{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T01:55:26Z","timestamp":1767837326263,"version":"3.49.0"},"reference-count":33,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,9,3]],"date-time":"2020-09-03T00:00:00Z","timestamp":1599091200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100009392","name":"Prince Sattam bin Abdulaziz University","doi-asserted-by":"publisher","award":["\u200e2020\/01\/16595\u200e"],"award-info":[{"award-number":["\u200e2020\/01\/16595\u200e"]}],"id":[{"id":"10.13039\/100009392","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The goal of this investigation is to explore the influence of viscous dissipation and Brownian motion on Jeffrey nanofluid flow over an unsteady moving surface with thermophoresis and mixed convection. Zero mass flux is also addressed at the surface such that the nanoparticles fraction of maintains itself on huge obstruction. An aiding transformation is adopted to renovate the governing equations into a set of partial differential equations which is solved using a new fourth-order finite difference continuation method and various graphical outcomes are discussed in detail with several employed parameters. The spectacular influence of pertinent constraints on velocity and thermal curves are inspected through various plots. Computational data for the heat transfer rate and skin-friction coefficient are also reported graphically. Graphical outcomes indicate that an augmentation in buoyance ratio and thermophoretic parameter leads to diminish the velocity curves and increase the temperature curves. Furthermore, it is inspected that escalating Deborah number exhibits increasing in the skin friction and salient decreasing heat transmission. Increasing magnetic strength leads to a reduction in the skin friction and enhancement in the Nusselt number, whilst a reverse reaction is manifested with mixed convection aspects.<\/jats:p>","DOI":"10.3390\/sym12091450","type":"journal-article","created":{"date-parts":[[2020,9,3]],"date-time":"2020-09-03T11:22:43Z","timestamp":1599132163000},"page":"1450","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":31,"title":["Impacts of Viscous Dissipation and Brownian motion on Jeffrey Nanofluid Flow over an Unsteady Stretching Surface with Thermophoresis"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7266-1893","authenticated-orcid":false,"given":"Essam","family":"El-Zahar","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"},{"name":"Department of Basic Engineering Science, Faculty of Engineering, Menoufia University, Shebin El-Kom 32511, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1354-2610","authenticated-orcid":false,"given":"Ahmed","family":"Rashad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Aswan University, Aswan 81528, Egypt"}]},{"given":"Laila","family":"Seddek","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"},{"name":"Department of Engineering Mathematics and Physics, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,3]]},"reference":[{"key":"ref_1","unstructured":"Choi, S.U., and Eastman, J.A. 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