Artificial neural network-based prediction of hydromagnetic boundary layer nanofluid fluid flow and heat transportation over a porous wedge with brownian motion
6 affiliations
- 1Center for Scientific Research and Entrepreneurship, Northern Border University, Arar, 73213 Saudi Arabia
- 2Department of Mathematics and Statistics, FBAS, IIUI Islamabad, 36000 Islamabad, Pakistan
- 3Department of Mechanical Engineering, College of Engineering, Qassim University, Buraydah, 51452 Saudi Arabia
- 4Computer Department, College of Engineering and Computing in Al-Qunfudah, Umm Al-Qura University, Makkah, Saudi Arabia
- 5AI Center & Faculty of Computer and Information Systems, Islamic University of Madinah, Madinah, 42351 Saudi Arabia
- 6Cybersecurity Department, College of Engineering and Information Technology, Al-Qalam University for Humanities and Applied Sciences, IBB, IBB, Yemen
Abstract
The primary objective of the present study is to explore two dimensional steady MHD boundary layer nanofluid flow and heat transportation towards a wedge under the inspiration of a magnetic field, porosity parameter, thermophoresis and Brownian motion parameters. The nonlinear PDEs of momentum, energy and concentration are transformed into an ordinary differential equations (ODEs) by applying the similarity approach. The resulting system of ODEs is solved numerically with Bvp4c approach. For further assessment the predictive capability, of the numerical solutions, a Levenberg–Marquardt artificial neural network (LMA-ANN) model is developed using generated dataset, which is split into 15% validation, 15% testing and 70% training. Outcomes elucidates that increasing the magnetic parameter M suppresses velocity due to the opposing Lorentz (resistive) force while higher Lewis number Le significantly reduces concentration profiles, while enhancing the Sherwood number. The close agreement between the numerical and ANN forecasts demonstrates high accuracy and predictive performance of the proposed LMA–ANN model. Specifically, the present model provides a high regression coefficient and a low mean squared error for the velocity profile, confirming its effectiveness in accurately predicting the flow characteristics. The impact of pertinent constraints on temperature, velocity, and concentration fields is discussed graphically and in tabular form in detail. Key findings from the ANN predictions and the computed physical quantities. In particular, the best validation MSE for the ANN is 4.77 × 10⁻⁹ at epoch 150, with regression coefficients approaching R = 1, demonstrating excellent agreement between the ANN predictions and the BVP4C results. For the representative parameter set, the computed skin-friction coefficient, heat-transfer rate, and mass-transfer rate are \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}−f′ ′ (0) = 1.9338\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}−θ ′ (0) = 0.2737\end{document}, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}−ϕ ′ (0) = 0.1769\end{document} .
Graphical Abstract:
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BibTeX
@article{darem2026artificial,
title = {{Artificial neural network-based prediction of hydromagnetic boundary layer nanofluid fluid flow and heat transportation over a porous wedge with brownian motion}},
author = {Abdulbasit A. Darem and Aaqib Majeed and Parvez Ali and Abdullah Salem Alqahtani and Abdallah Namoun and Asma A. Alhashmi},
journal = {Discover Nano},
year = {2026},
month = oct,
doi = {10.1186/s11671-026-05066-8},
url = {https://doi.org/10.1186/s11671-026-05066-8},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - JOUR
TI - Artificial neural network-based prediction of hydromagnetic boundary layer nanofluid fluid flow and heat transportation over a porous wedge with brownian motion
AU - Abdulbasit A. Darem
AU - Aaqib Majeed
AU - Parvez Ali
AU - Abdullah Salem Alqahtani
AU - Abdallah Namoun
AU - Asma A. Alhashmi
PY - 2026
DA - 2026/10/26
JO - Discover Nano
DO - 10.1186/s11671-026-05066-8
UR - https://doi.org/10.1186/s11671-026-05066-8
AB - The primary objective of the present study is to explore two dimensional steady MHD boundary layer nanofluid flow and heat transportation towards a wedge under the inspiration of a magnetic field, porosity parameter, thermophoresis and Brownian motion parameters. The nonlinear PDEs of momentum, energy and concentration are transformed into an ordinary differential equations (ODEs) by applying the similarity approach. The resulting system of ODEs is solved numerically with Bvp4c approach. For further assessment the predictive capability, of the numerical solutions, a Levenberg–Marquardt artificial neural network (LMA-ANN) model is developed using generated dataset, which is split into 15% validation, 15% testing and 70% training. Outcomes elucidates that increasing the magnetic parameter M suppresses velocity due to the opposing Lorentz (resistive) force while higher Lewis number Le significantly reduces concentration profiles, while enhancing the Sherwood number. The close agreement between the numerical and ANN forecasts demonstrates high accuracy and predictive performance of the proposed LMA–ANN model. Specifically, the present model provides a high regression coefficient and a low mean squared error for the velocity profile, confirming its effectiveness in accurately predicting the flow characteristics. The impact of pertinent constraints on temperature, velocity, and concentration fields is discussed graphically and in tabular form in detail. Key findings from the ANN predictions and the computed physical quantities. In particular, the best validation MSE for the ANN is 4.77 × 10⁻⁹ at epoch 150, with regression coefficients approaching R = 1, demonstrating excellent agreement between the ANN predictions and the BVP4C results. For the representative parameter set, the computed skin-friction coefficient, heat-transfer rate, and mass-transfer rate are \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}−f′ ′ (0) = 1.9338\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}−θ ′ (0) = 0.2737\end{document}, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}−ϕ ′ (0) = 0.1769\end{document} . Graphical Abstract:
SN - 2731-9229
ER -