scenarios on variation of Deborah, porosity, and magnetic numbers (ii) The mathematical modeling of the work is formulated with nonlinear coupled PDEs to MHDFF BLPSS. (v) The performance results of ANN-BLMS for solving the MHDFF BLPSS is further confirmed by the convergence plots of the mean squared errors, fitting graphs, histogram errors, and regression analysis curves

Problem Formulation

Solution Procedure of the New Stochastic Method

Regression studies

Analysis of Results

Conclusion