https://doi.org/10.1140/epjp/s13360-025-06410-0
Regular Article
Gradient descent and response surface optimisation for nonlinear dynamics over an unstable heated wedge: lie group and sensitivity analysis
1
Department of Mathematics, B V Raju Institute of Technology, 502313, Narsapur, Medak, Telangana, India
2
Department of Mathematics and Education, Universidad a Distancia de Madrid, 28400, Madrid, Spain
3
Department of Mathematics, Narasaraopeta Engineering College, Narasaraopet, India
4
Faculty of Sciences Aïn Chock, Hassan II University, Casablanca, Morocco
5
Faculty of Engineering, Kuwait College of Science and Technology, 35004, Doha District, Kuwait
a dineshmaddina319@gmail.com, India.dineshmaddina319@gmail.com
Received:
10
April
2024
Accepted:
8
May
2025
Published online:
11
June
2025
Thermal conductivity and thermodynamic properties make nanofluids highly effective in thermal analysis and engineering applications. Ternary hybrid nanofluids flow over wedge surfaces can significantly enhance hydraulics and geothermal applications. This study explores a novel approach to optimising manufacturing processes in industries like plastic film production, heat exchangers, glass fibres, petroleum, polymer sheets, and electronic cooling systems. A key innovation of this work is the application of H(OCH₂CH₂)ₙOH–H₂O as a base fluid with AA7072 (nanofluid), ZrO₂ + AA7072 (hybrid nanofluid), and MgO + AA7072 + ZrO₂ (ternary hybrid nanofluid). The study investigates the heat transfer characteristics of these fluids as they flow over a wedge under the influence of various boundary conditions. Response surface methodology (RSM) and prediction through gradient descent-based machine learning is employed to optimise the thermal performance. The BVP4C solver in MATLAB is used to solve the governing equations numerically, and the gradient descent technique provides accurate predictions of the thermal behaviour through Python programming. From Table 3, the optimisation results indicate that the minimum value of 0.062983 is observed in case 2. In contrast, the maximum value of 13.5527 is recorded in case 3, demonstrating the significant impact of ternary hybrid nanofluids on heat transfer enhancement.
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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.
