{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T23:52:25Z","timestamp":1778197945684,"version":"3.51.4"},"reference-count":65,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,9,25]],"date-time":"2022-09-25T00:00:00Z","timestamp":1664064000000},"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>Interpreting the complex interaction of nanostructured fluid flow with a dipole in a duct, with peripherally uniform temperature distribution, is the main focus of the current work. This paper also sheds light on the changes in the Nusselt number, temperature profiles, and velocity distributions for the fully developed nanofluid flow in a vertical rectangular duct due to a dipole placed near a corner of the duct. A finite volume approach has been incorporated for the numerical study of the problem. It is interesting to note the unusually lower values of the Nusselt number for the higher values of the ratio Gr\/Re. Due to the nanostructure in the fluid, an enhancement in the Nusselt number has been noted, which is strongly supported by the magnetic field caused by the dipole. However, as the duct shape is transformed from rectangular to square, the Nusselt number is reduced remarkably. Further, as the dipole is brought nearer to the duct corner, the Nusselt number increases significantly. On the other hand, the flow reversal in the middle of the duct has been noted at higher values of the ratio Gr\/Re. The dipole is noted to have a low impact on the reversal flow as well as on the temperature distribution.<\/jats:p>","DOI":"10.3390\/sym14102007","type":"journal-article","created":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T01:23:16Z","timestamp":1664414596000},"page":"2007","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["Molecular Interaction and Magnetic Dipole Effects on Fully Developed Nanofluid Flowing via a Vertical Duct Applying Finite Volume Methodology"],"prefix":"10.3390","volume":"14","author":[{"given":"Kashif","family":"Ali","sequence":"first","affiliation":[{"name":"Department of Basic Sciences and Humanities, Muhammad Nawaz Sharif University of Engineering and Technology, Multan 60000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7152-1354","authenticated-orcid":false,"given":"Shabbir","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9829-9917","authenticated-orcid":false,"given":"Sohail","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences and Humanities, Muhammad Nawaz Sharif University of Engineering and Technology, Multan 60000, Pakistan"},{"name":"Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9438-6132","authenticated-orcid":false,"given":"Wasim","family":"Jamshed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Capital University of Science & Technology, Islamabad 44000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1847-4776","authenticated-orcid":false,"given":"Syed M.","family":"Hussain","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3151-9967","authenticated-orcid":false,"given":"El Sayed M.","family":"Tag El Din","sequence":"additional","affiliation":[{"name":"Electrical Engineering, Faculty of Engineering and Technology, Future University in Egypt, New Cairo 11835, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1647","DOI":"10.1007\/s00231-012-1009-7","article-title":"Entropy generation in non-Newtonian fluids due to heat and mass transfer in the entrance region of ducts","volume":"48","author":"Galanis","year":"2012","journal-title":"Heat Mass Transf."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.ijheatfluidflow.2007.07.008","article-title":"Parallel and non-parallel laminar mixed convection flow in an inclined tube: The effect of the boundary conditions","volume":"29","author":"Barletta","year":"2008","journal-title":"Int. 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