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Ternary Hybrid Nanofluid with First and Second Order Velocity Slips: Dual Solutions with Stability Analysis

by Nur Syahirah Wahid1,*, Nor Ain Azeany Mohd Nasir2,3, Norihan Md Arifin1,3, Ioan Pop4,5

1 Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia (UPM), Serdang, 43400, Malaysia
2 Department of Mathematics, Centre for Defence Foundation Studies, Universiti Pertahanan Nasional Malaysia, Kuala Lumpur, 57000, Malaysia
3 Institute for Mathematical Research, Universiti Putra Malaysia (UPM), Serdang, 43400, Malaysia
4 Department of Mathematics, Babeş-Bolyai University, Cluj-Napoca, 400084, Romania
5 Academy of Romanian Scientists, Bucharest, 050044, Romania

* Corresponding Author: Nur Syahirah Wahid. Email: email

(This article belongs to the Special Issue: Innovative Computational Methods and Applications of Nanofluids in Engineering)

Computer Modeling in Engineering & Sciences 2025, 142(2), 1865-1881. https://doi.org/10.32604/cmes.2024.059508

Abstract

Modeling the boundary layer flow of ternary hybrid nanofluids is important for understanding and optimizing their thermal performance, particularly in applications where enhanced heat transfer and fluid dynamics are essential. This study numerically investigates the boundary layer flow of alumina-copper-silver/water nanofluid over a permeable stretching/shrinking sheet, incorporating both first and second-order velocity slip. The mathematical model is solved in MATLAB facilitated by the bvp4c function that employs the finite difference scheme and Lobatto IIIa formula. The solver successfully generates dual solutions for the model, and further analysis is conducted to assess their stability. The findings reported that only one of the solutions is stable. For the shrinking sheet case, increasing the first-order velocity slip delays boundary layer separation and enhances heat transfer, while, when the sheet is stretched, the second-order velocity slip accelerates separation and improves heat transfer. Boundary layer separation is most likely to occur when the sheet is shrinking; however, this can be controlled by adjusting the velocity slip with the inclusion of boundary layer suction.

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Cite This Article

APA Style
Wahid, N.S., Mohd Nasir, N.A.A., Arifin, N.M., Pop, I. (2025). Ternary hybrid nanofluid with first and second order velocity slips: dual solutions with stability analysis. Computer Modeling in Engineering & Sciences, 142(2), 1865–1881. https://doi.org/10.32604/cmes.2024.059508
Vancouver Style
Wahid NS, Mohd Nasir NAA, Arifin NM, Pop I. Ternary hybrid nanofluid with first and second order velocity slips: dual solutions with stability analysis. Comput Model Eng Sci. 2025;142(2):1865–1881. https://doi.org/10.32604/cmes.2024.059508
IEEE Style
N. S. Wahid, N. A. A. Mohd Nasir, N. M. Arifin, and I. Pop, “Ternary Hybrid Nanofluid with First and Second Order Velocity Slips: Dual Solutions with Stability Analysis,” Comput. Model. Eng. Sci., vol. 142, no. 2, pp. 1865–1881, 2025. https://doi.org/10.32604/cmes.2024.059508



cc Copyright © 2025 The Author(s). Published by Tech Science Press.
This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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