{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T12:53:18Z","timestamp":1780491198061,"version":"3.54.1"},"reference-count":44,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,15]],"date-time":"2025-08-15T00:00:00Z","timestamp":1755216000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU)","award":["IMSIU-DDRSP2502"],"award-info":[{"award-number":["IMSIU-DDRSP2502"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This work investigates the intricate dynamics of the Carreau hybrid nanofluid\u2019s inclined magnetohydrodynamic (MHD) flow, exploring both active and passive control modes. The study incorporates critical factors, including Arrhenius activation energy across a stretched sheet, chemical interactions, and nonlinear thermal radiation. The formulation of the boundary conditions and governing equations is inherently influenced by symmetric considerations in the physical geometry and flow assumptions. Such symmetry-inspired modeling facilitates dimensional reduction and numerical tractability. The analysis employs realistic boundary conditions, including convective heat transfer and control of nanoparticle concentration, which are solved numerically using MATLAB\u2019s bvp5c solver. Findings indicate that an increase in activation energy results in a steeper concentration boundary layer under active control, while it flattens in passive scenarios. An increase in the Biot number (Bi) and relaxation parameter (\u0393) enhances heat transfer and thermal response, leading to a rise in temperature distribution in both cases. Additionally, the 3D surface plot illustrates elevation variations from the surface at low inclination angles, narrowing as the angle increases. The Nusselt number demonstrates a contrasting trend, with thermal boundary layer thickness increasing with higher radiation parameters. A graphical illustration of the average values of skin friction, Nusselt number, and Sherwood number for both active and passive scenarios highlights the impact of each case. Under active control, the Brownian motion\u2019s effect diminishes, whereas it intensifies in passive control. Passive techniques, such as zero-flux conditions, offer effective and low-maintenance solutions for systems without external regulation, while active controls, like wall heating and setting a nanoparticle concentration, maximize heat and mass transfer in shear-thinning Carreau fluids.<\/jats:p>","DOI":"10.3390\/sym17081330","type":"journal-article","created":{"date-parts":[[2025,8,15]],"date-time":"2025-08-15T08:39:07Z","timestamp":1755247147000},"page":"1330","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Inclined MHD Flow of Carreau Hybrid Nanofluid over a Stretching Sheet with Nonlinear Radiation and Arrhenius Activation Energy Under a Symmetry-Inspired Modeling Perspective"],"prefix":"10.3390","volume":"17","author":[{"given":"Praveen","family":"Kumari","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Chaudhary Charan Singh Haryana Agricultural University, Hisar 125004, Haryana, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hemant","family":"Poonia","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Chaudhary Charan Singh Haryana Agricultural University, Hisar 125004, Haryana, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6876-8276","authenticated-orcid":false,"given":"Pardeep","family":"Kumar","sequence":"additional","affiliation":[{"name":"School of Basic and Applied Sciences, KR Mangalam University, Gurugram 122103, Haryana, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9343-0725","authenticated-orcid":false,"given":"Md","family":"Aquib","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 65892, Riyadh 11566, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,15]]},"reference":[{"key":"ref_1","unstructured":"Choi, S.U., and Eastman, J.A. (1995). Enhancing Thermal Conductivity of Fluids with Nanoparticles, Argonne National Lab. (ANL). Technical Report."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1016\/j.csite.2018.07.003","article-title":"Numerical investigation of heat transfers in the water jacket of heavy duty diesel engine by considering boiling phenomenon","volume":"12","author":"Gholinia","year":"2018","journal-title":"Case Stud. Therm. Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.cmpb.2019.05.012","article-title":"Theoretical investigation of Ree\u2013Eyring nanofluid flow with entropy optimization and Arrhenius activation energy between two rotating disks","volume":"177","author":"Hayat","year":"2019","journal-title":"Comput. Methods Programs Biomed."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.ijheatmasstransfer.2016.06.055","article-title":"Inclined magnetic field and heat source\/sink aspects in flow of nanofluid with nonlinear thermal radiation","volume":"103","author":"Hayat","year":"2016","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Algehyne, E.A., Lone, S.A., Raizah, Z., Eldin, S.M., Saeed, A., and Galal, A.M. (2023). Chemically reactive hybrid nanofluid flow past a Riga plate with nonlinear thermal radiation and a variable heat source\/sink. Front. Mater., 10.","DOI":"10.3389\/fmats.2023.1179265"},{"key":"ref_6","first-page":"4","article-title":"Effect of Inclined Magnetic Field and Chemical Reaction on Radiative Hybrid Nanofluid Flow Through an Exponentially Stretched Porous Surface in the Presence of Heat Source","volume":"20","author":"Fatima","year":"2025","journal-title":"J. Mech. Contin. Math. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2450102","DOI":"10.1142\/S0217984924501021","article-title":"Influence of exponential heat source, variable viscosity and shape factor on a hybrid nanofluid flow over a flat plate when thermal radiation and chemical reaction are significant","volume":"38","author":"Sreenivasulu","year":"2024","journal-title":"Mod. Phys. Lett. B"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1108\/HFF-10-2020-0636","article-title":"MHD and nonlinear thermal radiation effects on hybrid nanofluid past a wedge with heat source and entropy generation","volume":"32","author":"Mabood","year":"2022","journal-title":"Int. J. Numer. Methods Heat Fluid Flow"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1866","DOI":"10.1080\/10407782.2023.2212130","article-title":"Significance of irregular heat source and Arrhenius energy on electro-magnetohydrodynamic hybrid nanofluid flow over a rotating stretchable disk with nonlinear radiation","volume":"85","author":"Kumar","year":"2024","journal-title":"Numer. Heat Transf. Part Appl."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Ali, K., Faridi, A.A., Ahmad, S., Jamshed, W., Hussain, S.M., and Tag-Eldin, E.S.M. (2022). Quasi-linearization analysis for entropy generation in MHD mixed-convection flow of Casson nanofluid over nonlinear stretching sheet with Arrhenius activation energy. Symmetry, 14.","DOI":"10.3390\/sym14091940"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"e23934","DOI":"10.1016\/j.heliyon.2023.e23934","article-title":"Impact of activation energy on carreau nanofluid flow over non-linear stretching surface","volume":"10","author":"Bilal","year":"2024","journal-title":"Heliyon"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"100774","DOI":"10.1016\/j.csite.2020.100774","article-title":"An investigation on Arrhenius activation energy of second grade nanofluid flow with active and passive control of nanomaterials","volume":"22","author":"Kalaivanan","year":"2020","journal-title":"Case Stud. Therm. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"123964","DOI":"10.1016\/j.physa.2019.123964","article-title":"Analysis of active and passive control of nanoparticles in viscoelastic nanomaterial inspired by activation energy and chemical reaction","volume":"550","author":"Ramesh","year":"2020","journal-title":"Phys. Stat. Mech. Its Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"104890","DOI":"10.1016\/j.icheatmasstransfer.2020.104890","article-title":"Entropy optimization in passive and active flow of liquid hydrogen based nanoliquid transport by a curved stretching sheet","volume":"119","author":"Khan","year":"2020","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_15","first-page":"1","article-title":"Active-passive controls on magneto CNTs nanofluid flow over a wavy rotating disc","volume":"43","author":"Duari","year":"2023","journal-title":"Int. J. Model. Simul."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1080\/10407782.2023.2269475","article-title":"Insight into the dynamics of active and passive controls over the measurement of thermal conductivity of nanofluids subject to magnetic field and thermal radiation through the stretching surface","volume":"86","author":"Kumar","year":"2025","journal-title":"Numer. Heat Transf. Part Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3714","DOI":"10.1080\/10407782.2023.2240955","article-title":"Aspects of active-passive controls of nanoparticles of chemically reactive and radiative nanofluid flow past a frequently moving thin needle with thermal and velocity slip: A numerical framework","volume":"85","author":"Bag","year":"2024","journal-title":"Numer. Heat Transf. Part Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1615\/ComputThermalScien.2018024409","article-title":"Nanofluid slip flow through porous medium with elastic deformation and uniform heat source\/sink effects","volume":"11","author":"Hakeem","year":"2019","journal-title":"Comput. Therm. Sci. Int. J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1992","DOI":"10.1016\/j.apt.2016.07.002","article-title":"On magnetohydrodynamic flow of second grade nanofluid over a convectively heated nonlinear stretching surface","volume":"27","author":"Hayat","year":"2016","journal-title":"Adv. Powder Technol."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Hakeem, A., Kalaivanan, R., Ganga, B., and Ganesh, N.V. (2018). Effect of elastic deformation on nano-second grade fluid flow over a stretching surface. Front. Heat Mass Transf., 10.","DOI":"10.5098\/hmt.10.20"},{"key":"ref_21","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_22","doi-asserted-by":"crossref","unstructured":"Alsaadi, F.E., Hayat, T., Khan, S.A., Alsaadi, F.E., and Khan, M.I. (2020). Investigation of physical aspects of cubic autocatalytic chemically reactive flow of second grade nanomaterial with entropy optimization. Comput. Methods Programs Biomed., 183.","DOI":"10.1016\/j.cmpb.2019.105061"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"16878132241293958","DOI":"10.1177\/16878132241293958","article-title":"Hydrothermal dynamics of darcy Forchheimer ternary hybrid nanofluid flow past bended surface with active\u2014Passive controls","volume":"16","author":"Mumtaz","year":"2024","journal-title":"Adv. Mech. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"20240035","DOI":"10.1515\/ntrev-2024-0035","article-title":"A numerical investigation of the magnetized water-based hybrid nanofluid flow over an extending sheet with a convective condition: Active and passive controls of nanoparticles","volume":"13","author":"Yasmin","year":"2024","journal-title":"Nanotechnol. Rev."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"123063","DOI":"10.1016\/j.physa.2019.123063","article-title":"Numerical study for Carreau nanofluid flow over a convectively heated nonlinear stretching surface with chemically reactive species","volume":"540","author":"Eid","year":"2020","journal-title":"Phys. Stat. Mech. Its Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"106303","DOI":"10.1016\/j.icheatmasstransfer.2022.106303","article-title":"Heat transfer analysis of hybrid nanofluid flow with thermal radiation through a stretching sheet: A comparative study","volume":"138","author":"Waqas","year":"2022","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Aly, E.H., Ro\u015fca, A.V., Ro\u015fca, N.C., and Pop, I. (2021). Convective heat transfer of a hybrid nanofluid over a nonlinearly stretching surface with radiation effect. Mathematics, 9.","DOI":"10.3390\/math9182220"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Shah, S.A.A., Ahammad, N.A., Din, E.M.T.E., Gamaoun, F., Awan, A.U., and Ali, B. (2022). Bio-convection effects on prandtl hybrid nanofluid flow with chemical reaction and motile microorganism over a stretching sheet. Nanomaterials, 12.","DOI":"10.3390\/nano12132174"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1166\/jon.2024.2137","article-title":"Heat Transfer in Hybrid Nanofluid Flow Past an Infinite Orthogonal Plate with Biot Number and Velocity Slip Effects","volume":"13","author":"Zaki","year":"2024","journal-title":"J. Nanofluids"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"5773","DOI":"10.1080\/17455030.2021.2012303","article-title":"Characteristic of thermophoretic effect and convective thermal conditions on flow of hybrid nanofluid over a moving thin needle","volume":"34","author":"Madhukesh","year":"2024","journal-title":"Waves Random Complex Media"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"215401","DOI":"10.1088\/1361-6528\/acbda1","article-title":"Significance of the inclined magnetic field on the water-based hybrid nanofluid flow over a nonlinear stretching sheet","volume":"34","author":"Algehyne","year":"2023","journal-title":"Nanotechnology"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Choudhary, S., Mehta, R., and Mehta, T. (2025). A comparative analysis: Heat transfer in thermally stratified MHD Carreau ternary (Cu-Al2O3-TiO2) hybrid nanofluid flow across an inclined vertical cylinder in presence of radiation. J. Therm. Anal. Calorim., 1\u201314.","DOI":"10.1007\/s10973-025-14210-y"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"106","DOI":"10.59400\/mea.v1i1.106","article-title":"Analysing entropy generation of MHD (50: 50) slip flow over an inclined needle","volume":"1","author":"Priya","year":"2023","journal-title":"Mech. Eng. Adv."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"012019","DOI":"10.1088\/1742-6596\/2844\/1\/012019","article-title":"Numerical analysis of heat and mass transport of hybrid nanofluid over a nonlinear stretchable sheet with magnetic field in presence of Soret and dufour Effect","volume":"2844","author":"Jat","year":"2024","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Rafique, K., Mahmood, Z., Ansari, M.A., Kumar, A., and Khan, U. (2025). Investigating Soret\u2013Dufour effects and discharge concentration on accelerating hybrid nanofluid flow over radiative disk embedded in porous media under convective conditions. Can. J. Phys.","DOI":"10.1139\/cjp-2024-0307"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"4133","DOI":"10.1002\/htj.21585","article-title":"Numerical treatment of magneto Carreau nanofluid over a stretching sheet considering Joule heating impact and nonlinear thermal ray","volume":"48","author":"Ghobadi","year":"2019","journal-title":"Heat Transf. Res."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1166\/jon.2022.1884","article-title":"Effects of nonlinear thermal radiation and heat generation\/absorption on magnetohydrodynamic (MHD) Carreau nanofluid flow on a nonlinear stretching surface through a porous medium","volume":"11","author":"Mohamed","year":"2022","journal-title":"J. Nanofluids"},{"key":"ref_38","first-page":"853","article-title":"Influence of Soret and Dufour effects on unsteady 3D MHD slip flow of Carreau nanofluid over a slendering stretchable sheet with chemical reaction","volume":"24","author":"Reddy","year":"2019","journal-title":"Nonlinear Anal. Model. Control"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1016\/j.cjph.2021.03.016","article-title":"Irreversibility analysis in hybrid nanofluid flow between two rotating disks with activation energy and cross-diffusion effects","volume":"72","author":"Raju","year":"2021","journal-title":"Chin. J. Phys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"5170","DOI":"10.1002\/htj.22120","article-title":"Statistical approach on 3D hydromagnetic flow of water-based nanofluid between two vertical porous plates moving in opposite directions","volume":"50","author":"Neethu","year":"2021","journal-title":"Heat Transf."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"428","DOI":"10.1016\/j.powtec.2017.09.006","article-title":"Investigation on thermophysical properties of Tio2\u2013Cu\/H2O hybrid nanofluid transport dependent on shape factor in MHD stagnation point flow","volume":"322","author":"Ghadikolaei","year":"2017","journal-title":"Powder Technol."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.jtice.2019.01.028","article-title":"Natural convection MHD flow due to MoS2\u2013Ag nanoparticles suspended in C2H6O2H2O hybrid base fluid with thermal radiation","volume":"97","author":"Ghadikolaei","year":"2019","journal-title":"J. Taiwan Inst. Chem. Eng."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"2477","DOI":"10.1016\/j.ijheatmasstransfer.2010.01.032","article-title":"Boundary-layer flow of a nanofluid past a stretching sheet","volume":"53","author":"Khan","year":"2010","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"5652","DOI":"10.1002\/htj.22142","article-title":"Effects of multislip and distinct heat source on MHD Carreau nanofluid flow past an elongating cylinder using the statistical method","volume":"50","author":"Sabu","year":"2021","journal-title":"Heat Transf."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/8\/1330\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:27:57Z","timestamp":1760034477000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/8\/1330"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,15]]},"references-count":44,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["sym17081330"],"URL":"https:\/\/doi.org\/10.3390\/sym17081330","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,15]]}}}