{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T21:53:48Z","timestamp":1773525228739,"version":"3.50.1"},"reference-count":43,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2024,4,18]],"date-time":"2024-04-18T00:00:00Z","timestamp":1713398400000},"content-version":"vor","delay-in-days":1,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007446","name":"King Khalid University","doi-asserted-by":"publisher","award":["RGP2\/157\/45"],"award-info":[{"award-number":["RGP2\/157\/45"]}],"id":[{"id":"10.13039\/501100007446","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,5,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This analysis considers the magnetized third-grade fluid stream and microorganisms over a non-linear stretchy cylinder. The radiation impacts are taken into consideration. The effects of the governing flow at the cylinder are represented in the form of PDEs employing boundary layer approximations. The system of the PDEs is further reduced in dimensionless form after applying the similarity transformations. The dimensionless system of non-linear ODEs is solved through the numerical technique bvp4c. The effects of radiation and magnetism on the third-grade liquid over a non-linear extending cylinder are highlighted in graphs and numerically in tabular form. The influence of fluid variables on the velocity curve, such as third-grade parameters, second-grade coefficients, and Reynolds number, is illustrated and explored. Suitable ranges for the parameters $( {1 \\le \\eta \\le 10,\\ 0.2 \\le {{\\alpha }_1} \\le 0.5,\\ 0 \\le {{\\alpha }_1} \\le 1.5,\\ 0.1 \\le \\beta \\le 0.3,\\ 0.1 \\le \\gamma \\le 1.6,\\ 0.05 \\le M \\le 0.15,\\ 0.5 \\le \\delta \\le 2.0,\\ 0.7 \\le Pr \\le 1.3,\\ 0.1 \\le Rd \\le 0.4,0.1 \\le}$ \u00a0${e \\le 0.4} )$ are chosen depending upon the convergence of the numerical method. The widths of the velocity and momentum boundary layers are revealed to be increasing functions of the curvature parameter. The temperature curve declines when boosting third-grade parameters, thermal stratification, and Hartmann number while boosting up for curvature and radiation parameters.<\/jats:p>","DOI":"10.1093\/jcde\/qwae038","type":"journal-article","created":{"date-parts":[[2024,4,18]],"date-time":"2024-04-18T02:04:00Z","timestamp":1713405840000},"page":"72-90","source":"Crossref","is-referenced-by-count":2,"title":["Radiation-influenced magnetohydrodynamic third-grade nanofluid flow around non-linearly stretched cylinder"],"prefix":"10.1093","volume":"11","author":[{"given":"Asia Ali","family":"Akbar","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of the Punjab , Lahore 54590 , Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3184-3652","authenticated-orcid":false,"given":"Aziz Ullah","family":"Awan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of the Punjab , Lahore 54590 , Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shafiullah","family":"Niazai","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Education Faculty, Laghman University , Mitarlam 2701 , Afghanistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sohail","family":"Nadeem","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University 45320 , Islamabad 44000 , Pakistan"},{"name":"Department of Mathematics, Wenzhou University , Wenzhou 325035 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"N Ameer","family":"Ahammad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Tabuk , P. 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