{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T06:11:24Z","timestamp":1768284684493,"version":"3.49.0"},"reference-count":50,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,9,5]],"date-time":"2022-09-05T00:00:00Z","timestamp":1662336000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research, Islamic University of MaDinah, Ministry of Education","award":["Research Group Program\/1\/804"],"award-info":[{"award-number":["Research Group Program\/1\/804"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Heat transfer is a vital fact of daily life, engineering, and industrial mechanisms such as cryogenic systems, spaceborne thermal radiometers, electronic cooling, aircraft engine cooling, aircraft environmental control systems, etc. The addition of nanoparticles helps to stabilize the flowing of a nanofluid and keeps the symmetry of the flowing structure. Purpose: In this attempt, the effect of endothermic\/exothermic chemical reactions accompanied by activation energy on a ternary hybrid nanofluid with the geometry of a wedge is taken into consideration. The mathematical form of PDEs is obtained by Navier\u2013Stokes equations, the second law of thermodynamics, and Fick\u2019s second law of diffusion. The geometric model is therefore described using a symmetry technique. Formulation: The MATLAB built-in Lobatto III A structure is utilized to find the computational solution of the dimensionless ODEs. All computational outcomes are presented by graphs and statistical graphs in order to check the performance of various dimensionless quantities against drag force factor and Nusselt quantity. Finding: the addition of tri-hybridizing nanomolecules in the standard liquid improves the thermic performance of the liquid much better in comparison to simple hybrid nanofluids. Wedge angle parameter \u03b1 brings about a decrement in fluid velocity and augmentation in thermal conductivity \u03f5, thermal radiation Rd, thermophoresis parameter Nt and endothermic\/exothermic reaction \u03a9, and fitted rate constant n accelerates the heat transmission rate. Novelty: The effect of tri-hybridizing nanomolecules along with endothermic\/exothermic reactions on the fluid past a wedge have not been investigated before in the available literature.<\/jats:p>","DOI":"10.3390\/sym14091850","type":"journal-article","created":{"date-parts":[[2022,9,8]],"date-time":"2022-09-08T09:51:09Z","timestamp":1662630669000},"page":"1850","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":56,"title":["Trace of Chemical Reactions Accompanied with Arrhenius Energy on Ternary Hybridity Nanofluid Past a Wedge"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6130-3660","authenticated-orcid":false,"given":"Tanveer","family":"Sajid","sequence":"first","affiliation":[{"name":"Department of Mathematics, Capital University of Science and Technology, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9956-6730","authenticated-orcid":false,"given":"Assad","family":"Ayub","sequence":"additional","affiliation":[{"name":"Department of Mathematics & Statistics, Hazara University, Manshera 21300, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6085-0275","authenticated-orcid":false,"given":"Syed Zahir Hussain","family":"Shah","sequence":"additional","affiliation":[{"name":"Department of Mathematics & Statistics, Hazara University, Manshera 21300, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9438-6132","authenticated-orcid":false,"given":"Wasim","family":"Jamshed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Capital University of Science and Technology, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2479-9809","authenticated-orcid":false,"given":"Mohamed R.","family":"Eid","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, New Valley University, Al-Kharga 72511, Al-Wadi Al-Gadid, Egypt"},{"name":"Department of Mathematics, Faculty of Science, Northern Border University, Arar 1321, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3151-9967","authenticated-orcid":false,"given":"El Sayed M. Tag","family":"El Din","sequence":"additional","affiliation":[{"name":"Electrical Engineering, Faculty of Engineering and Technology, Future University in Egypt, New Cairo 11835, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5793-3598","authenticated-orcid":false,"given":"Rida","family":"Irfan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sahiwal Campus, COMSATS University Islamabad, Islamabad 45550, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1847-4776","authenticated-orcid":false,"given":"Syed M.","family":"Hussain","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5315","DOI":"10.1007\/s13204-020-01334-w","article-title":"Analysis of activation energy and its impact on hybrid nanofluid in the presence of Hall and ion slip currents","volume":"10","author":"Ahmad","year":"2020","journal-title":"Appl. Nanosci."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Waqas, H., Khan, S.U., Tlili, I., Awais, M., and Shadloo, M.S. (2020). Significance of bioconvective and thermally dissipation flow of viscoelastic nanoparticles with activation energy features: Novel biofuels significance. Symmetry, 12.","DOI":"10.3390\/sym12020214"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"20669","DOI":"10.1038\/s41598-021-00107-x","article-title":"Radiation effects on 3D rotating flow of Cu-water nanoliquid with viscous heating and prescribed heat flux using modified Buongiorno model","volume":"11","author":"Owhaib","year":"2021","journal-title":"Sci. Rep."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Rosca, N.C., Rosca, A.V., Aly, E.H., and Pop, I. (2021). Flow and Heat Transfer Past a Stretching\/Shrinking Sheet Using Modified Buongiorno Nanoliquid Model. Mathematics, 9.","DOI":"10.3390\/math9233047"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.camwa.2021.09.010","article-title":"Numerical and sensitivity computations of three-dimensional flow and heat transfer of nanoliquid over a wedge using modified Buongiorno model","volume":"101","author":"Rana","year":"2021","journal-title":"Comput. Math. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1007\/s10973-019-08006-0","article-title":"Effects of temperature and particles volume concentration on the thermophysical properties and the rheological behavior of CuO\/MgO\/TiO2 aqueous ternary hybrid nanofluid","volume":"137","author":"Mousavi","year":"2019","journal-title":"J. Therm. Anal. Calorim."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/j.powtec.2021.05.029","article-title":"An experimental study on dynamic viscosity and thermal conductivity of water-Cu-SiO2-MWCNT ternary hybrid nanofluid and the development of practical correlations","volume":"389","author":"Dezfulizadeh","year":"2021","journal-title":"Powder Technol."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Munjam, S.R., Gangadhar, K., Seshadri, R., and Rajeswar, M. (2021). Novel technique MDDIM solutions of MHD flow and radiative Prandtl-Eyring fluid over a stretching sheet with convective heating. Int. J. Ambient. Energy, 1\u201310.","DOI":"10.1080\/01430750.2021.1922498"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1515\/jnet-2020-0092","article-title":"Theoretical analysis of activation energy effect on Prandtl\u2013Eyring nanoliquid flow subject to melting condition","volume":"47","author":"Ullah","year":"2022","journal-title":"J. Non-Equil. Thermodyn."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"101581","DOI":"10.1016\/j.csite.2021.101581","article-title":"A case study of MHD driven Prandtl-Eyring hybrid nanofluid flow over a stretching sheet with thermal jump conditions","volume":"28","author":"Qureshi","year":"2021","journal-title":"Case Stud. Therm. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3196","DOI":"10.1002\/htj.22024","article-title":"Higher order chemical process with heat transport of magnetized cross nanofluid over wedge geometry","volume":"50","author":"Shah","year":"2021","journal-title":"Heat Transf."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"6465","DOI":"10.1002\/htj.22188","article-title":"Nanoscale energy transport of inclined magnetized 3D hybrid nanofluid with Lobatto IIIA scheme","volume":"50","author":"Ayub","year":"2021","journal-title":"Heat Transf."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"100971","DOI":"10.1016\/j.surfin.2021.100971","article-title":"Combined experimental thin films, TDDFT-DFT theoretical method, and spin effect on [PEG-H2O\/ZrO2+MgO] hybrid nanofluid flow with higher chemical rate","volume":"23","author":"Eid","year":"2021","journal-title":"Surf. Interfaces"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"105778","DOI":"10.1016\/j.icheatmasstransfer.2021.105778","article-title":"Effects of homogeneous-heterogeneous and Lorentz forces on 3-D radiative magnetized cross nanofluid using two rotating disks","volume":"130","author":"Ayub","year":"2022","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1625","DOI":"10.1016\/j.cjph.2021.10.045","article-title":"A comparative study of unsteady MHD Falkner\u2013Skan wedge flow for non-Newtonian nanofluids considering thermal radiation and activation energy","volume":"77","author":"Ali","year":"2022","journal-title":"Chin. J. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1140\/epjp\/s13360-022-02410-6","article-title":"Aspects of infinite shear rate viscosity and heat transport of magnetized Carreau nanofluid","volume":"137","author":"Ayub","year":"2022","journal-title":"Eur. Phys. J. Plus"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"106115","DOI":"10.1016\/j.icheatmasstransfer.2022.106115","article-title":"Multiple linear regression on bioconvective MHD hybrid nanofluid flow past an exponential stretching sheet with radiation and dissipation effects","volume":"135","author":"Neethu","year":"2022","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1622","DOI":"10.1002\/htj.22367","article-title":"Inclined magnetized and energy transportation aspect of infinite shear rate viscosity model of Carreau nanofluid with multiple features over wedge geometry","volume":"51","author":"Shah","year":"2022","journal-title":"Heat Transf."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Shah, S.L., Ayub, A., Dehraj, S., Wahab, H.A., Sagayam, K.M., Ali, M.R., Sadat, R., and Sabir, Z. (2022). Magnetic dipole aspect of binary chemical reactive Cross nanofluid and heat transport over composite cylindrical panels. Waves Random Complex Media, 1\u201324.","DOI":"10.1080\/17455030.2021.2020373"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1616","DOI":"10.1177\/09544089211070667","article-title":"Impact of nonlinear radiation on magnetohydrodynamic flow of hybrid nanofluid with heat source effect, P.I","volume":"236","author":"Sandeep","year":"2022","journal-title":"Proc. Inst. Mech. Eng. Part E J. Process Mech. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Ellahi, R., Zeeshan, A., Hussain, F., and Asadollahi, A. (2019). Peristaltic blood flow of couple stress fluid suspended with nanoparticles under the influence of chemical reaction and activation energy. Symmetry, 11.","DOI":"10.3390\/sym11020276"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.1615\/HeatTransRes.2018028397","article-title":"Effects of chemical reaction on third-grade MHD fluid flow under the influence of heat and mass transfer with variable reactive index","volume":"50","author":"Khan","year":"2019","journal-title":"Heat Transf. Res."},{"key":"ref_23","first-page":"26","article-title":"Analysis of Arrhenius activation energy in electrically conducting Casson fluid flow induced due to permeable elongated sheet with chemical reaction and viscous dissipation","volume":"15","author":"Vijaya","year":"2020","journal-title":"Front. Heat Mass Transf."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"6039","DOI":"10.1007\/s13369-020-05324-6","article-title":"Insight into the dynamics of Oldroyd-B fluid over an upper horizontal surface of a paraboloid of revolution subject to chemical reaction dependent on the first-order activation energy","volume":"46","author":"Ali","year":"2021","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"035005","DOI":"10.1088\/1402-4896\/ab5558","article-title":"Numerical analysis of effective Prandtl model on mixed convection flow of \u03b3Al2O3\u2013H2O nanoliquids with micropolar liquid driven through wedge","volume":"95","author":"Zaib","year":"2020","journal-title":"Phys. Scr."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"106141","DOI":"10.1016\/j.icheatmasstransfer.2022.106141","article-title":"Numerical investigation for MHD Prandtl nanofluid transportation due to a moving wedge: Keller box approach","volume":"35","author":"Habib","year":"2022","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"4402","DOI":"10.1038\/s41598-020-61125-9","article-title":"Radiative MHD Casson Nanofluid Flow with Activation energy and chemical reaction over past nonlinearly stretching surface through Entropy generation","volume":"10","author":"Shah","year":"2020","journal-title":"Sci. Rep."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2029","DOI":"10.1007\/s10973-020-09492-3","article-title":"Study of Arrhenius activation energy on the thermo-bioconvection nanofluid flow over a Riga plate","volume":"143","author":"Bhatti","year":"2021","journal-title":"J. Therm. Anal. Calorim."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Gowda, R.J.P., Kumar, R.N., Jyothi, A.M., Prasannakumara, B.C., and Sarris, I.E. (2021). Impact of binary chemical reaction and activation energy on heat and mass transfer of marangoni driven boundary layer flow of a non-Newtonian nanofluid. Processes, 9.","DOI":"10.3390\/pr9040702"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Ullah, Z., Ullah, I., Zaman, G., and Sun, T.C. (2022). A numerical approach to interpret melting and activation energy phenomenon on the magnetized transient flow of Prandtl\u2013Eyring fluid with the application of Cattaneo\u2013Christov theory. Waves Random Complex Media, 1\u201321.","DOI":"10.1080\/17455030.2022.2032472"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"101519","DOI":"10.1016\/j.asej.2021.06.005","article-title":"On the role of bioconvection and activation energy for time dependent nanofluid slip transpiration due to extenDing domain in the presence of electric and magnetic fields","volume":"13","author":"Habib","year":"2022","journal-title":"Ain Shams Eng. J."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"105761","DOI":"10.1016\/j.icheatmasstransfer.2021.105761","article-title":"Double diffusive convection and cross diffusion effects on Casson fluid over a Lorentz force driven Riga plate in a porous medium with heat sink: An analytical approach","volume":"131","author":"Asogwa","year":"2022","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1016\/j.csite.2018.06.006","article-title":"Thermal aspects of Carreau fluid around a wedge","volume":"12","author":"Ali","year":"2018","journal-title":"Case Stud. Therm. Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"109538","DOI":"10.1016\/j.oceaneng.2021.109538","article-title":"Study on the wedge penetrating fluid interfaces characterized by different density-ratios: Numerical investigations with a multi-phase SPH model","volume":"237","author":"Lyu","year":"2021","journal-title":"Ocean Eng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"5473","DOI":"10.1016\/j.aej.2021.03.042","article-title":"MHD thermal boundary layer flow of a Casson fluid over a penetrable stretching wedge in the existence of nonlinear radiation and convective boundary condition","volume":"60","author":"Hussain","year":"2021","journal-title":"Alex. Eng. J."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"e202000349","DOI":"10.1002\/zamm.202000349","article-title":"Magnetized bioconvection flow of Sutterby fluid characterized by the suspension of nanoparticles across a wedge with activation energy","volume":"101","author":"Waqas","year":"2021","journal-title":"ZAMM J. Appl. Math. Mech."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/BF01251888","article-title":"Uniform suction\/blowing effect on forced convection about a wedge: Uniform heat flux","volume":"128","author":"Yih","year":"1998","journal-title":"Acta Mech."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.ijthermalsci.2010.10.008","article-title":"Falkner\u2013Skan problem for a static or moving wedge in nanofluids","volume":"50","author":"Yacob","year":"2011","journal-title":"Int. J. Therm. Sci."},{"key":"ref_39","unstructured":"White, F.M. (1991). Viscous Fluid Flow, McGraw-Hill. [2nd ed.]."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"809","DOI":"10.2298\/TSCI160115169A","article-title":"Impact of heat transfer analysis on Carreau fluid flow past a static\/moving wedge","volume":"22","author":"Ali","year":"2018","journal-title":"Therm. Sci."},{"key":"ref_41","first-page":"1","article-title":"Entropy Analysis of TiO2-Cu\/EG Casson Hybrid Nanofluid via Cattaneo-Christov Heat Flux Model","volume":"8","author":"Jamshed","year":"2018","journal-title":"Appl. Nanosci."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"10696","DOI":"10.1002\/er.6554","article-title":"Computational single phase comparative study of Williamson nanofluid in parabolic trough solar collector via Keller box method","volume":"45","author":"Jamshed","year":"2021","journal-title":"Int. J. Energy Res."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"065202","DOI":"10.1088\/1402-4896\/abecc0","article-title":"Single phase-based study of Ag-Cu\/EO Williamson hybrid nanofluid flow over a stretching surface with shape factor","volume":"96","author":"Jamshed","year":"2021","journal-title":"Phys. Scr."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1016\/j.jmrt.2021.06.031","article-title":"Thermal expansion optimization in solar aircraft using tangent hyperbolic hybrid nanofluid: A solar thermal application","volume":"14","author":"Jamshed","year":"2021","journal-title":"J. Mater. Res. Technol."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"102190","DOI":"10.1016\/j.csite.2022.102171","article-title":"Irregular heat source impact on Carreau nanofluid flowing via exponential expanDing cylinder: A thermal case study","volume":"36","author":"Akram","year":"2022","journal-title":"Case Stud. Therm. Eng."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Shahzad, F., Jamshed, W., Ahmad, A., Safdar, R., Alam, M.M., and Ullah, I. (2022). Efficiency evaluation of solar water-pump using nanofluids in parabolic trough solar collector: 2nd order convergent approach. Waves Random Complex Media, 1\u201337.","DOI":"10.1080\/17455030.2022.2083265"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"102233","DOI":"10.1016\/j.csite.2022.102233","article-title":"Numerical analysis of heat and mass transfer in micropolar nanofluids flow through lid driven cavity: Finite volume approach","volume":"37","author":"Batool","year":"2022","journal-title":"Case Stud. Therm. Eng."},{"key":"ref_48","first-page":"1236","article-title":"Sensitivity analysis for Walters-B nanoliquid flow over a radiative Riga surface by RSM","volume":"29","author":"Shafiq","year":"2022","journal-title":"Sci. Iran."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Rasool, G., Saeed, A.M., Lare, A.I., Abderrahmane, A., Guedri, K., Vaidya, H., and Marzouki, R. (2022). Darcy-Forchheimer flow of water conveying multi-walled carbon nanoparticles through a vertical cleveland Z-staggered cavity subject to entropy generation. Micromachines, 13.","DOI":"10.3390\/mi13050744"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Rasool, G., Shafiq, A., Hussain, S., Zaydan, M., Wakif, A., Chamkha, A.J., and Bhutta, M.S. (2022). Significance of Rosseland\u2019s radiative process on reactive Maxwell nanofluid flows over an isothermally heated stretching sheet in the presence of Darcy\u2013Forchheimer and Lorentz forces: Towards a new perspective on Buongiorno\u2019s model. Micromachines, 13.","DOI":"10.3390\/mi13030368"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/9\/1850\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:23:55Z","timestamp":1760142235000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/9\/1850"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,5]]},"references-count":50,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["sym14091850"],"URL":"https:\/\/doi.org\/10.3390\/sym14091850","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,5]]}}}