{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T09:59:57Z","timestamp":1773827997378,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,7,10]],"date-time":"2024-07-10T00:00:00Z","timestamp":1720569600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Universiti Putra Malaysia","award":["GP-GPB 9711400"],"award-info":[{"award-number":["GP-GPB 9711400"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>For efficient heating and cooling applications, minimum wall shear stress and maximum heat transfer rate are desired. The current study optimized the local skin friction coefficient and Nusselt number in Al2O3-Cu\/water hybrid nanofluid flow over a permeable shrinking rotating disk. First, the governing equations and boundary conditions are solved numerically using the bvp4c solver in MATLAB. Von K\u00e1rm\u00e1n\u2019s transformations are used to reduce the partial differential equations into solvable non-linear ordinary differential equations. The augmentation of the mass transfer parameter is found to reduce the local skin friction coefficient and Nusselt number. Higher values of these physical quantities of interest are observed in the injection case than in the suction case. Meanwhile, the increase in the magnitude of the shrinking parameter improved and reduced the local skin friction coefficient and Nusselt number, respectively. Then, response surface methodology (RSM) is conducted to understand the interactive impacts of the controlling parameters in optimizing the physical quantities of interest. With a desirability of 66%, the local skin friction coefficient and Nusselt number are optimized at 1.528780016 and 0.888353037 when the shrinking parameter (\u03bb) and mass transfer parameter (S) are \u22120.8 and \u22120.6, respectively.<\/jats:p>","DOI":"10.3390\/computation12070141","type":"journal-article","created":{"date-parts":[[2024,7,10]],"date-time":"2024-07-10T13:34:38Z","timestamp":1720618478000},"page":"141","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Hybrid Nanofluid Flow over a Shrinking Rotating Disk: Response Surface Methodology"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9026-4178","authenticated-orcid":false,"given":"Rusya Iryanti","family":"Yahaya","sequence":"first","affiliation":[{"name":"Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400, Malaysia"}]},{"given":"Norihan Md","family":"Arifin","sequence":"additional","affiliation":[{"name":"Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400, Malaysia"},{"name":"Department of Mathematics and Statistics, Universiti Putra Malaysia, Serdang 43400, Malaysia"}]},{"given":"Ioan","family":"Pop","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Babe\u015f-Bolyai University, 400084 Cluj-Napoca, Romania"}]},{"given":"Fadzilah Md","family":"Ali","sequence":"additional","affiliation":[{"name":"Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400, Malaysia"},{"name":"Department of Mathematics and Statistics, Universiti Putra Malaysia, Serdang 43400, Malaysia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2710-9861","authenticated-orcid":false,"given":"Siti Suzilliana Putri Mohamed","family":"Isa","sequence":"additional","affiliation":[{"name":"Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400, Malaysia"},{"name":"Centre of Foundation Studies for Agricultural Science, Universiti Putra Malaysia, Serdang 43400, Malaysia"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"125205","DOI":"10.1088\/1402-4896\/ac1a89","article-title":"Mixed Convection Flow of Viscoelastic Ag-Al2O3\/Water Hybrid Nanofluid Past a Rotating Disk","volume":"96","author":"Gamachu","year":"2021","journal-title":"Phys. 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