{
  "abstract": "Boundary layer flow over a moving and curved surface is very important in modern industrial processes like steel extrusion, polymer lamination, and advanced cooling technologies, where heat moves affects how efficient and high-quality the products are. This study investigates the dual solutions and temporal stability of Eyring-Powell tri-hybrid nanofluid flow and heat transfer over a permeable shrinking cylinder under an applied magnetic field and Joule heating. The tri-hybrid nanofluid consists of copper, aluminum oxide, and titanium dioxide nanoparticles suspended in water. The governing continuity, momentum, and energy equations are formulated under the boundary-layer approximation and transformed into a nonlinear system of ordinary differential equations using similarity transformations. The resulting boundary-value problem is solved numerically using MATLAB's bvp4c solver, while the temporal stability of the dual solutions is determined through an eigenvalue analysis. The numerical formulation is validated against published studies, with good agreement obtained for the limiting cases. The solution exhibits duality over a finite range of shrinking parameters, with the solutions merging at the critical value [Formula: see text]. The upper branch possesses positive smallest eigenvalues and is therefore temporally stable, whereas the lower branch is unstable. Increasing the Eckert number reduces the heat-transfer rate, while increasing the curvature parameter slightly extends the range of dual solutions. Suction enhances flow stability and heat transfer. The results demonstrate that the combined effects of non-Newtonian rheology, tri-hybrid nanoparticles, magnetic forces, Joule heating, and cylindrical curvature provide useful control of boundary-layer transport and stability in thermal-fluid systems.",
  "abstract_shown": true,
  "affiliations": [
    "Centre for Mathematical Sciences, Universiti Malaysia Pahang Al-Sultan Abdullah (UMPSA), Gambang, 26300, Pahang, Malaysia. rahmanmohd@umpsa.edu.my.",
    "Centre for Mathematical Sciences, Universiti Malaysia Pahang Al-Sultan Abdullah (UMPSA), Gambang, 26300, Pahang, Malaysia.",
    "Fakulti Teknologi dan Kejuruteraan Mekanikal, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, Durian Tunggal, Melaka, 76100, Malaysia.",
    "Federal College of Education, Iwo, 232102, Nigeria.",
    "Fakulti Sains Komputer dan Matematik (FSKM), Universiti Teknologi MARA, Cawangan Pahang Kampus Jengka, 26400 Bandar Tun Abdul Razak Jengka, Pahang, Malaysia.",
    "School of Computer Science and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg, Braamfontein, 2050, South Africa."
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 7,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Abdul Rahman Mohd Kasim",
      "orcid": "0000-0001-9359-428X"
    },
    {
      "affs": [
        1
      ],
      "name": "Puteri Ereena Shafira Mustafa"
    },
    {
      "affs": [
        1
      ],
      "name": "Ahlam Aljabali"
    },
    {
      "affs": [
        2
      ],
      "name": "Nurul Amira Zainal"
    },
    {
      "affs": [
        1,
        3
      ],
      "name": "Adeshina Taofeeq Adeosun"
    },
    {
      "affs": [
        4
      ],
      "name": "Noor Amalina Nisa Ariffin"
    },
    {
      "affs": [
        5
      ],
      "name": "Yusuf Olatunji Tijani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5c968nwcqme2p.bib",
  "cited_by": 0,
  "doi": "10.1186/s11671-026-05053-z",
  "fulltext_url": "https://europepmc.org/articles/PMC13694650",
  "id": "5c968nwcqme2p",
  "issns": [
    "2731-9229"
  ],
  "landing_url": "https://europepmc.org/article/MED/42909801",
  "language": "eng",
  "licence": "CC-BY-NC-ND",
  "licence_label": "CC BY-NC-ND",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2204|Nanofluid Flow and Heat Transfer"
    ]
  ],
  "openalex": "W7223398913",
  "pdf_url": "https://europepmc.org/articles/PMC13694650?pdf=render",
  "pmcid": "PMC13694650",
  "pmid": "42909801",
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5c968nwcqme2p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:10Z",
      "native_id": "MED:42909801",
      "source": "europepmc",
      "url": "https://europepmc.org/article/MED/42909801"
    }
  ],
  "subjects": [],
  "title": "Stability and heat transfer of mhd eyring powell tri hybrid nanofluid flow over a permeable shrinking cylinder.",
  "title_text": "Stability and heat transfer of mhd eyring powell tri hybrid nanofluid flow over a permeable shrinking cylinder.",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:20:10Z",
  "url": "https://research.draconitic.com/paper/5c968nwcqme2p",
  "venue": "Discover nano",
  "versions": []
}