{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T07:57:14Z","timestamp":1790668634593,"version":"4.1.0"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T00:00:00Z","timestamp":1790640000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T00:00:00Z","timestamp":1790640000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discover Nano"],"DOI":"10.1186\/s11671-026-04940-9","type":"journal-article","created":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T07:31:11Z","timestamp":1790667071000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Computational investigation of MHD stagnation point flow of Eyring-Powell nanofluid with microorganisms over a cylinder under Cattaneo-Christov heat and mass flux"],"prefix":"10.1186","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-0782-4489","authenticated-orcid":false,"given":"P.","family":"Jayasri","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1753-7088","authenticated-orcid":false,"given":"P.","family":"Durgaprasad","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,9,29]]},"reference":[{"key":"4940_CR1","doi-asserted-by":"publisher","unstructured":"Choi SUS. Enhancing thermal conductivity of fluids with nanoparticles. In: ASME International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers. 1995; 17421:99-105. https:\/\/doi.org\/10.1115\/IMECE1995-0926.","DOI":"10.1115\/IMECE1995-0926"},{"key":"4940_CR2","doi-asserted-by":"publisher","unstructured":"Buongiorno J. Convective transport in nanofluids. ASME. Journal of Heat Transfer. 2006; 128(3): 240\u2013250. https:\/\/doi.org\/10.1115\/1.2150834.","DOI":"10.1115\/1.2150834"},{"key":"4940_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1002\/mma.10723","volume":"9999","author":"M Jawad","year":"2025","unstructured":"Jawad M, Saidani T, Alsaydi HA, Abdallah SA, Alhushaybari A. Dynamics of bioconvection on darcy\u2013forchheimer flow of electromagnetic Reiner\u2013philippoff nanofluid with characteristics of nonlinear thermal radiation and activation energy. Mathematical Methods in the Applied Sciences. 2025. https:\/\/doi.org\/10.1002\/mma.10723","journal-title":"Mathematical Methods in the Applied Sciences"},{"key":"4940_CR4","doi-asserted-by":"publisher","DOI":"10.1016\/j.csite.2024.104178","volume":"55","author":"MA Basit","year":"2024","unstructured":"Basit MA, Imran M, Safdar R, Tahir M, Ali MR, Hendy AS, et al. Thermally radiative bioconvective nanofluid flow on a wavy cylinder with buongiorno model: a sensitivity analysis using response surface methodology. Case Studies in Thermal Engineering. 2024;55:104178 https:\/\/doi.org\/10.1016\/j.csite.2024.104178","journal-title":"Case Studies in Thermal Engineering"},{"key":"4940_CR5","doi-asserted-by":"publisher","DOI":"10.1016\/j.csite.2025.106054","volume":"69","author":"MA Raja","year":"2025","unstructured":"Raja MA, Latif A, Shamim M, Nisar KS, Shoaib M. Design of artificial neural network for buongiorno model with nanofluids flow through stretching sheet. Case Studies in Thermal Engineering. 2025;69:106054 https:\/\/doi.org\/10.1016\/j.csite.2025.106054","journal-title":"Case Studies in Thermal Engineering"},{"issue":"4","key":"4940_CR6","doi-asserted-by":"publisher","first-page":"4418","DOI":"10.1007\/s12668-024-01368-2","volume":"14","author":"K Rafique","year":"2024","unstructured":"Rafique K, Alqahtani AM, Ahmad S, Alotaibi H, Khan I, Singh A. Buongiorno model of micropolar nanofluid with surface inclination and Soret effect. BioNanoScience. 2024;14(4):4418\u201328. https:\/\/doi.org\/10.1007\/s12668-024-01368-2","journal-title":"BioNanoScience"},{"key":"4940_CR7","doi-asserted-by":"publisher","unstructured":"Faizan M, Zafar SS, Ali F, Khan U, Zaib A, Khashi\u2019ie NS. Radiative features of darcy forchheimer flow of entropy-optimized cross flow conveying ternary hybrid nanofluid past a stretching cylinder. Frontiers in Heat and Mass Transfer. 2026;24(1). https:\/\/doi.org\/10.32604\/fhmt.2026.075018.","DOI":"10.32604\/fhmt.2026.075018"},{"key":"4940_CR8","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijft.2024.100616","volume":"22","author":"S Karthik","year":"2024","unstructured":"Karthik S, Iranian D, Al-Mdallal QM. Numerical simulation of magneto-hydrodynamic fluid flow with heat sink, chemical diffusion and powell eyring fluid behavior using cattaneo\u2013christov source term. International Journal of Thermofluids. 2024;22:100616 https:\/\/doi.org\/10.1016\/j.ijft.2024.100616","journal-title":"International Journal of Thermofluids"},{"issue":"2","key":"4940_CR9","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1080\/02286203.2023.2205988","volume":"45","author":"PM Patil","year":"2025","unstructured":"Patil PM, Benawadi S. The bioconvective flow of an eyring-powell nanoliquid: the influence of entropy. International Journal of Modelling and Simulation. 2025;45(2):405\u201319. https:\/\/doi.org\/10.1080\/02286203.2023.2205988","journal-title":"International Journal of Modelling and Simulation"},{"key":"4940_CR10","doi-asserted-by":"publisher","DOI":"10.3389\/fenrg.2022.1021491","volume":"10","author":"CN Raju","year":"2022","unstructured":"Raju CN, Reddy CS, Alyami MA, Eldin SM, Adnan, Asogwa KK, et al. MHD eyring\u2013powell nanofluid flow across a wedge with convective and thermal radiation. Frontiers in Energy Research. 2022;10:1021491 https:\/\/doi.org\/10.3389\/fenrg.2022.1021491","journal-title":"Frontiers in Energy Research"},{"issue":"3","key":"4940_CR11","doi-asserted-by":"publisher","DOI":"10.1002\/adts.202501643","volume":"9","author":"B Ahmed","year":"2026","unstructured":"Ahmed B, Nisar Z, Aziz A, Hussain Z, Liu D. Numerical simulation for bioconvection radiative peristaltic flow of eyring\u2010powell nanomaterial. Advanced Theory and Simulations. 2026;9(3):e01643 https:\/\/doi.org\/10.1002\/adts.202501643","journal-title":"Advanced Theory and Simulations"},{"issue":"27","key":"4940_CR12","doi-asserted-by":"publisher","DOI":"10.1002\/adfm.202421051","volume":"35","author":"AA Odebowale","year":"2025","unstructured":"Odebowale AA, Berhe A, Ogundare RT, Abdo S, Abdulghani A, Hattori HT, et al. Advances in radiative heat transfer: bridging far\u2010field fundamentals and emerging near\u2010field innovations. Advanced Functional Materials. 2025;35(27):2421051 https:\/\/doi.org\/10.1002\/adfm.202421051","journal-title":"Advanced Functional Materials"},{"key":"4940_CR13","doi-asserted-by":"publisher","DOI":"10.1016\/j.padiff.2022.100318","volume":"5","author":"MO Lawal","year":"2022","unstructured":"Lawal MO, Kasali KB, Ogunseye HA, Oni MO, Tijani YO, Lawal YT. On the mathematical model of eyring\u2013powell nanofluid flow with non-linear radiation, variable thermal conductivity and viscosity. Partial Differential Equations in Applied Mathematics. 2022;5:100318 https:\/\/doi.org\/10.1016\/j.padiff.2022.100318","journal-title":"Partial Differential Equations in Applied Mathematics"},{"key":"4940_CR14","doi-asserted-by":"publisher","first-page":"1899","DOI":"10.1016\/j.rinp.2017.06.002","volume":"7","author":"M Khan","year":"2017","unstructured":"Khan M, Irfan M, Khan WA, Ahmad L. Modeling and simulation for 3D magneto eyring\u2013powell nanomaterial subject to nonlinear thermal radiation and convective heating. Results in Physics. 2017;7:1899\u2013906. https:\/\/doi.org\/10.1016\/j.rinp.2017.06.002","journal-title":"Results in Physics"},{"key":"4940_CR15","doi-asserted-by":"publisher","DOI":"10.1016\/j.csite.2024.104409","volume":"58","author":"SO Salawu","year":"2024","unstructured":"Salawu SO, Yusuf TA, Obalalu AM, Fatunmbi EO. Thermal radiation and propagation of tiny particles in magnetized eyring\u2013powell binary reactive fluid with generalized Arrhenius kinetics. Case Studies in Thermal Engineering. 2024;58:104409 https:\/\/doi.org\/10.1016\/j.csite.2024.104409","journal-title":"Case Studies in Thermal Engineering"},{"key":"4940_CR16","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1016\/j.aej.2024.07.033","volume":"108","author":"T Salahuddin","year":"2024","unstructured":"Salahuddin T, Awais M. Implementing the predictor-corrector approach to examine the thermo-solutal convection for buongiorno eyring-powell nanofluid model with squeezed microcantilivier surface. Alexandria Engineering Journal. 2024;108:40\u20139. https:\/\/doi.org\/10.1016\/j.aej.2024.07.033","journal-title":"Alexandria Engineering Journal"},{"issue":"7","key":"4940_CR17","doi-asserted-by":"publisher","first-page":"5227","DOI":"10.1007\/s13369-020-04379-9","volume":"45","author":"SR Reddy","year":"2020","unstructured":"Reddy SR, Bala Anki Reddy P, Rashad AM. Activation energy impact on chemically reacting eyring\u2013powell nanofluid flow over a stretching cylinder. Arabian Journal for Science and Engineering. 2020;45(7):5227\u201342. https:\/\/doi.org\/10.1007\/s13369-020-04379-9","journal-title":"Arabian Journal for Science and Engineering"},{"key":"4940_CR18","doi-asserted-by":"publisher","DOI":"10.1016\/j.csite.2025.106406","volume":"72","author":"Z Abbas","year":"2025","unstructured":"Abbas Z, Arslan MS, Rafiq MY, Rangra N. Computational analysis of Powell-Eyring nanomaterials flow: mixed convection dynamics, metachronal wave phenomenon and Buongiorno model. Case Studies in Thermal Engineering. 2025;72:106406 https:\/\/doi.org\/10.1016\/j.csite.2025.106406","journal-title":"Case Studies in Thermal Engineering"},{"key":"4940_CR19","doi-asserted-by":"publisher","DOI":"10.1016\/j.csite.2022.102048","volume":"34","author":"M Azam","year":"2022","unstructured":"Azam M. Effects of cattaneo-christov heat flux and nonlinear thermal radiation on MHD maxwell nanofluid with arrhenius activation energy. Case Studies in Thermal Engineering. 2022;34:102048 https:\/\/doi.org\/10.1016\/j.csite.2022.102048","journal-title":"Case Studies in Thermal Engineering"},{"key":"4940_CR20","doi-asserted-by":"publisher","DOI":"10.1016\/j.csite.2022.102427","volume":"39","author":"N Anjum","year":"2022","unstructured":"Anjum N, Khan WA, Hobiny A, Azam M, Waqas M, Irfan M. Numerical analysis for thermal performance of modified eyring powell nanofluid flow subject to activation energy and bioconvection dynamic. Case Studies in Thermal Engineering. 2022;39:102427 https:\/\/doi.org\/10.1016\/j.csite.2022.102427","journal-title":"Case Studies in Thermal Engineering"},{"key":"4940_CR21","doi-asserted-by":"publisher","DOI":"10.1016\/j.csite.2025.105960","volume":"69","author":"U Farooq","year":"2025","unstructured":"Farooq U, Imran M. Analysis of bio-convection in casson hybrid nanofluid flow with motile microorganisms and heat transfer using cattaneo-christov heat and mass flux theory over a cylinder. Case Studies in Thermal Engineering. 2025;69:105960 https:\/\/doi.org\/10.1016\/j.csite.2025.105960","journal-title":"Case Studies in Thermal Engineering"},{"key":"4940_CR22","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijft.2024.100735","volume":"23","author":"Y Aboel-Magd","year":"2024","unstructured":"Aboel-Magd Y, Basem A, Farooq U, Fatima N, Noreen S, Waqas H, et al. Computational modeling of thermal radiation and activation energy effects in Casson nanofluid flow with bioconvection and microorganisms over a disk. International Journal of Thermofluids. 2024;23:100735 https:\/\/doi.org\/10.1016\/j.ijft.2024.100735","journal-title":"International Journal of Thermofluids"},{"key":"4940_CR23","doi-asserted-by":"publisher","unstructured":"Ali U, Irfan M. Thermal performance of joule heating in radiative eyring-powell nanofluid with Arrhenius activation energy and gyrotactic motile microorganisms. Heliyon. 2024;10(3). https:\/\/doi.org\/10.1016\/j.heliyon.2024.e25070.","DOI":"10.1016\/j.heliyon.2024.e25070"},{"key":"4940_CR24","doi-asserted-by":"publisher","DOI":"10.1016\/j.csite.2024.104903","volume":"61","author":"K Batool","year":"2024","unstructured":"Batool K, Haq F, Zainab S, Anwar S, Younis J, Hussain A, et al. An investigation of heat transfer and optimization of entropy in bio-convective flow of Eyring-Powell nanomaterial with gyrotactic microorganisms. Case Studies in Thermal Engineering. 2024;61:104903 https:\/\/doi.org\/10.1016\/j.csite.2024.104903","journal-title":"Case Studies in Thermal Engineering"},{"key":"4940_CR25","doi-asserted-by":"publisher","DOI":"10.1016\/j.icheatmasstransfer.2022.106299","volume":"137","author":"SA Shah","year":"2022","unstructured":"Shah SA, Ahammad NA, Ali B, Guedri K, Awan AU, Gamaoun F, et al. Significance of bio-convection, MHD, thermal radiation and activation energy across prandtl nanofluid flow: a case of stretching cylinder. International Communications in Heat and Mass Transfer. 2022;137:106299 https:\/\/doi.org\/10.1016\/j.icheatmasstransfer.2022.106299","journal-title":"International Communications in Heat and Mass Transfer"},{"issue":"2","key":"4940_CR26","doi-asserted-by":"publisher","first-page":"725","DOI":"10.1007\/s12668-024-01437-6","volume":"14","author":"S Bilal","year":"2024","unstructured":"Bilal S, Asadullah, Malik MY. Computational analysis to explore bioconvective Williamson nanofluid non-Darcian flow over a convective cylindrical surface with Gyrotactic microorganisms and activation energy aspects. BioNanoScience. 2024;14(2):725\u201347. https:\/\/doi.org\/10.1007\/s12668-024-01437-6","journal-title":"BioNanoScience"},{"issue":"19","key":"4940_CR27","doi-asserted-by":"publisher","first-page":"6936","DOI":"10.1080\/10407782.2024.2345873","volume":"86","author":"Z Nisar","year":"2025","unstructured":"Nisar Z, Ahmed B, Alhuthali AM, Hussien M. Nonlinear thermal radiation analysis for bioconvection peristaltic transport of fourth-grade nanofluid. Numerical Heat Transfer, Part A: Applications. 2025;86(19):6936\u201353. https:\/\/doi.org\/10.1080\/10407782.2024.2345873","journal-title":"Numerical Heat Transfer, Part A: Applications"},{"issue":"3","key":"4940_CR28","doi-asserted-by":"publisher","DOI":"10.1007\/s12043-025-02904-9","volume":"99","author":"F Ali","year":"2025","unstructured":"Ali F, Faizan M, Zafar SS, Khan MI, Abdullaeva BS. Stagnation point flow of a Casson nanomaterial with the cattaneo\u2013christov dual diffusion and motile micro-organism past a porous vertical sheet causing an entropy generation. Pramana. 2025;99(3):83 https:\/\/doi.org\/10.1007\/s12043-025-02904-9","journal-title":"Pramana"},{"issue":"9","key":"4940_CR29","doi-asserted-by":"publisher","DOI":"10.1177\/1687814020924894","volume":"12","author":"F Haq","year":"2020","unstructured":"Haq F, Khan MI, Khan SA, Hayat T. Investigation of suspended nanoliquid flow of Eyring\u2013powell fluid with gyrotactic microorganisms and density number. Advances in Mechanical Engineering. 2020;12(9):1687814020924894 https:\/\/doi.org\/10.1177\/1687814020924894","journal-title":"Advances in Mechanical Engineering"},{"key":"4940_CR30","doi-asserted-by":"publisher","DOI":"10.1016\/j.ceja.2024.100637","volume":"19","author":"HA Nabwey","year":"2024","unstructured":"Nabwey HA, El-Hakiem AM, Khan WA, Rashad AM, Sayed G. Heat and mass transport micropolar maxwell and williamson nanofluids flow past a perpendicular cylinder using combined convective flow. Chemical Engineering Journal Advances. 2024;19:100637 https:\/\/doi.org\/10.1016\/j.ceja.2024.100637","journal-title":"Chemical Engineering Journal Advances"},{"issue":"7","key":"4940_CR31","doi-asserted-by":"publisher","first-page":"6425","DOI":"10.1002\/htj.22178","volume":"50","author":"ER EL\u2010Zahar","year":"2021","unstructured":"EL\u2010Zahar ER, Mansour MA, Rashad AM, EL\u2010Mky HA, EL\u2010Hakiem AM. Micropolar nanoliquid flow via mixed convective over an orthogonal cylinder. Heat Transfer. 2021;50(7):6425\u201343. https:\/\/doi.org\/10.1002\/htj.22178","journal-title":"Heat Transfer"},{"issue":"3","key":"4940_CR32","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1145\/502800.502801","volume":"27","author":"J Kierzenka","year":"2001","unstructured":"Kierzenka J, Shampine LF. A BVP solver based on residual control and the Maltab PSE. ACM Transactions on Mathematical Software (TOMS). 2001;27(3):299\u2013316. https:\/\/doi.org\/10.1145\/502800.502801","journal-title":"ACM Transactions on Mathematical Software (TOMS)"},{"issue":"13","key":"4940_CR33","doi-asserted-by":"publisher","first-page":"7442","DOI":"10.1177\/09544062211072457","volume":"236","author":"S Jakeer","year":"2022","unstructured":"Jakeer S, Reddy PB. Entropy generation on the variable magnetic field and magnetohydrodynamic stagnation point flow of eyring\u2013powell hybrid dusty nanofluid: solar thermal application. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. 2022;236(13):7442\u201355. https:\/\/doi.org\/10.1177\/09544062211072457","journal-title":"Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science"},{"key":"4940_CR34","doi-asserted-by":"publisher","DOI":"10.1016\/j.csite.2023.103794","volume":"53","author":"SR Reddy","year":"2024","unstructured":"Reddy SR, Jakeer S, Sathishkumar VE, Basha HT, Cho J. Numerical study of TC4-NiCr\/EG+ Water hybrid nanofluid over a porous cylinder with Thompson and Troian slip boundary condition: Artificial neural network model. Case Studies in Thermal Engineering. 2024;53:103794 https:\/\/doi.org\/10.1016\/j.csite.2023.103794","journal-title":"Case Studies in Thermal Engineering"},{"issue":"8","key":"4940_CR35","doi-asserted-by":"publisher","first-page":"3993","DOI":"10.1016\/j.amc.2012.10.034","volume":"219","author":"K Vajravelu","year":"2012","unstructured":"Vajravelu K, Prasad KV, Santhi SR. Axisymmetric magneto-hydrodynamic (MHD) flow and heat transfer at a non-isothermal stretching cylinder. Applied Mathematics and computation. 2012;219(8):3993\u20134005. https:\/\/doi.org\/10.1016\/j.amc.2012.10.034","journal-title":"Applied Mathematics and computation"},{"key":"4940_CR36","unstructured":"Bird RB, Stewart WE, Lightfoot EN. Transport Phenomena. 2nd ed. New York: John Wiley & Sons. 2002."}],"container-title":["Discover Nano"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s11671-026-04940-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s11671-026-04940-9","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s11671-026-04940-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T07:31:14Z","timestamp":1790667074000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1186\/s11671-026-04940-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,29]]},"references-count":36,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,12]]}},"alternative-id":["4940"],"URL":"https:\/\/doi.org\/10.1186\/s11671-026-04940-9","relation":{},"ISSN":["2731-9229"],"issn-type":[{"value":"2731-9229","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,29]]},"assertion":[{"value":"6 February 2026","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 September 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 September 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Not applicable. This study did not involve human participants or animals.","order":1,"name":"Ethics","label":"Ethical approval","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","label":"Consent to participate","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":3,"name":"Ethics","label":"Consent to publish","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":4,"name":"Ethics","label":"Competing interests","group":{"name":"EthicsHeading","label":"Declarations"}}],"article-number":"481"}}