{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T04:35:49Z","timestamp":1777005349636,"version":"3.51.4"},"reference-count":51,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,12,5]],"date-time":"2021-12-05T00:00:00Z","timestamp":1638662400000},"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>Thermal management is a crucial task in the present era of miniatures and other gadgets of compact heat density. This communication presents the momentum and thermal transportation of nanofluid flow over a sheet that stretches exponentially. The fluid moves through a porous matrix in the presence of a magnetic field that is perpendicular to the flow direction. To achieve the main objective of efficient thermal transportation with increased thermal conductivity, the possible settling of nano entities is avoided with the bioconvection of microorganisms. Furthermore, thermal radiation, heat source dissipation, and activation energy are also considered. The formulation in the form of a partial differential equation is transmuted into an ordinary differential form with the implementation of appropriate similarity variables. Numerical treatment involving Runge\u2013Kutta along with the shooting technique method was chosen to resolve the boundary values problem. To elucidate the physical insights of the problem, computational code was run for suitable ranges of the involved parameters. The fluid temperature directly rose with the buoyancy ratio parameter, Rayleigh number, Brownian motion parameter, and thermophoresis parameter. Thus, thermal transportation enhances with the inclusion of nano entities and the bioconvection of microorganisms. The findings are useful for heat exchangers working in various technological processors. The validation of the obtained results is also assured through comparison with the existing result. The satisfactory concurrence was also observed while comparing the present symmetrical results with the existing literature.<\/jats:p>","DOI":"10.3390\/sym13122334","type":"journal-article","created":{"date-parts":[[2021,12,7]],"date-time":"2021-12-07T02:48:13Z","timestamp":1638845293000},"page":"2334","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":51,"title":["Impact of Bioconvection and Chemical Reaction on MHD Nanofluid Flow Due to Exponential Stretching Sheet"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1484-5114","authenticated-orcid":false,"given":"Muhammad Imran","family":"Asjad","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0051-1041","authenticated-orcid":false,"given":"Noman","family":"Sarwar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5501-4181","authenticated-orcid":false,"given":"Bagh","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an 710072, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1403-057X","authenticated-orcid":false,"given":"Sajjad","family":"Hussain","sequence":"additional","affiliation":[{"name":"School of Aerospace and Mechanical Engineering, Nanyang Technological University, Singapore 639798, Singapore"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8455-1402","authenticated-orcid":false,"given":"Thanin","family":"Sitthiwirattham","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand"}]},{"given":"Jiraporn","family":"Reunsumrit","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,5]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","unstructured":"Ali, B., Rasool, G., Hussain, S., Baleanu, D., and Bano, S. (2020). Finite element study of magnetohydrodynamics (MHD) and activation energy in Darcy-Forchheimer rotating flow of Casson Carreau nanofluid. Processes, 8.","DOI":"10.3390\/pr8091185"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Abdal, S., Ali, B., Younas, S., Ali, L., and Mariam, A. (2020). Thermo-diffusion and multislip effects on MHD mixed convection unsteady flow of micropolar nanofluid over a shrinking\/stretching sheet with radiation in the presence of heat source. Symmetry, 12.","DOI":"10.3390\/sym12010049"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/s12648-019-01474-y","article-title":"Slip role for unsteady MHD mixed convection of nanofluid over stretching sheet with thermal radiation and electric field","volume":"94","author":"Daniel","year":"2020","journal-title":"Indian J. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"100826","DOI":"10.1016\/j.csite.2020.100826","article-title":"Thermal radiation impact on MHD heat transfer natural convective nano fluid flow over an impulsively started vertical plate","volume":"24","author":"Kumar","year":"2021","journal-title":"Case Stud. Therm. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1697","DOI":"10.1002\/htj.21948","article-title":"Entropy and radiation on a pipe MHD flow with variable viscosity","volume":"50","year":"2021","journal-title":"Heat Transf."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2077","DOI":"10.1016\/j.aej.2017.05.025","article-title":"Stability analysis of MHD outer velocity flow on a stretching cylinder","volume":"57","author":"Poply","year":"2018","journal-title":"Alex. Eng. J."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"100870","DOI":"10.1016\/j.csite.2021.100870","article-title":"Joule heating in magnetohydrodynamic micropolar boundary layer flow past a stretching sheet with chemical reaction and microstructural slip","volume":"25","author":"Dawar","year":"2021","journal-title":"Case Stud. Therm. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s42452-019-1831-3","article-title":"Multiple slip effects on MHD unsteady viscoelastic nano-fluid flow over a permeable stretching sheet with radiation using the finite element method","volume":"2","author":"Khan","year":"2020","journal-title":"SN Appl. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"9685482","DOI":"10.1155\/2020\/9685482","article-title":"Analysis of MHD fluids around a linearly stretching sheet in porous media with thermophoresis, radiation, and chemical reaction","volume":"2020","author":"Jabeen","year":"2020","journal-title":"Math. Probl. Eng."},{"key":"ref_11","unstructured":"Choi, S.U.S., and Eastman, J.A. (1995, January 12\u201317). Enhancing thermal conductivity of fluids with nanoparticles. Proceedings of the ASME International Mechanical Engineering Congress and Exposisition, American Society of Mechanical Engineers, San Francisco, FL, USA."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1861","DOI":"10.1016\/j.aej.2020.11.034","article-title":"Numerical analysis of higher order chemical reaction on electrically MHD nanofluid under influence of viscous dissipation","volume":"60","author":"Gopal","year":"2021","journal-title":"Alex. Eng. J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"100898","DOI":"10.1016\/j.csite.2021.100898","article-title":"Solar radiation effects on MHD stagnation point flow and heat transfer of a nanofluid over a stretching sheet","volume":"25","author":"Ghasemi","year":"2021","journal-title":"Case Stud. Therm. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3043","DOI":"10.1016\/j.asej.2020.10.028","article-title":"Radiation absorption on MHD convective flow of nanofluids through vertically travelling absorbent plate","volume":"12","author":"Krishna","year":"2021","journal-title":"Ain Shams Eng. J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.cjph.2020.11.019","article-title":"Models base study of inclined MHD of hybrid nanofluid flow over nonlinear stretching cylinder","volume":"69","author":"Abbas","year":"2021","journal-title":"Chin. J. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1016\/j.aej.2020.10.020","article-title":"Stability analysis of MHD hybrid nanofluid flow over a stretching\/shrinking sheet with quadratic velocity","volume":"60","author":"Zainal","year":"2021","journal-title":"Alex. Eng. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s42452-020-3011-x","article-title":"Heat and mass transfer analysis of unsteady hybrid nanofluid flow over a stretching sheet with thermal radiation","volume":"2","author":"Sreedevi","year":"2020","journal-title":"SN Appl. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-020-75254-8","article-title":"Numerical investigation for rotating flow of MHD hybrid nanofluid with thermal radiation over a stretching sheet","volume":"10","author":"Shoaib","year":"2020","journal-title":"Sci. Rep."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1733","DOI":"10.24996\/ijs.2020.61.7.22","article-title":"Numerical study of radiative magnetohydrodynamics viscous nanofluid due to convective stretching sheet with the chemical reaction effect","volume":"61","author":"Narender","year":"2020","journal-title":"Iraqi J. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Rashid, U., Baleanu, D., Iqbal, A., and Abbas, M. (2020). Shape effect of nanosize particles on magnetohydrodynamic nanofluid flow and heat transfer over a stretching sheet with entropy generation. Entropy, 22.","DOI":"10.3390\/e22101171"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1007\/BF01587695","article-title":"Flow past a stretching plate","volume":"21","author":"Crane","year":"1970","journal-title":"Z. F\u00fcr Angew. Math. Und Phys. ZAMP"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"744","DOI":"10.1002\/cjce.5450550619","article-title":"Heat and mass transfer on a stretching sheet with suction or blowing","volume":"55","author":"Gupta","year":"1977","journal-title":"Can. J. Chem. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-020-61439-8","article-title":"Study of heat and mass transfer in MHD flow of micropolar fluid over a curved stretching sheet","volume":"10","author":"Yasmin","year":"2020","journal-title":"Sci. Rep."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"e05338","DOI":"10.1016\/j.heliyon.2020.e05338","article-title":"Viscous dissipation and joule heating effect on MHD flow and heat transfer past a stretching sheet embedded in a porous medium","volume":"6","author":"Swain","year":"2020","journal-title":"Heliyon"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"020017","DOI":"10.1063\/5.0014438","article-title":"Effect of heat generation\/absorption on MHD copper-water nanofluid flow over a non-linear stretching\/shrinking sheet","volume":"2246","author":"Reddy","year":"2020","journal-title":"AIP Conf. Proc."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-019-52597-5","article-title":"Mass transpiration in nonlinear MHD flow due to porous stretching sheet","volume":"9","author":"Singh","year":"2019","journal-title":"Sci. Rep."},{"key":"ref_27","first-page":"38","article-title":"A note on MHD flow and heat transfer over a curved stretching sheet by considering variable thermal conductivity","volume":"12","author":"Murtaza","year":"2018","journal-title":"Int. J. Math. Comput. Sci."},{"key":"ref_28","first-page":"6450","article-title":"A numerical solution for magnetohydrodynamic stagnation-point flow towards a stretching sheet","volume":"12","author":"Narsingani","year":"2021","journal-title":"Turk. J. Comput. Math. Educ. (TURCOMAT)"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Ali, B., Naqvi, R.A., Nie, Y., Khan, S.A., Sadiq, M.T., Rehman, A.U., and Abdal, S. (2020). Variable viscosity effects on unsteady MHD an axisymmetric nanofluid flow over a stretching surface with thermo-diffusion: Fem approach. Symmetry, 12.","DOI":"10.3390\/sym12020234"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1016\/j.cjph.2020.04.011","article-title":"Magnetohydrodynamic tangent hyperbolic fluid flow past a stretching sheet","volume":"66","author":"Ullah","year":"2020","journal-title":"Chin. J. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1766","DOI":"10.1126\/science.133.3466.1766","article-title":"Bioconvection zatterns in cultures of free-swimming organisms","volume":"133","author":"Platt","year":"1961","journal-title":"Science"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Ferdows, M., Zaimi, K., Rashad, A.M., and Nabwey, H.A. (2020). MHD bioconvection flow and heat transfer of nanofluid through an exponentially stretchable sheet. Symmetry, 12.","DOI":"10.3390\/sym12050692"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-021-88935-9","article-title":"Numerical study of nano-biofilm stagnation flow from a nonlinear stretching\/shrinking surface with variable nanofluid and bioconvection transport properties","volume":"11","author":"Alsenafi","year":"2021","journal-title":"Sci. Rep."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"111231","DOI":"10.1016\/j.molliq.2019.111231","article-title":"Analysis on the bioconvection flow of modified second-grade nanofluid containing gyrotactic microorganisms and nanoparticles","volume":"291","author":"Waqas","year":"2019","journal-title":"J. Mol. Liq."},{"key":"ref_35","first-page":"86","article-title":"Magneto-hydrodynamics (MHD) bioconvection nanofluid slip flow over a stretching sheet with microorganism concentration and bioconvection P\u00e9clet number effects","volume":"4","author":"Ayodeji","year":"2019","journal-title":"Am. J. Mech. Ind. Eng."},{"key":"ref_36","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"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"5945","DOI":"10.1007\/s13369-020-04985-7","article-title":"Numerical investigation for bio-convection flow of viscoelastic nanofluid with magnetic dipole and motile microorganisms","volume":"46","author":"Alshomrani","year":"2021","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_38","first-page":"95","article-title":"Linear stability of thermal-bioconvection in a suspension of gyrotactic micro-organisms","volume":"126","author":"Zhao","year":"2018","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"100539","DOI":"10.1016\/j.tsep.2020.100539","article-title":"Numerical study of mixed bio-convection associated with a micropolar fluid","volume":"18","author":"Zadeh","year":"2020","journal-title":"Therm. Sci. Eng. Prog."},{"key":"ref_40","first-page":"43","article-title":"Novel computational study on MHD flow of nanofluid flow with gyrotactic microorganism due to porous stretching sheet","volume":"52","author":"Jawad","year":"2020","journal-title":"Punjab Univ. J. Math."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"BAbd-el-Malek, M., ABadran, N., MAmin, A., and MHanafy, A. (2021). Lie Symmetry Group for Unsteady Free Convection Boundary-Layer Flow over a Vertical Surface. Symmetry, 13.","DOI":"10.3390\/sym13020175"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Lund, L.A., Omar, Z., Dero, S., Baleanu, D., and Khan, I. (2020). Rotating 3D flow of hybrid nanofluid on exponentially shrinking sheet: Symmetrical solution and duality. Symmetry, 12.","DOI":"10.3390\/sym12101637"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"2399","DOI":"10.1002\/qre.2864","article-title":"Reliability analysis incorporating exponentiated inverse Weibull distribution and inverse power law","volume":"37","author":"Sindhu","year":"2021","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1016\/j.ijmecsci.2017.07.048","article-title":"Bioconvective MHD flow of tangent hyperbolic nanofluid with newtonian heating","volume":"133","author":"Shafiq","year":"2017","journal-title":"Int. J. Mech. Sci."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"100879","DOI":"10.1016\/j.csite.2021.100879","article-title":"Chemical reaction impact on MHD natural convection flow through porous medium past an exponentially stretching sheet in presence of heat source\/sink and viscous dissipation","volume":"25","author":"Reddy","year":"2021","journal-title":"Case Stud. Therm. Eng."},{"key":"ref_46","first-page":"1","article-title":"On radiation effects on hydromagnetic Newtonian liquid flow due to an exponential stretching sheet","volume":"2012","author":"Kameswaran","year":"2016","journal-title":"Bound. Value Probl."},{"key":"ref_47","first-page":"391","article-title":"MHD boundary layer flow due to an exponentially stretching sheet with radiation effect","volume":"40","author":"Ishak","year":"2011","journal-title":"Sains Malays."},{"key":"ref_48","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_49","doi-asserted-by":"crossref","unstructured":"Shateyi, S., and Muzara, H. (2020). On the numerical analysis of unsteady MHD boundary layer flow of Williamson fluid Over a stretching sheet and heat and mass transfers. Computation, 8.","DOI":"10.3390\/computation8020055"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1016\/j.asej.2020.02.011","article-title":"Thermophyical properties and internal energy change in Casson fluid flow along with activation energy","volume":"11","author":"Salahuddin","year":"2020","journal-title":"Ain Shams Eng. J."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1016\/j.asej.2012.10.007","article-title":"Slip effects on MHD boundary layer flow over an exponentially stretching sheet with suction\/blowing and thermal radiation","volume":"4","author":"Mukhopadhyay","year":"2013","journal-title":"Ain Shams Eng. J."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/12\/2334\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:40:00Z","timestamp":1760168400000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/12\/2334"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,5]]},"references-count":51,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["sym13122334"],"URL":"https:\/\/doi.org\/10.3390\/sym13122334","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,5]]}}}