{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T21:16:59Z","timestamp":1762377419921,"version":"build-2065373602"},"reference-count":69,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,6,27]],"date-time":"2023-06-27T00:00:00Z","timestamp":1687824000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004768","name":"Universiti Teknikal Malaysia Melaka","doi-asserted-by":"publisher","award":["JURNAL\/2019\/FTKMP\/Q00042"],"award-info":[{"award-number":["JURNAL\/2019\/FTKMP\/Q00042"]}],"id":[{"id":"10.13039\/501100004768","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The boundary layer flows exhibit symmetrical characteristics. In such cases, the flow patterns and variables are symmetrical with respect to a particular axis or plane. This symmetry simplifies the analysis and enables the use of symmetry-based boundary conditions or simplifications in mathematical models. Therefore, by using these concepts, the governing equations of the radiative flow of a hybrid nanofluid past a stretched and shrunken surface with the effect of a magnetic dipole are examined in this paper. Here, we consider copper (Cu) and alumina (Al2O3) as hybrid nanoparticles and use water as a base fluid. The heat transfer rate is enhanced in the presence of hybrid nanoparticles. It is observed that the heat transfer rate is increased by 10.92% for the nanofluid, while it has a 15.13% increment for the hybrid nanofluid compared to the base fluid. Also, the results reveal that the non-uniqueness of the solutions exists for a certain suction and shrinking strength. Additionally, the ferrohydrodynamic interaction has the tendency to reduce the skin friction and the heat transfer coefficients for both solution branches. For the upper branch solutions, the heat transfer rate increased over a stretching sheet but decreased for the shrinking sheet in the presence of the radiation. It is confirmed by the temporal stability analysis that one of the solutions is stable and acceptable as time evolves.<\/jats:p>","DOI":"10.3390\/sym15071318","type":"journal-article","created":{"date-parts":[[2023,6,28]],"date-time":"2023-06-28T00:25:21Z","timestamp":1687911921000},"page":"1318","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Magnetic Dipole Effects on Radiative Flow of Hybrid Nanofluid Past a Shrinking Sheet"],"prefix":"10.3390","volume":"15","author":[{"given":"Iskandar","family":"Waini","sequence":"first","affiliation":[{"name":"Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, Durian Tunggal, Melaka 76100, Malaysia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9092-8288","authenticated-orcid":false,"given":"Najiyah Safwa","family":"Khashi\u2019ie","sequence":"additional","affiliation":[{"name":"Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, Durian Tunggal, Melaka 76100, Malaysia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3045-302X","authenticated-orcid":false,"given":"Nurul Amira","family":"Zainal","sequence":"additional","affiliation":[{"name":"Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, Durian Tunggal, Melaka 76100, Malaysia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0332-7853","authenticated-orcid":false,"given":"Khairum Bin","family":"Hamzah","sequence":"additional","affiliation":[{"name":"Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, Durian Tunggal, Melaka 76100, Malaysia"}]},{"given":"Abdul Rahman Mohd","family":"Kasim","sequence":"additional","affiliation":[{"name":"Centre for Mathematical Sciences, Universiti Malaysia Pahang, Gambang 26300, Malaysia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2353-5919","authenticated-orcid":false,"given":"Anuar","family":"Ishak","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, UKM Bangi, Bangi 43600, Malaysia"}]},{"given":"Ioan","family":"Pop","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Babe\u015f-Bolyai University, 400084 Cluj-Napoca, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,27]]},"reference":[{"key":"ref_1","unstructured":"Choi, S.U.S., and Eastman, J.A. 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