{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T06:52:31Z","timestamp":1784703151538,"version":"3.55.0"},"reference-count":39,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,6,16]],"date-time":"2020-06-16T00:00:00Z","timestamp":1592265600000},"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>Ferro liquids derive their magneto\u2013viscous behavior from the suspended magnetic nanomaterial that enables tunable changes in temperature, as well as nano-structured fluid characteristics. A theoretical model that depicts the bioconvection flow of cross nanofluid with a magnetic dipole subjected to a cylindrical surface was developed and numerically solved. The model encountered nonlinear thermal radiation, activation energy, and second order slip. The flow equations were reduced and are presented in dimensionless forms, and they were solved numerically using the shooting technique, which is a built-in feature of MatLab. The model encountered symmetrical constraints for predicting velocity, temperature, concentration, and gyrotactic microorganism distribution and profiles. Moreover, the numerical values were computed for local Nusselt number, local Sherwood number, and motile density number against each physical parameter.<\/jats:p>","DOI":"10.3390\/sym12061019","type":"journal-article","created":{"date-parts":[[2020,6,16]],"date-time":"2020-06-16T13:20:43Z","timestamp":1592313643000},"page":"1019","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Bioconvection in Cross Nano-Materials with Magnetic Dipole Impacted by Activation Energy, Thermal Radiation, and Second Order Slip"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3007-5930","authenticated-orcid":false,"given":"Zahra","family":"Abdelmalek","sequence":"first","affiliation":[{"name":"Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam"},{"name":"Faculty of Medicine, Duy Tan University, Da Nang 550000, Vietnam"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9686-6834","authenticated-orcid":false,"given":"Kamel","family":"Al-Khaled","sequence":"additional","affiliation":[{"name":"Department of Mathematics &amp; Statistics, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0388-8506","authenticated-orcid":false,"given":"Hassan","family":"Waqas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University, Faisalabad 38000, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.","family":"Aldabesh","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Faculty of Engineering, Albaha University, Al Bahah 65527, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sami Ullah","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Sahiwal 57000, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sa\u2019ed A.","family":"Musmar","sequence":"additional","affiliation":[{"name":"Industrial Engineering Department, The University of Jordan, Amman 11942, Jordan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Iskander","family":"Tlili","sequence":"additional","affiliation":[{"name":"Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam"},{"name":"Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,16]]},"reference":[{"key":"ref_1","unstructured":"Choi, S.U.S. (1995). 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