https://doi.org/10.1140/epjp/s13360-025-06022-8
Regular Article
Analysis for 3D thermal conducting micropolar nanofluid via artificial neural network
1
Department of Aeronautics and Astronautics, Institute of Space Technology, Islamabad, Pakistan
2
Department of Mechanical Engineering, Faculty of Engineering, King Khalid University, Abha, Saudi Arabia
3
Department of Applied Mathematics and Statistics, Institute of Space Technology, Islamabad, Pakistan
4
Department of Mathematics, City University of Science and Information Technology, Peshawar, Pakistan
5
Department of Architectural Engineering, College of Engineering, University of Ha’il, Ha’il, Saudi Arabia
6
Department of Mechanical Engineering, College of Engineering, University of Ha’il, Ha’il, Saudi Arabia
a
zafariqbalabbasi67@gmail.com
Received:
11
September
2024
Accepted:
13
January
2025
Published online:
4
February
2025
This paper considers the Darcy–Forchheimer flow over a micropolar nanofluid by using an intelligent backpropagated neural network with Levenberg–Marquardt scheme. The PDEs governing the DFF-MNFM are reduced into ODEs through some appropriate transformations. A reference dataset is prepared from HAM by changing several key parameters, such as the porosity parameter (γ), Reynolds number (Re), coupling parameter (N1), rotation parameter (Kr), coefficient of inertia (Fr), viscosity gradient parameter (N2), and Brownian motion parameter (Nb), for all proposed IBNN-LMS scenarios. The estimated solutions of the IBNN-LMS are analyzed and compared with reference results. The results suggest that for high values of the Reynolds number, Re, the fluid velocity is increased at the surface, and with Kr, increasing velocity on the surface of the fluid increases but decreases beyond the surface. A rise in the value of γ enhances velocity closer to the surface while diminishing the velocity beyond the surface distance. The rise of N1 enhances the speed of the microrotation of fluid closer to the surface. In addition, the higher temperature and concentration profiles enhance the value of Nb. For the validation of IBNN-LMS approach, its efficiency is justified through convergence analysis of MSE, regression indices, and error spectrum evaluations that represent its robustness in solving complicated fluid flow problems.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
