{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T23:48:13Z","timestamp":1781912893761,"version":"3.54.5"},"reference-count":36,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,4]],"date-time":"2020-02-04T00:00:00Z","timestamp":1580774400000},"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>The present study investigated the unsteady magnetohydrodynamic (MHD) nanofluid flow over a radially nonlinear stretching sheet along with the viscosity dependent on temperature, convective boundary condition, thermo-diffusion, and the radiation effects. Moreover, the nanofluid\u2019s viscous effects were considered dependent on temperature and the exponential Reynolds model was considered in this context. It was additionally assumed that a uniform suspension of nanoparticles is present in the base fluid. The Buongiorno model, which involves the thermophoresis and Brownian motion effects, was considered. For the sake of a solution, the variational finite element method was selected with coding in MATLAB and the numerical results were contrasted with the published articles. The influence of various physical parameters on the velocity, temperature, and concentration profiles are discussed by the aid of graphs and tables. It was detected that the nanofuid viscosity parameter declines the fluid flow velocity, while, for the temperature and the concentration profiles, it accomplished the reverse phenomenon.<\/jats:p>","DOI":"10.3390\/sym12020234","type":"journal-article","created":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T03:13:27Z","timestamp":1581045207000},"page":"234","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":58,"title":["Variable Viscosity Effects on Unsteady MHD an Axisymmetric Nanofluid Flow over a Stretching Surface with Thermo-Diffusion: FEM Approach"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5501-4181","authenticated-orcid":false,"given":"Bagh","family":"Ali","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Dongxiang Road, Chang\u2019an District, Xi\u2019an 710129, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7473-8441","authenticated-orcid":false,"given":"Rizwan Ali","family":"Naqvi","sequence":"additional","affiliation":[{"name":"Department of Intelligent Mechatronics, Sejong University, Seoul 100083, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7881-5806","authenticated-orcid":false,"given":"Yufeng","family":"Nie","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Dongxiang Road, Chang\u2019an District, Xi\u2019an 710129, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3900-002X","authenticated-orcid":false,"given":"Shahid Ali","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Dongxiang Road, Chang\u2019an District, Xi\u2019an 710129, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7410-5951","authenticated-orcid":false,"given":"Muhammad Tariq","family":"Sadiq","sequence":"additional","affiliation":[{"name":"School of Automation, Northwestern Polytechnical University, 127 West Youyi Road, Xi\u2019an 710072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5203-0621","authenticated-orcid":false,"given":"Ateeq Ur","family":"Rehman","sequence":"additional","affiliation":[{"name":"College of Internet of Things Engineering, Hohai University, Changzhou 213022, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7724-4340","authenticated-orcid":false,"given":"Sohaib","family":"Abdal","sequence":"additional","affiliation":[{"name":"School of Mathematics, Northwest University, No. 229 North Taibai Avenue, Xi\u2019an 7100069, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.ijthermalsci.2012.01.011","article-title":"Free convection boundary layer flow past a horizontal flat plate embedded in porous medium filled by nanofluid containing gyrotactic microorganisms","volume":"56","author":"Aziz","year":"2012","journal-title":"Int. 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