Dual solutions of hybrid nanofluid flow past a permeable melting shrinking sheet with higher-order slips, shape factor and viscous dissipation effect
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) an...
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| Format: | Article |
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Emerald Publishing
2025
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| Online Access: | http://psasir.upm.edu.my/id/eprint/120178/ |
| _version_ | 1848868132043620352 |
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| author | Abu Bakar, Shahirah Pop, Ioan Md Arifin, Norihan |
| author_facet | Abu Bakar, Shahirah Pop, Ioan Md Arifin, Norihan |
| author_sort | Abu Bakar, Shahirah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-15T14:47:31Z |
| format | Article |
| id | upm-120178 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T14:47:31Z |
| publishDate | 2025 |
| publisher | Emerald Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1201782025-09-24T04:19:02Z http://psasir.upm.edu.my/id/eprint/120178/ Dual solutions of hybrid nanofluid flow past a permeable melting shrinking sheet with higher-order slips, shape factor and viscous dissipation effect Abu Bakar, Shahirah Pop, Ioan Md Arifin, Norihan 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. Emerald Publishing 2025 Article PeerReviewed Abu Bakar, Shahirah and Pop, Ioan and Md Arifin, Norihan (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 and Fluid Flow, 35 (1). art. no. undefined. pp. 199-230. ISSN 0961-5539 https://www.emerald.com/hff/article/35/1/199-230/1240970 10.1108/HFF-10-2024-0735 |
| spellingShingle | Abu Bakar, Shahirah Pop, Ioan Md Arifin, Norihan Dual solutions of hybrid nanofluid flow past a permeable melting shrinking sheet with higher-order slips, shape factor and viscous dissipation effect |
| title | Dual solutions of hybrid nanofluid flow past a permeable melting shrinking sheet with higher-order slips, shape factor and viscous dissipation effect |
| title_full | Dual solutions of hybrid nanofluid flow past a permeable melting shrinking sheet with higher-order slips, shape factor and viscous dissipation effect |
| title_fullStr | Dual solutions of hybrid nanofluid flow past a permeable melting shrinking sheet with higher-order slips, shape factor and viscous dissipation effect |
| title_full_unstemmed | Dual solutions of hybrid nanofluid flow past a permeable melting shrinking sheet with higher-order slips, shape factor and viscous dissipation effect |
| title_short | Dual solutions of hybrid nanofluid flow past a permeable melting shrinking sheet with higher-order slips, shape factor and viscous dissipation effect |
| title_sort | dual solutions of hybrid nanofluid flow past a permeable melting shrinking sheet with higher-order slips, shape factor and viscous dissipation effect |
| url | http://psasir.upm.edu.my/id/eprint/120178/ http://psasir.upm.edu.my/id/eprint/120178/ http://psasir.upm.edu.my/id/eprint/120178/ |