{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T20:24:56Z","timestamp":1772137496136,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,21]],"date-time":"2020-02-21T00:00:00Z","timestamp":1582243200000},"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>In recent decades, an interest has been developed towards the thermal consequences of nanofluid because of utilization of nano-materials to improve the thermal conductivity of traditional liquid and subsequently enhance the heat transportation phenomenon. Following this primarily concept, this current work investigates the thermal developed flow of third-grade nanofluid configured by a stretched surface with additional features of activation energy, viscous dissipation and second-order slip. Buongiorno\u2019s nanofluid model is used to explore the thermophoresis and Brownian motion features based on symmetry fundamentals. It is further assumed that the nanoparticles contain gyrotactic microorganisms, which are associated with the most fascination bioconvection phenomenon. The flow problem owing to the partial differential equations is renovated into dimensional form, which is numerically simulated with the help of bvp4c, by using MATLAB software. The aspects of various physical parameters associated to the current analysis are graphically examined against nanoparticles\u2019 velocity, temperature, concentration and gyrotactic microorganisms\u2019 density distributions. Further, the objective of local Nusselt number, local Sherwood number and motile density number are achieved numerically with variation of various parameters. The results presented here may find valuable engineering applications, like cooling liquid metals, solar systems, power production, solar energy, thermal extrusion systems cooling of machine equipment, transformer oil and microelectronics. Further, flow of nanoparticles containing gyrotactic microorganisms has interesting applications in microbial fuel cells, microfluidic devices, bio-technology and enzyme biosensors.<\/jats:p>","DOI":"10.3390\/sym12020309","type":"journal-article","created":{"date-parts":[[2020,2,26]],"date-time":"2020-02-26T04:18:29Z","timestamp":1582690709000},"page":"309","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":45,"title":["Utilization of Second Order Slip, Activation Energy and Viscous Dissipation Consequences in Thermally Developed Flow of Third Grade Nanofluid with Gyrotactic Microorganisms"],"prefix":"10.3390","volume":"12","author":[{"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"}]},{"given":"Sami","family":"Ullah Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Sahiwal 57000, Pakistan"}]},{"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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7167-3822","authenticated-orcid":false,"given":"Hossam","family":"A. Nabwey","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 Basic Engineering Science, Faculty of Engineering, Menoufia University, Shebin El-Kom 32511, Egypt"}]},{"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":[[2020,2,21]]},"reference":[{"key":"ref_1","first-page":"99","article-title":"Enhancing thermal conductivity of fluids with nanoparticles","volume":"231","author":"Choi","year":"1995","journal-title":"ASME Pub. Fed."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1115\/1.2150834","article-title":"Convective transport in nanofluids","volume":"128","author":"Buongiorno","year":"2006","journal-title":"J. Heat Transf."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1016\/j.asej.2016.02.008","article-title":"Momentum and heat transfer behaviour of Jeffrey, Maxwell and Oldroyd-B nanofluids past a stretching surface with non-uniform heat source\/sink","volume":"9","author":"Sandeep","year":"2018","journal-title":"Ain Shams Eng. J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1016\/j.ijmecsci.2016.12.023","article-title":"Thermal radiation and MHD effects on boundary layer flow of micropolar nanofluid past a stretching sheet with non-uniform heat source\/sink","volume":"126","author":"Pal","year":"2016","journal-title":"Int. J. Mech. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1016\/j.rinp.2018.03.034","article-title":"Impact of heat source\/sink on radiative heat transfer to Maxwell nanofluid subject to revised mass flux condition","volume":"9","author":"Khan","year":"2018","journal-title":"Results Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1618","DOI":"10.1016\/j.rinp.2018.04.054","article-title":"Melting heat transfer and induced magnetic field effects on flow of water based nanofluid over a rotating disk with variable thickness","volume":"9","author":"Hayat","year":"2018","journal-title":"Results Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.rinp.2017.12.013","article-title":"Multiple slips effects on MHD SA-Al2O3 and SA-Cu non-Newtonian nanofluids flow over a stretching cylinder in porous medium with radiation and chemical reaction","volume":"8","author":"Tlili","year":"2018","journal-title":"Results Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"095202","DOI":"10.1088\/1402-4896\/ab0661","article-title":"Brownian movement and thermophoretic aspects in third grade nanofluid over oscillatory moving sheet","volume":"94","author":"Khan","year":"2019","journal-title":"Phys. Scr."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1255","DOI":"10.1007\/s10483-019-2518-9","article-title":"Slip flow of Maxwell viscoelasticity-based micropolar nano particles with porous medium: A numerical study","volume":"40","author":"Waqas","year":"2019","journal-title":"Appl. Math. Mech."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1016\/j.ijheatmasstransfer.2017.05.042","article-title":"Micropolar nanofluid flow with MHD and viscous dissipation effects towards a stretching sheet with multimedia feature","volume":"112","author":"Hsiao","year":"2017","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1039","DOI":"10.1016\/j.ijheatmasstransfer.2017.04.070","article-title":"Forced convection of nanofluid in presence of constant magnetic field considering shape effects of nanoparticles","volume":"111","author":"Sheikholeslami","year":"2017","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"104997","DOI":"10.1016\/j.cmpb.2019.104997","article-title":"Fully developed slip flow in a concentric annuli via single and dual phase nanofluids models","volume":"179","author":"Turkyilmazoglu","year":"2019","journal-title":"Comput. Methods Programs Biomed."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1421","DOI":"10.1016\/j.icheatmasstransfer.2010.08.015","article-title":"The onset of nanofluid bioconvection in a suspension containing both nanoparticles and gyrotactic microorganisms","volume":"37","author":"Kuznetsov","year":"2010","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1186\/1556-276X-6-100","article-title":"Nanofluid bioconvection in water-based suspensions containing nanoparticles and oxytactic microorganisms: Oscillatory instability","volume":"6","author":"Kuznetsov","year":"2011","journal-title":"Nanoscale Res. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2562","DOI":"10.1016\/j.camwa.2016.09.018","article-title":"Numerical solutions for gyrotactic bioconvection in nanofluid-saturated porous media with Stefan blowing and multiple slip effects","volume":"72","author":"Uddin","year":"2016","journal-title":"Comput. Math. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.1016\/j.ijheatmasstransfer.2017.04.074","article-title":"Bioconvection in rotating system immersed in nanofluid with temperature dependent viscosity and thermal conductivity","volume":"111","author":"Xun","year":"2017","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1016\/j.apt.2016.10.026","article-title":"Radiative flow of Casson fluid over a moving wedge filled with gyrotactic microorganisms","volume":"28","author":"Raju","year":"2017","journal-title":"Adv. Powder Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1016\/j.apt.2016.10.002","article-title":"Magnetohydrodynamic (MHD) stratified bioconvective flow of nanofluid due to gyrotactic microorganisms","volume":"28","author":"Alsaedi","year":"2017","journal-title":"Adv. Powder Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.euromechflu.2019.01.002","article-title":"Natural bioconvection flow of a nanofluid containing gyrotactic microorganisms about a truncated cone","volume":"75","author":"Khan","year":"2019","journal-title":"Eur. J. Mech. B Fluids"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Alwatban, A.M., Khan, S.U., Waqas, H., and Tlili, I. (2019). Interaction of Wu\u2019s slip features in bioconvection of Eyring Powell nanoparticles with activation energy. Processes, 7.","DOI":"10.3390\/pr7110859"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Tlili, I., Waqas, H., Almaneea, A., Khan, S.U., and Imran, M. (2019). Activation energy and second order slip in bioconvection of Oldroyd-B nanofluid over a stretching cylinder: A proposed mathematical model. Processes, 7.","DOI":"10.3390\/pr7120914"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.euromechflu.2014.02.005","article-title":"Fully developed mixed convection flow in a horizontal channel filled by a nanofluid containing both nanoparticles and gyrotactic microorganisms","volume":"46","author":"Xu","year":"2014","journal-title":"Eur. J. Mech. B Fluids"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/s11242-014-0297-4","article-title":"Thermo-Bioconvection in a Square Porous Cavity Filled by Oxytactic Microorganisms","volume":"103","author":"Pop","year":"2014","journal-title":"Transp. Porous Med."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1016\/0020-7225(94)00078-X","article-title":"Fluids of differential type: Critical review and thermodynamic analysis","volume":"33","author":"Dunn","year":"1995","journal-title":"Int. Jr. Eng. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1515\/nleng-2015-0019","article-title":"Unsteady Flow of Third Grade Fluid over an Oscillatory Stretching Sheet with Thermal Radiation and Heat Source\/Sink","volume":"4","author":"Ali","year":"2015","journal-title":"Nonlinear Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1140\/epjp\/i2017-11423-y","article-title":"Application of Legendre wavelets method to parallel plate flow of a third grade fluid and forced convection in a porous duct","volume":"132","author":"Ali","year":"2017","journal-title":"Eur. Phys. J. Plus"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"195","DOI":"10.18869\/acadpub.jafm.68.224.24004","article-title":"Diffusion of Chemically Reactive Species in Stagnation-Point Flow of a Third Grade Fluid: A Hybrid Numerical Method","volume":"9","author":"Abbas","year":"2016","journal-title":"J. Appl. Fluid Mech."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"253103","DOI":"10.1063\/1.3052923","article-title":"A slip model for rarefied gas flows at arbitrary Knudsen number","volume":"93","author":"Wu","year":"2008","journal-title":"Appl. Phys. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"111231","DOI":"10.1016\/j.molliq.2019.111231","article-title":"Analysis for bioconvection flow of modified second grade fluid containing gyrotactic microorganisms and nanoparticles","volume":"291","author":"Waqas","year":"2019","journal-title":"J. Mol. Liq."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"125211","DOI":"10.1088\/1402-4896\/ab399f","article-title":"Theoretical analysis for tangent hyperbolic nanoparticles with combined electrical MHD, activation energy and Wu\u2019s slip features: A mathematical model","volume":"94","author":"Khan","year":"2019","journal-title":"Phys. Scr."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3723","DOI":"10.1016\/j.rinp.2017.09.041","article-title":"Magnetohydrodynamics (MHD) flow of a tangent hyperbolic fluid with nanoparticles past a stretching sheet with second order slip and convective boundary condition","volume":"7","author":"Ibrahim","year":"2017","journal-title":"Results Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/j.ijmecsci.2013.10.011","article-title":"The analytical solution of mixed convection heat transfer and fluid flow of a MHD viscoelastic fluid over a permeable stretching surface","volume":"77","author":"Turkyilmazoglu","year":"2013","journal-title":"Int. J. Mech. Sci."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/2\/309\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:59:41Z","timestamp":1760173181000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/2\/309"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,21]]},"references-count":32,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,2]]}},"alternative-id":["sym12020309"],"URL":"https:\/\/doi.org\/10.3390\/sym12020309","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,21]]}}}