{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T23:53:13Z","timestamp":1773013993671,"version":"3.50.1"},"reference-count":42,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2020,3,31]],"date-time":"2020-03-31T00:00:00Z","timestamp":1585612800000},"content-version":"vor","delay-in-days":1,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper is concerned with the investigation of variable viscosity bioconvection flow of nanofluid containing motile gyrotactic microorganisms over a nonlinear stretching sheet in the presence of nonlinear thermal radiation, chemical reaction, internal heat source, and suction\/injection effects. The homotopy analysis method has been developed for solving the governing nonlinear differential equations of the boundary layer flow of nanofluid over a stretching sheet. The scaling group transformation (a special form of Lie group transformation) has been applied to find the similarity variable $\\eta $. Figures are drawn by using Mathematica software to analyze the results that correspond to some important physical parameters and bioconvection parameters on velocity, temperature, nanoparticle concentration, and density of gyrotactic microorganisms. It is found that the influence of variable viscosity on velocity profiles showed that there is an increase in the velocity profiles of nanofluid and the reverse effect is observed on its temperature distribution. It is seen that the thermal radiation parameter increases the temperature distribution, whereas it decreases the nanoparticle concentration distribution. It is also found that the inverse Darcy number reduces the velocity profile, whereas it enhances the temperature distribution. This work may find applications in advanced nanomechanical bioconvection energy conversion devices, bio-nanocoolant systems, etc.<\/jats:p>","DOI":"10.1093\/jcde\/qwaa021","type":"journal-article","created":{"date-parts":[[2020,2,10]],"date-time":"2020-02-10T20:09:51Z","timestamp":1581365391000},"page":"251-267","source":"Crossref","is-referenced-by-count":47,"title":["Computational analysis of bioconvective flow of nanofluid containing gyrotactic microorganisms over a nonlinear stretching sheet with variable viscosity using HAM"],"prefix":"10.1093","volume":"7","author":[{"given":"Surya Kanta","family":"Mondal","sequence":"first","affiliation":[{"name":"Department of Mathematics, Abhedananda Mahavidyalaya, Sainthia 731234, West Bengal, India"}]},{"given":"Dulal","family":"Pal","sequence":"first","affiliation":[{"name":"Department of Mathematics, Institute of Science, Visva Bharati University, Santiniketan 731235, West Bengal, India"}]}],"member":"286","published-online":{"date-parts":[[2020,3,30]]},"reference":[{"issue":"4","key":"2020042510555219900_bib1","first-page":"177","article-title":"Unsteady forced bioconvection slip flow of a micropolar nanofluid from a stretching\/shrinking sheet","volume":"230","author":"Abdul\u00a0Latiff","year":"2016","journal-title":"Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanomaterials, Nanoengineering and Nanosystems"},{"issue":"4","key":"2020042510555219900_bib2","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1007\/s10483-016-2044-9","article-title":"Laminar MHD natural convection of nanofluid containing gyrotactic microorganisms over vertical wavy surface saturated non-Darcian porous media","volume":"37","author":"Ahmed","year":"2016","journal-title":"Applied Mathematics and Mechanics"},{"key":"2020042510555219900_bib3","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.jmmm.2016.02.075","article-title":"Magnetic field analysis in a suspension of gyrotactic microorganisms and nanoparticles over a stretching surface","volume":"410","author":"Akbar","year":"2016","journal-title":"Journal of Magnetism and Magnetic Materials"},{"key":"2020042510555219900_bib4","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/j.molliq.2017.02.016","article-title":"Nanofluid bioconvection with variable thermophysical properties","volume":"231","author":"Begum","year":"2017","journal-title":"Journal of Molecular Liquids"},{"issue":"1","key":"2020042510555219900_bib5","first-page":"1","article-title":"Lie group analysis for MHD effects on the convectively heated stretching porous surface with the heat source\/sink","volume":"63","author":"Cao","year":"2015","journal-title":"Boundary Value Problems"},{"issue":"8","key":"2020042510555219900_bib6","doi-asserted-by":"crossref","first-page":"1658","DOI":"10.1016\/j.ijthermalsci.2008.12.018","article-title":"Combined effect of heat generation or absorption and first-order chemical reaction on micropolar fluid flows over a uniformly stretched permeable surface","volume":"48","author":"Damseh","year":"2009","journal-title":"International Journal of Thermal Sciences"},{"issue":"3","key":"2020042510555219900_bib7","doi-asserted-by":"crossref","first-page":"1000152","DOI":"10.4172\/2168-9792.1000152","article-title":"Hydromagnetic nanofluid flow in the presence of radiation and heat generation\/absorption past an exponential stretching sheet with slip boundary conditions using HAM","volume":"4","author":"Daniel","year":"2015","journal-title":"Journal of Aeronautics and Aerospace Engineering"},{"issue":"2","key":"2020042510555219900_bib8","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1016\/j.jcde.2017.09.001","article-title":"Thermal stratification effects on MHD radiative flow of nanofluid over nonlinear stretching sheet with variable thickness","volume":"5","author":"Daniel","year":"2018","journal-title":"Journal of Computational Design and Engineering"},{"issue":"11","key":"2020042510555219900_bib9","doi-asserted-by":"crossref","first-page":"4841","DOI":"10.1007\/s12206-015-1031-z","article-title":"Nanofluid bioconvection in presence of gyrotactic microorganisms and chemical reaction in a porous medium","volume":"29","author":"Das","year":"2015","journal-title":"Journal of Mechanical Science and Technology"},{"key":"2020042510555219900_bib10","doi-asserted-by":"crossref","first-page":"967","DOI":"10.1016\/j.asej.2014.03.008","article-title":"MHD effects on heat transfer over stretching sheet embedded in porous medium with variable viscosity, viscous dissipation and heat source\/sink","volume":"5","author":"Dessie","year":"2014","journal-title":"Ain Shams Engineering Journal"},{"key":"2020042510555219900_bib11","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.jtice.2016.07.001","article-title":"Lie group analysis for bioconvection MHD slip flow and heat transfer of nanofluid over an inclined sheet: Multiple solutions","volume":"66","author":"Dhanai","year":"2016","journal-title":"Journal of Taiwan Institute of Chemical Engineers"},{"issue":"1","key":"2020042510555219900_bib12","first-page":"11","article-title":"Flow and heat transfer of electrically conducting nanofluid over a nonlinearly stretching sheet","volume":"7","author":"Dhanalaxmi","year":"2015","journal-title":"Journal of Applied Mathematics and Fluid Mechanics"},{"issue":"3","key":"2020042510555219900_bib13","doi-asserted-by":"crossref","first-page":"1451","DOI":"10.1016\/j.apm.2012.04.004","article-title":"The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nanofluid in a pipe: Analytical solutions","volume":"37","author":"Ellahi","year":"2013","journal-title":"Applied Mathematical Modelling"},{"issue":"2","key":"2020042510555219900_bib14","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1080\/15567265.2010.549931","article-title":"Natural convective boundary layer flow over a nonisothermal vertical plate embedded in a porous medium saturated with a nanofluid","volume":"15","author":"Gorla","year":"2011","journal-title":"Nanoscale and Microscale Thermophysical Engineering"},{"issue":"38","key":"2020042510555219900_bib15","doi-asserted-by":"crossref","first-page":"2749","DOI":"10.1016\/j.physleta.2018.06.026","article-title":"Convective heat transfer flow of nanofluid in a porous medium over wavy surface","volume":"382","author":"Hassan","year":"2018","journal-title":"Physics Letters A"},{"issue":"9","key":"2020042510555219900_bib16","doi-asserted-by":"crossref","first-page":"e0133831","DOI":"10.1371\/journal.pone.0133831","article-title":"Effects of convective heat and mass transfer in flow of Powell\u2013Eyring fluid past an exponentially stretching sheet","volume":"10","author":"Hayat","year":"2015","journal-title":"PLoS One"},{"key":"2020042510555219900_bib17","doi-asserted-by":"crossref","first-page":"778","DOI":"10.1016\/j.ijheatmasstransfer.2016.11.074","article-title":"Nanofluid flow and heat transfer in porous media: A review of the latest developments","volume":"107","author":"Kasaeian","year":"2017","journal-title":"International Journal of Heat and Mass Transfer"},{"issue":"3","key":"2020042510555219900_bib19","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/s13538-018-0567-7","article-title":"Bioconvection in second grade nanofluid flow containing nanoparticles and gyrotactic microorganisms","volume":"48","author":"Khan","year":"2018","journal-title":"Brazilian Journal of Physics"},{"key":"2020042510555219900_bib18","doi-asserted-by":"crossref","first-page":"4033","DOI":"10.1016\/j.rinp.2017.10.017","article-title":"Mixed convection in gravity-driven thin film non-Newtonian nanofluids flow with gyrotactic microorganisms","volume":"7","author":"Khan","year":"2017","journal-title":"Results in Physics"},{"key":"2020042510555219900_bib20","volume-title":"Advances in the homotopy analysis method","author":"Liao","year":"2013"},{"key":"2020042510555219900_bib21","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/j.ijthermalsci.2016.06.003","article-title":"Bioconvection in MHD nanofluid flow with nonlinear thermal radiation and quartic autocatalysis chemical reaction past an upper surface of a paraboloid of revolution","volume":"109","author":"Makinde","year":"2016","journal-title":"International Journal of Thermal Sciences"},{"key":"2020042510555219900_bib22","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1016\/j.jcde.2019.01.003","article-title":"Dual solutions for three-dimensional magnetohydrodynamic nanofluid flow with entropy generation","volume":"6","author":"Mondal","year":"2019","journal-title":"Journal of Computational Design and Engineering"},{"key":"2020042510555219900_bib23","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.compfluid.2014.02.026","article-title":"Hydromagnetic bioconvection of nanofluid over a permeable vertical plate due to gyrotactic micro-organisms","volume":"95","author":"Mutuku","year":"2014","journal-title":"Computer and Fluids"},{"key":"2020042510555219900_bib24","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.jcde.2019.04.001","article-title":"Mathematical analysis of bio-convective micropolar nanofluid","volume":"6","author":"Nadeem","year":"2018","journal-title":"Journal of Computational Design and Engineering"},{"issue":"4","key":"2020042510555219900_bib26","doi-asserted-by":"crossref","first-page":"2889","DOI":"10.1007\/s40819-016-0241-0","article-title":"Magnetohydrodynamic heat transfer of nanofluids past a stretching cylinder with non-uniform heat source\/sink and chemical reaction","volume":"3","author":"Pal","year":"2016","journal-title":"International Journal of Applied and Computational Mathematics"},{"issue":"1","key":"2020042510555219900_bib25","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.amc.2009.02.013","article-title":"Influence of temperature-dependent viscosity and thermal radiation on MHD forced convection over a non-isothermal wedge","volume":"212","author":"Pal","year":"2009","journal-title":"Applied Mathematics and Computation"},{"issue":"1","key":"2020042510555219900_bib27","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1007\/s12668-017-0474-3","article-title":"MHD nanofluid bioconvection over an exponentially stretching sheet in the presence of gyrotactic microorganisms and thermal radiation","volume":"8","author":"Pal","year":"2018","journal-title":"BioNanoScience"},{"issue":"4","key":"2020042510555219900_bib28","doi-asserted-by":"crossref","first-page":"1065","DOI":"10.1007\/s12668-018-0555-y","article-title":"Influence of chemical reaction and nonlinear thermal radiation on bioconvection of nanofluid containing gyrotactic microorganisms with magnetic field","volume":"8","author":"Pal","year":"2018","journal-title":"BioNanoScience"},{"key":"2020042510555219900_bib29","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1166\/jon.2019.1624","article-title":"Unsteady magneto-bioconvection flow of chemically reactive Powell\u2013Eyring nanofluid having gyrotactic microorganisms over an inclined stretching sheet with non-uniform heat source\/sink and thermal radiation","volume":"8","author":"Pal","year":"2019","journal-title":"Journal of Nanofluids"},{"key":"2020042510555219900_bib30","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1016\/j.ijheatmasstransfer.2013.04.032","article-title":"Soret effect on mixed convection flow in a nanofluid under convective boundary condition","volume":"64","author":"RamReddy","year":"2013","journal-title":"International Journal of Heat and Mass Transfer"},{"key":"2020042510555219900_bib31","doi-asserted-by":"crossref","first-page":"4277","DOI":"10.1108\/HFF-02-2019-0158","article-title":"Magneto-bioconvection flow of a Casson thin film with nanoparticles over an unsteady stretching sheet: HAM and GDQ computation","volume":"29","author":"Ray","year":"2019","journal-title":"International Journal of Numerical Methods for Heat and Fluid Flow"},{"issue":"3","key":"2020042510555219900_bib32","doi-asserted-by":"crossref","first-page":"233","DOI":"10.2298\/TAM1203233R","article-title":"Lie group analysis of heat and mass transfer effects on steady MHD free convection dissipative fluid flow past an inclined porous surface with heat generation","volume":"39","author":"Reddy","year":"2012","journal-title":"Theoretical and Applied Mechanics"},{"issue":"3","key":"2020042510555219900_bib33","doi-asserted-by":"crossref","first-page":"1008","DOI":"10.1016\/j.apt.2017.01.005","article-title":"MHD heat and mass transfer flow of a nanofluid over an inclined vertical porous plate with radiation and heat generation\/absorption","volume":"28","author":"Reddy","year":"2017","journal-title":"Advanced Powder Technology"},{"key":"2020042510555219900_bib34","doi-asserted-by":"crossref","first-page":"24","DOI":"10.4236\/jamp.2014.22004","article-title":"Influence of chemical reaction and thermal radiation on MHD boundary layer flow and heat transfer of a nanofluid over an exponentially stretching sheet","volume":"2","author":"Rudraswamy","year":"2014","journal-title":"Journal of Applied Mathematics and Physics"},{"issue":"4","key":"2020042510555219900_bib35","doi-asserted-by":"crossref","first-page":"895","DOI":"10.29252\/jafm.11.04.28062","article-title":"A bio-thermal convection in water-based nanofluid containing gyrotactic microorganisms: Effect of vertical through flow","volume":"11","author":"Saini","year":"2018","journal-title":"Journal of Applied Fluid Mechanics"},{"key":"2020042510555219900_bib36","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1002\/htj.21337","article-title":"Magnetic field and viscous dissipation effect on bioconvection in a permeable sphere embedded in a porous medium with a nanofluid containing gyrotactic microorganisms","volume":"47","author":"Shaw","year":"2018","journal-title":"Heat Transfer\u2014Asian Research"},{"issue":"6A","key":"2020042510555219900_bib37","doi-asserted-by":"crossref","first-page":"2347","DOI":"10.2298\/TSCI150424128S","article-title":"Bioconvection heat transfer of a nanofluid over a stretching sheet with velocity slip and temperature jump","volume":"21","author":"Shen","year":"2017","journal-title":"Journal of Thermal Science"},{"key":"2020042510555219900_bib38","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.powtec.2017.03.059","article-title":"Heat and mass transfer analysis of nanofluid over linear and non-linear stretching surfaces with thermal radiation and chemical reaction","volume":"315","author":"Sreedevi","year":"2017","journal-title":"Powder Technology"},{"key":"2020042510555219900_bib40","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":"Computers and Mathematics with Applications"},{"issue":"5","key":"2020042510555219900_bib39","doi-asserted-by":"crossref","first-page":"846","DOI":"10.1016\/j.camwa.2015.06.002","article-title":"Lie group analysis and numerical solution of magnetohydrodynamic free convective slip flow of micropolar fluid over a moving plate with heat transfer","volume":"70","author":"Uddin","year":"2015","journal-title":"Computers and Mathematics with Applications"},{"issue":"5","key":"2020042510555219900_bib41","doi-asserted-by":"crossref","first-page":"2048","DOI":"10.1016\/j.cjph.2017.08.005","article-title":"Bioconvection nanofluid slip flow past a wavy surface with applications in nano-biofuel cells","volume":"55","author":"Uddin","year":"2017","journal-title":"Chinese Journal of Physics"},{"issue":"1","key":"2020042510555219900_bib42","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1016\/j.cjph.2017.08.031","article-title":"Anisotropic slip magneto-bioconvection flow from a rotating cone to a nanofluid with Stefan blowing effects","volume":"56","author":"Zohra","year":"2018","journal-title":"Chinese Journal of Physics"}],"container-title":["Journal of Computational Design and Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/jcde\/article-pdf\/7\/2\/251\/33127572\/qwaa021.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/jcde\/article-pdf\/7\/2\/251\/33127572\/qwaa021.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,25]],"date-time":"2020-04-25T14:57:19Z","timestamp":1587826639000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jcde\/article\/7\/2\/251\/5813878"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,30]]},"references-count":42,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,3,30]]},"published-print":{"date-parts":[[2020,4,1]]}},"URL":"https:\/\/doi.org\/10.1093\/jcde\/qwaa021","relation":{},"ISSN":["2288-5048"],"issn-type":[{"value":"2288-5048","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2020,4]]},"published":{"date-parts":[[2020,3,30]]}}}