{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T12:41:17Z","timestamp":1774701677613,"version":"3.50.1"},"reference-count":60,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,9,14]],"date-time":"2020-09-14T00:00:00Z","timestamp":1600041600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this analysis, we aim to examine the heat transfer and flow characteristics of a copper-aluminum\/water hybrid nanofluid in the presence of viscous dissipation, magnetohydrodynamic (MHD), and porous medium effect over the shrinking sheet. The governing equations of the fluid model have been acquired by employment of the model of Tiwari and Das, with additional properties of the hybrid nanofluid. The system of partial differential equations (PDEs) has been converted into ordinary differential equations (ODEs) by adopting the exponential similarity transformation. Similarity transformation is an essential class of phenomenon where the symmetry of the scale helps to reduce the number of independent variables. Note that ODE solutions demonstrate the PDEs symmetrical behavior for the velocity and temperature profiles. With BVP4C solver in the MATLAB program, the system of resulting equations has been solved. We have compared the present results with the published results and found in excellent agreements. The findings of the analysis are also displayed and discussed in depth graphically and numerically. It is discovered that two solutions occur in definite ranges of suction and magnetic parameters. Dual (no) similarity solutions can be found in the range of Sc\u2264S\u00a0and\u00a0Mc\u2264M (Sc&gt;S\u00a0and\u00a0Mc&gt;M). By performing stability analysis, the smallest values of eigenvalue are obtained, suggesting that a stable solution is the first one. Furthermore, the graph of the smallest eigenvalue shows symmetrical behavior. By enhancing the Eckert number values the temperature of the fluid is raised.<\/jats:p>","DOI":"10.3390\/sym12091513","type":"journal-article","created":{"date-parts":[[2020,9,15]],"date-time":"2020-09-15T10:24:09Z","timestamp":1600165449000},"page":"1513","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":36,"title":["Magnetized Flow of Cu + Al2O3 + H2O Hybrid Nanofluid in Porous Medium: Analysis of Duality and Stability"],"prefix":"10.3390","volume":"12","author":[{"given":"Liaquat Ali","family":"Lund","sequence":"first","affiliation":[{"name":"School of Quantitative Sciences, Universiti Utara Malaysia, Sintok 06010, Malaysia"},{"name":"KCAET Khairpur Mirs, Sindh Agriculture University, Tandojam Sindh 70060, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zurni","family":"Omar","sequence":"additional","affiliation":[{"name":"School of Quantitative Sciences, Universiti Utara Malaysia, Sintok 06010, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2776-9376","authenticated-orcid":false,"given":"Sumera","family":"Dero","sequence":"additional","affiliation":[{"name":"Faculty of Engineering and Technology, University of Sindh, Jamshoro 76080, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2056-9371","authenticated-orcid":false,"given":"Ilyas","family":"Khan","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 72915, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0286-7244","authenticated-orcid":false,"given":"Dumitru","family":"Baleanu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Cankaya University, Ankara 06790, Turkey"},{"name":"Institute of Space Sciences, 077125 Magurele, Romania"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40447, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5769-4320","authenticated-orcid":false,"given":"Kottakkaran Sooppy","family":"Nisar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,14]]},"reference":[{"key":"ref_1","unstructured":"Choi, S.U., and Eastman, J.A. 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