Open Access

ARTICLE

Evaluating Effect of Magnetic Field on Nusselt Number and Friction Factor of Fe₃O₄-TiO₂/Water Nanofluids in Heat-Sink Using Artificial Intelligence Techniques

L. S. Sundar^*, Sérgio M. O. Tavares, António M. B. Pereira, Antonio C. M. Sousa

Centre for Mechanical Technology and Automation, Department of Mechanical Engineering, University of Aveiro, Aveiro, 3810-131, Portugal

* Corresponding Author: L. S. Sundar. Email:

Frontiers in Heat and Mass Transfer 2025, 23(1), 131-162. https://doi.org/10.32604/fhmt.2025.055854

Received 08 July 2024; Accepted 22 August 2024; Issue published 26 February 2025

Abstract

The experimental analysis takes too much time-consuming process and requires considerable effort, while, the Artificial Neural Network (ANN) algorithms are simple, affordable, and fast, and they allow us to make a relevant analysis in establishing an appropriate relationship between the input and output parameters. This paper deals with the use of back-propagation ANN algorithms for the experimental data of heat transfer coefficient, Nusselt number, and friction factor of water-based Fe₃O₄-TiO₂ magnetic hybrid nanofluids in a mini heat sink under magnetic fields. The data considered for the ANN network is at different Reynolds numbers (239 to 1874), different volume concentrations (0% to 2.0%), and different magnetic fields (250 to 1000 G), respectively. Three types of ANN back-propagation algorithms Levenberg-Marquardt (LM), Broyden-Fletcher-Goldfarb-Shanno Quasi Newton (BFGS), and Variable Learning Rate Gradient Descent (VLGD) were used to train the heat transfer coefficient, Nusselt number, and friction factor data, respectively. The ANOVA t-test analysis was also performed to determine the relative accuracy of the three ANN algorithms. The Nusselt number of 2.0% vol. of Fe₃O₄-TiO₂ hybrid nanofluid is enhanced by 38.16% without a magnetic field, and it is further enhanced by 88.93% with the magnetic field of 1000 Gauss at a Reynolds number of 1874, with respect to the base fluid. A total of 126 datasets of heat transfer coefficient, Nusselt number, and friction factor were used as input and output data. The three ANN algorithms of LM, BFGS, and VLGD, have shown good acceptance with the experimental data with root-mean-square errors of 0.34883, 0.25341, and 1.0202 with correlation coefficients (R²) of 0.99954, 0.9967, and 0.94501, respectively, for the Nusselt number data. Moreover, the three ANN algorithms predict root-mean-square errors of 0.001488, 0.005041, and 0.006924 with correlation coefficients (R²) of 0.99982, 0.99976, and 0.99486, respectively, for the friction factor data. Compared to BFGS and VLGD algorithms, the LM algorithm predicts high accuracy for Nusselt number, and friction factor data. The proposed Nusselt number and friction factor correlations are also discussed.

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Keywords

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