Variational iteration method along with intelligent computing system for the radiated flow of electrically conductive viscous fluid through porous medium

Muhammad Shoaib; Farooq Ahmed Shah; Kottakkaran Sooppy Nisar; Muhammad Asif Zahoor Raja; Ehsan Ul Haq; Aqsa Zafar Abbasi; Qazi Mahmood Ul Hassan; Nuha Al-Harbi; Abdel-Haleem Abdel-Aty

doi:10.1016/j.heliyon.2023.e14365

Variational iteration method along with intelligent computing system for the radiated flow of electrically conductive viscous fluid through porous medium

Heliyon. 2023 Mar 9;9(3):e14365. doi: 10.1016/j.heliyon.2023.e14365. eCollection 2023 Mar.

Authors

Affiliations

¹ Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan.
² Yuan Ze University, AI Center, Taoyuan 320, Taiwan.
³ Department of Mathematics, College of Science and Humanities, Prince Sattam Bin Abdulaziz University, Al Kharj, 16278, Saudi Arabia.
⁴ School of Technology, Woxsen University- Hyderabad, 502345, Telangana State, India.
⁵ Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section .3, Douliou, Yunlin 64002, Taiwan.
⁶ Department of Mathematics, University of Wah, Wah Cantt., Pakistan.
⁷ Department of Applied Mathematics and Statistics, Institute of Space Technology, Islamabad, Pakistan.
⁸ Department of Physics, Faculty of Applied Sciences, Umm Al-Qura University, Makkah, Saudi Arabia.
⁹ Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia.
¹⁰ Physics Department, Faculty of Science, Al-Azhar University, Assiut, 71524, Egypt.

Abstract

This article aims to investigate the analytical nature and approximate solution of the radiated flow of electrically conductive viscous fluid into a porous medium with slip effects (RFECVF). In order to build acceptable accurate solutions for RFECVF, this study presented an efficient Levenberg-Marquardt technique of artificial neural networks (LMT-ANNs) approach. One of its fastest back-propagation algorithms for nonlinear lowest latency is the LMT. To turn a quasi-network of PDEs expressing RFECVF into a set of standards, the appropriate adjustments are required. During the flow, the boundary is assumed to be convective. The flow and heat transfer are governed by partial differential equations, and similarity transform is the main tool to convert it into a coupled nonlinear system of ODEs. The usefulness of the constructed LMT-ANNs for such a modelled issue is demonstrated by the best promising algebraic outputs in the E-03 to E-08 range, as well as error histogram and regression analysis measures. Mu is a controller that oversees the entire training procedure. The LMT-ANNs mainly focuses on the higher accuracy of nonlinear systems. Analytical results for the improved boundary layer ODEs are produced using the Variational Iteration Method, a tried-and-true method (VIM). The Lagrange Multiplier is a powerful tool in the suggested method for reducing the amount of computing required. Further, a tabular comparison is provided to demonstrate the usefulness of this study. The final results of the Variational Iteration Method (VIM) in MATLAB have accurately depicted the physical characteristics of a number of parameters, including Eckert, Prandtl, Magnetic, and Thermal radiation parameters.

Keywords: Analytical technique; Artificial neural networks; Levenberg-Marquardt technique; Magnetic field; Partial slip; Stretchable surface; Variational iteration method (VIM).