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ORIGINAL RESEARCH article

Front. Phys.
Sec. Fluid Dynamics
Volume 12 - 2024 | doi: 10.3389/fphy.2024.1408933
This article is part of the Research Topic Dynamics of Complex Fluids View all articles

A Qualitative Analysis of The Artificial Neural Network Model And Numerical Solution For The Nanofluid Flow Through An Exponentially Stretched Surface

Provisionally accepted
Asad Ullah Asad Ullah 1*Hongxing Yao Hongxing Yao 2Waseem . Waseem . 2Abdus Saboor Abdus Saboor 3Fuad Awwad Fuad Awwad 4Emad Ismail Emad Ismail 4
  • 1 University of Lakki Marwat, Lakki Marwat, Pakistan
  • 2 Jiangsu University, Zhenjiang, Jiangsu Province, China
  • 3 Kohat University of Science and Technology, Kohat, Khyber Pakhtunkhwa, Pakistan
  • 4 King Saud University, Riyadh, Riyadh, Saudi Arabia

The final, formatted version of the article will be published soon.

    This article aims to analyze the two-dimensional (2D) nanofluid (Ag/C 2 H 6 O 2 ) flow past an exponentially stretched sheet. The magnetic field impact, heat 1 source/sink, and convection in the thermal profile are taken into account.The complexity of the problem is reduced by introducing a dimensionless group of functions. The reduced model is transformed into a system of first-order Ordinary Differential Equations (ODEs). This system is further analyzed with the Artificial Neural Network (ANN), which is trained with the Levenberg-Marquardt algorithm. The whole data set is sub divided into three parts; training (70%), validation (15%) and testing (15%). The impact of nonlinear heat source/sink parameter, magnetic parameter, volume fraction of nanoparticles, and Prandtl number is displayed through graphs. The heat source, volume fraction, and the Prandtl number cause to increase in the thermal profile with its larger values. The magnetic parameter causes to decline in both the thermal and momentum boundary layers with its higher values. The analysis shows that the thermal energy profile is enhanced with the larger values of the volume fraction of silver nanopartilces and heat source. For each case study, the residual error (RE), regression line, and validation of the results are presented. The performance of the proposed methodology is numerically tabulated for the nanoparticles volume fraction in Table 3, where the minimum absolute error (AE) is 5.3373e -11 at ϕ = 0.05. Based on this, we recommend ϕ = 0.05 for better performance.The AEs for ANN and bvp4c are computed for the state variables in Table 4 and 5 for the magnetic parameter M = 5, 10 and 15. These tables show that overall performance of ANN and further validate the present study.We have also validated the results of ANN through mean squared error graphically, where the accuracy of the proposed methodology is proved.

    Keywords: artificial neural network, Convection, Ethylene-glycol, heat transfer, magnetic field, Nanofluid, Nonlinear problems, Thermal Energy

    Received: 29 Mar 2024; Accepted: 12 Aug 2024.

    Copyright: © 2024 Ullah, Yao, ., Saboor, Awwad and Ismail. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Asad Ullah, University of Lakki Marwat, Lakki Marwat, Pakistan

    Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.