https://doi.org/10.1140/epjs/s11734-024-01247-7
Regular Article
Physics-informed Hermite neural networks for wetted porous fin under the local thermal non-equilibrium condition: application of clique polynomial method
1
Amrita School of Artificial Intelligence, Amrita Vishwa Vidyapeetham, 560035, Bengaluru, Karnataka, India
2
Department of Studies in Mathematics, Davangere University, 577002, Davangere, Karnataka, India
3
Computational Science Lab, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, 560035, Bengaluru, India
4
Department of Mechanical Engineering, School of Engineering and Technology, Jain (Deemed-to-be) University, 560069, Bengaluru, Karnataka, India
5
Department of Pure and Applied Mathematics, School of Mathematical Sciences, Sunway University, 47500, Petaling Jaya, Selangor Darul Ehsan, Malaysia
6
Department of Mathematics, College of Science, King Khalid University, 61413, Abha, Saudi Arabia
Received:
9
April
2024
Accepted:
5
July
2024
Published online:
23
July
2024
The proposed investigation highlights the thermal variation and heat transmission behavior of a wetted porous fin under a local thermal non-equilibrium state (LTNE). The fluid–solid interaction is governed by the Darcy formulation. The two-equation model of LTNE is utilized to depict the energy transfer for both the solid and fluid phases. The pertinent thermal distribution problems are represented as highly nonlinear ordinary differential equations (ODEs) with boundary conditions for both solid and fluid phases. The governing heat equations have been transformed into a non-dimensional form by employing dimensionless variables. The application of the clique polynomial method with Laplace–Pade approximant (CPMLPA) for these modified governing equations is the unique objective of the present research endeavor. Furthermore, physics-informed Hermite neural network (PIHNN) is employed to solve the resulting non-dimensional heat equations of the wetted porous fin. An explanation and visual demonstration of the impact of embedded thermal variables on the temperature profiles are provided. As the values of the convection–conduction and surface-ambient radiation parameters rise, the thermal profile diminishes. Augmentation of the Rayleigh number diminishes temperature dispersion in the fin. The upsurge in values of the radiation parameter intensifies the temperature profile. This study compares the temperature values of PIHNN, CPMLPA, and the clique polynomial method and reveals a strong correlation.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2024. 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.
