{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T20:57:10Z","timestamp":1792184230194,"version":"4.4.0"},"reference-count":59,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,12,23]],"date-time":"2020-12-23T00:00:00Z","timestamp":1608681600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004055","name":"King Fahd University of Petroleum and Minerals","doi-asserted-by":"publisher","award":["SB191007"],"award-info":[{"award-number":["SB191007"]}],"id":[{"id":"10.13039\/501100004055","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, heat transfer and entropy of steady Williamson nanofluid flow based on the fundamental symmetry is studied. The fluid is positioned over a stretched flat surface moving non-uniformly. Nanofluid is analyzed for its flow and thermal transport properties by consigning it to a convectively heated slippery surface. Thermal conductivity is assumed to be varied with temperature impacted by thermal radiation along with axisymmetric magnetohydrodynamics (MHD). Boundary layer approximations lead to partial differential equations, which are transformed into ordinary differential equations in light of a single phase model accounting for Cu-water and TiO2-water nanofluids. The resulting ODEs are solved via a finite difference based Keller box scheme. Various formidable physical parameters affecting fluid movement, difference in temperature, system entropy, skin friction and Nusselt number around the boundary are presented graphically and numerically discussed. It has also been observed that the nanofluid based on Cu-water is identified as a superior thermal conductor rather than TiO2-water based nanofluid.<\/jats:p>","DOI":"10.3390\/sym13010010","type":"journal-article","created":{"date-parts":[[2020,12,23]],"date-time":"2020-12-23T12:19:51Z","timestamp":1608725991000},"page":"10","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":66,"title":["Numerical Simulation of Heat Transfer Flow Subject to MHD of Williamson Nanofluid with Thermal Radiation"],"prefix":"10.3390","volume":"13","author":[{"given":"Muhammad","family":"Amer Qureshi","sequence":"first","affiliation":[{"name":"PYP-Mathematics, College of General Studies, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,23]]},"reference":[{"key":"ref_1","first-page":"99","article-title":"Enhancing thermal conductivity of fluids with nanoparticles","volume":"Volume 66","author":"Choi","year":"1995","journal-title":"Proceedings of the ASME International Mechanical Engineering Congress and Exposition"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Eastman, J.A., Choi, S.U.S., Li, S., Thompson, L.J., and Lee, S. 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