{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T06:48:42Z","timestamp":1773557322718,"version":"3.50.1"},"reference-count":49,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,1,20]],"date-time":"2024-01-20T00:00:00Z","timestamp":1705708800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Many biotechnology sectors that depend on fluids and their physical characteristics, including the phenomenon of bioconvection, have generated a great deal of discussion. The term \u201cbioconvection\u201d describes the organized movement of microorganisms, such as bacteria or algae. Microorganisms that participate in bioconvection display directed movement, frequently in the form of upward or downward streaming, which can lead to the production of distinctive patterns. The interaction between the microbes\u2019 swimming behavior and the physical forces acting on them, such as buoyancy and fluid flow, is what drives these patterns. This work considers the laminar-mixed convection incompressible flow at the stagnation point with viscous and gyrotactic microorganisms in an unsteady electrically conducting hybrid nanofluid (Fe3O4-Cu\/water). In addition, hybrid nanofluid flow over a horizontal porous stretched sheet, as well as external and induced magnetic field effects, can be used in biological domains, including drug delivery and microcirculatory system flow dynamics. The governing system has been reduced to a set of ordinary differential equations (ODEs) through the use of the group technique. The current research was inspired by an examination of the impacts of multiple parameters, including Prandtl number, Pr, magnetic diffusivity, \u03b70, shape factor,\u00a0n, microorganism diffusion coefficient, Dn, Brownian motion coefficient, DB, thermophoresis diffusion coefficient, \u00a0DT, bioconvection Peclet number, Pe, temperature difference, \u00a0\u03b4t, and concentration difference, \u00a0\u03b4c. The results show that as Pr rises, temperature, heat flux, and nanoparticles all decrease. In contrast, when the \u03b70 value increases, the magnetic field and velocity decrease. Heat flow, bacterial density, and temperature decrease as the DB value rises, yet the number of nanoparticles increases. As the DT value increases, the temperature, heat flow, and concentration of nanoparticles all rise while the density of bacteria decreases. Even though temperature, heat flux, nanoparticles, and bacterial density all decrease as \u03b4c values climb, bacterial density rises as Dn values do although bacterial density falls with increasing, \u00a0\u03b4t and Pe values; on the other hand, when n values increase, temperature and heat flow increase but the density of bacteria and nanoparticle decrease. The physical importance and behavior of the present parameters were illustrated graphically.<\/jats:p>","DOI":"10.3390\/computation12010017","type":"journal-article","created":{"date-parts":[[2024,1,22]],"date-time":"2024-01-22T03:50:22Z","timestamp":1705895422000},"page":"17","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Influence of Gyrotactic Microorganisms on Bioconvection in Electromagnetohydrodynamic Hybrid Nanofluid through a Permeable Sheet"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7800-2768","authenticated-orcid":false,"given":"Ahmed S.","family":"Rashed","sequence":"first","affiliation":[{"name":"Department of Physics and Engineering Mathematics, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt"},{"name":"Basic Science Department, Faculty of Engineering, Delta University for Science and Technology, Gamasa 11152, Egypt"}]},{"given":"Ehsan H.","family":"Nasr","sequence":"additional","affiliation":[{"name":"Basic Science Department, Delta Higher Institute for Engineering and Technology, Mansoura 35681, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1877-3944","authenticated-orcid":false,"given":"Samah M.","family":"Mabrouk","sequence":"additional","affiliation":[{"name":"Department of Physics and Engineering Mathematics, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1007\/s40819-021-01144-w","article-title":"Investigation of cattaneo\u2013christov double diffusions theory in bioconvective slip flow of radiated magneto-cross-nanomaterial over stretching cylinder\/plate with activation energy","volume":"7","author":"Ali","year":"2021","journal-title":"Int. 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