Parametric optimization of heat transfer in unsteady squeezing nanofluid flow: an integrated analytical-machine learning approach

Abed A.M. DAMMAK B. Hajlaoui K. Kumar R. Kalimbetov G.P. Makhanova M.A. Safarova L. Sabirov S. Dauletov A. Ben Khedher N.
February 2026 Springer Science and Business Media B.V.

Journal of Thermal Analysis and Calorimetry
2026 #151 Issue 3 2485 - 2504 pp.

The purpose of this study is to develop an integrated analytical-machine learning framework for optimizing heat transfer in unsteady squeezing nanofluid flow between parallel plates. The research employs a higher-order Akbari–Ganji method (AGM) coupled with random forest regression to quantify the effects of squeeze number S(S<0: squeezing; S>0: expansion), Eckert squeeze number (S), Eckert number (Ec), and nanoparticle volume fraction (ϕ) on thermal performance. Four nanoparticles (TiO₂, Al₂O₃, Ag, Cu) dispersed in water were analyzed. The key findings demonstrate that: (1) The higher-order AGM achieved exceptional accuracy with maximum deviations of 3 × 10⁻⁷ for temperature and 5 × 10⁻⁸ for velocity profiles compared to numerical solutions; (2) machine learning analysis revealed Eckert number as the dominant parameter with 75.7% influence on Nusselt number, followed by volume fraction (12.3%) and squeeze number (12.0%); (3) increasing Ec from 0.5 to 2.0 resulted in 300% enhancement in Nusselt number; (4) silver nanoparticles provided 35% higher heat transfer rate compared to Al₂O₃ at ϕ = 0.05, though with 28% increase in friction factor; (5) optimal operating conditions were identified as Ec = 1.5–2.0, ϕ = 0.05–0.06, and S = − 1.0 to − 0.3, achieving maximum Nusselt number of 15.13. The integrated framework offers practical design guidelines for thermal management systems in microelectronics cooling, photovoltaic systems, and microfluidic heat exchangers, with potential for 40–50% improvement in heat transfer efficiency compared to conventional approaches.

Akbari–Ganji method , Heat transfer optimization , Machine learning , Nanofluid , Random forest , Squeezing flow

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Air Conditioning and Refrigeration Techniques Engineering Department, College of Engineering and Technologies, Al-Mustaqbal University, Babylon, 51001, Iraq
Department of Computer Science, Applied College, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, Saudi Arabia
College of Engineering, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia
Karnavati School of Research, Karnavati University, Gujarat, India
Department of Power Engineering, ALT University Named After Mukhamedzhan Tynyshpayev, 97 Shevchenko Str, Almaty, 050012, Kazakhstan
Kazakh Agrotechnical University Named After. S.Seifullina, Zhenis Ave., 62, Astana, 010011, Kazakhstan
New Uzbekistan University, Movarounnahr Street 1, Tashkent, 100000, Uzbekistan
Samarkand State University of Veterinary Medicine, Livestock and Biotechnologies, Samarkand, 140103, Uzbekistan
Kimyo International University in Tashkent, Shota Rustaveli Street, 156, Tashkent, 100121, Uzbekistan
Alfraganus University, Yukori Karakamish Street 2a, Tashkent, 100190, Uzbekistan
Department of Mechanical Engineering, College of Engineering, University of Ha’il, Ha’il City, 81451, Saudi Arabia

Air Conditioning and Refrigeration Techniques Engineering Department
Department of Computer Science
College of Engineering
Karnavati School of Research
Department of Power Engineering
Kazakh Agrotechnical University Named After. S.Seifullina
New Uzbekistan University
Samarkand State University of Veterinary Medicine
Kimyo International University in Tashkent
Alfraganus University
Department of Mechanical Engineering

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