Dual solutions of hybrid nanofluid flow past a permeable melting shrinking sheet with higher-order slips, shape factor and viscous dissipation effect
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 20 November 2024
Issue publication date: 27 January 2025
Abstract
Purpose
This paper aims to explore dual solutions for the flow of a hybrid nanofluid over a permeable melting stretching/shrinking sheet with nanoparticle shape factor, second-order velocity slip conditions and viscous dissipation. The hybrid nanofluid is formulated by dispersing alumina (Al2O3) and copper (Cu) nanoparticles into water (H2O).
Design/methodology/approach
The governing partial differential equations (PDEs) are first reduced to a system of ordinary differential equations (ODEs) using a mathematical method of similarity transformation technique. These ODEs are then numerically solved through MATLAB’s bvp4c solver.
Findings
Key parameters such as slip parameter, melting parameter, suction parameter, shrinking parameter and Eckert number are examined. The results reveal the existence of two distinct solutions (upper and lower branches) for the transformed ODEs when considering the shrinking parameter. Increasing value of Cu-volume fraction and the second-order velocity slip enhances boundary layer thicknesses, whereas the heat transfer rate diminishes with rising melting and suction parameters. These numerical results are illustrated through various figures and tables. Additionally, a stability analysis is performed and confirms the upper branch is stable and practical, while the lower branch is unstable.
Practical implications
The analysis of hybrid nanofluid flow over a shrinking surface has practical significance with applications in processes such as solar thermal management systems, automotive cooling systems, sedimentation, microelectronic cooling or centrifugal separation of particles. Both steady and unsteady hybrid nanofluid flows are relevant in these contexts.
Originality/value
While the study of hybrid nanofluid flow is well-documented, research focusing on the shrinking flow case with specific parameters in our study is still relatively scarce. This paper contributes to obtaining dual solutions specifically for the shrinking case, which has been less frequently addressed.
Keywords
Acknowledgements
The authors would like to acknowledge Takasago Engineering Co. Ltd. Japan and Universiti Teknologi Malaysia (UTM) through the Grant number RK130000.7343.4B792. In addition, the contribution of Ioan Pop was made possible with the support of Grant PN-III-P4-PCE-2021-0993 from UEFISCDI, Romania.
Data Availability Statement: No data associated in this manuscript.
Author’s contributions: I.P. – developed the flow model, S.A.B. – performed formal analysis and wrote the paper, N.M.A. – validated the analysis.
Statement and declaration: The authors declare that they have no personal affiliations or conflicts of interest.
Citation
Abu Bakar, S., Pop, I. and Md Arifin, N. (2025), "Dual solutions of hybrid nanofluid flow past a permeable melting shrinking sheet with higher-order slips, shape factor and viscous dissipation effect", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 35 No. 1, pp. 199-230. https://doi.org/10.1108/HFF-10-2024-0735
Publisher
:Emerald Publishing Limited
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