{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T08:47:39Z","timestamp":1768985259284,"version":"3.49.0"},"reference-count":39,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,3,3]],"date-time":"2020-03-03T00:00:00Z","timestamp":1583193600000},"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>This study is carried out to scrutinize the gyrotactic bioconvection effects on modified second-grade nanofluid with motile microorganisms and Wu\u2019s slip (second-order slip) features. The activation energy and thermal radiation are also incorporated. The suspended nanoparticles in a host fluid are practically utilized in numerous technological and industrial products such as metallic strips, energy enhancement, production processes, automobile engines, laptops, and accessories. Nanoparticles with high thermal characteristics and low volume fraction may improve the thermal performance of the base fluid. By employing the appropriate self-similar transformations, the governing set of partial differential equations (PDEs) are reduced into the ordinary differential equations (ODEs). A zero mass flux boundary condition is proposed for nanoparticle diffusion. Then, the transmuted set of ODEs is solved numerically with the help of the well-known shooting technique. The numerical and graphical illustrations are developed by using a collocation finite difference scheme and three-stage Lobatto III as the built-in function of the bvp4c solver via MATLAB. Behaviors of the different proficient physical parameters on the velocity field, temperature distribution, volumetric nanoparticles concentration profile, and the density of motile microorganism field are deliberated numerically as well as graphically.<\/jats:p>","DOI":"10.3390\/sym12030393","type":"journal-article","created":{"date-parts":[[2020,3,4]],"date-time":"2020-03-04T03:24:20Z","timestamp":1583292260000},"page":"393","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":115,"title":["A Numerical Exploration of Modified Second-Grade Nanofluid with Motile Microorganisms, Thermal Radiation, and Wu\u2019s Slip"],"prefix":"10.3390","volume":"12","author":[{"given":"Yurong","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics, Xijing University, Xi\u2019an 710123, China"}]},{"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, Punjab 38000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2363-5039","authenticated-orcid":false,"given":"Muhammad","family":"Imran","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University Faisalabad, Punjab 38000, Pakistan"}]},{"given":"Umar","family":"Farooq","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University Faisalabad, Punjab 38000, Pakistan"}]},{"given":"Fouad","family":"Mallawi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}]},{"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"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,3]]},"reference":[{"key":"ref_1","unstructured":"Choi, S.U., and Eastman, J.A. 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