{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T15:41:50Z","timestamp":1768405310781,"version":"3.49.0"},"reference-count":36,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,13]],"date-time":"2022-10-13T00:00:00Z","timestamp":1665619200000},"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>In (Al2O3-Cu\/H2O) hybridized nanofluid (HYNF) is an unsteady electro-hydrodynamic stagnation point flow. A stretchable (shrinkable) surface that was convectively heated was studied in the past. In addition to the traditional nonslip surface, the heat generating (absorbing) and the velocity slippage constraints are deliberated in this research. An obtained nonlinear scheme is resolved by the homotopy analysis method. Governing parameters are the electric field parameters, that is, the dimensionless parameters including the magnetic parameter, Prandtl quantity, heat generating factor, Eckert quantity, and unsteady factor. We discuss in detail the effects of these variables on the movement of problems and thermal transmission characteristics. Increasing the values of the magneto and electric force parameters increased the temperature. Increasing the Prandtl number lowered the temperature. For the Eckert parameter, an increase in temperature was recognized. The symmetric form of the geometry model displayed improved the fluid flow by the same amount both above and below the stagnation streamline, while it decreased the flow pressure by the same level. The more heat source uses to increase the temperature of the HYNF over the entire area, the more heat is supplied to the plate, but with a heat sink, the opposite effect is observed.<\/jats:p>","DOI":"10.3390\/sym14102136","type":"journal-article","created":{"date-parts":[[2022,10,14]],"date-time":"2022-10-14T01:44:13Z","timestamp":1665711853000},"page":"2136","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Unsteady Electro-Hydrodynamic Stagnating Point Flow of Hybridized Nanofluid via a Convectively Heated Enlarging (Dwindling) Surface with Velocity Slippage and Heat Generation"],"prefix":"10.3390","volume":"14","author":[{"given":"Abbas","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Haripur, Haripur 22620, Pakistan"}]},{"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 (CUST), Islamabad 44000, Pakistan"}]},{"given":"Mohamed R.","family":"Eid","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, New Valley University, Al-Kharga 72511, Egypt"},{"name":"Department of Mathematics, Faculty of Science, Northern Border University, Arar 1321, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1750-4574","authenticated-orcid":false,"given":"Amjad Ali","family":"Pasha","sequence":"additional","affiliation":[{"name":"Aerospace Engineering Department, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3151-9967","authenticated-orcid":false,"given":"El Sayed M.","family":"Tag El Din","sequence":"additional","affiliation":[{"name":"Electrical Engineering, Faculty of Engineering and Technology, Future University in Egypt, New Cairo 11835, Egypt"}]},{"given":"Hamiden Abd El-Wahed","family":"Khalifa","sequence":"additional","affiliation":[{"name":"Department of Operations Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 13613, Egypt"},{"name":"Department of Mathematics, College of Science and Arts, Qassim University, Al-Badaya 51951, Saudi Arabia"}]},{"given":"Samaher Khalaf","family":"Alharbi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Arts, Qassim University, Ar Rass 51921, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1515\/ijnsns-2016-0037","article-title":"Numerical investigation of hydromagnetic hybrid Cu\u2013Al2O3\/water nanofluid flow over a permeable stretching sheet with suction","volume":"17","author":"Devi","year":"2016","journal-title":"Int. J. Nonlinear Sci. Numer. Simul."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"490","DOI":"10.1139\/cjp-2015-0799","article-title":"Numerical investigation of three-dimensional hybrid Cu\u2013Al2O3\/water nanofluid flow over a stretching sheet with effecting Lorentz force subject to Newtonian heating","volume":"94","author":"Devi","year":"2016","journal-title":"Can. J. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2317","DOI":"10.1016\/j.rinp.2017.06.034","article-title":"Heat transfer enhancement with Ag\u2013CuO\/water hybrid nanofluid","volume":"7","author":"Hayat","year":"2017","journal-title":"Results Phys."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zainal, N.A., Nazar, R., Naganthran, K., and Pop, I. (2020). Unsteady stagnation point flow of hybrid nanofluid past a convectively heated stretching\/shrinking sheet with velocity slip. Mathematics, 8.","DOI":"10.3390\/math8101649"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"464","DOI":"10.1016\/j.jart.2017.05.007","article-title":"Double stratification effects on unsteady electrical MHD mixed convection flow of nanofluid with viscous dissipation and Joule heating","volume":"15","author":"Daniel","year":"2017","journal-title":"J. Appl. Res. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s11671-016-1546-y","article-title":"An investigation on the tribological performances of the SiO2\/MoS2 hybrid nanofluids for magnesium alloy-steel contacts","volume":"11","author":"Xie","year":"2016","journal-title":"Nanoscale Res. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.expthermflusci.2016.04.007","article-title":"Effects of temperature and nanoparticles concentration on rheological behavior of Fe3O4\u2013Ag\/EG hybrid nanofluid: An experimental study","volume":"77","author":"Afrand","year":"2016","journal-title":"Exp. Therm. Fluid Sci."},{"key":"ref_8","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_9","doi-asserted-by":"crossref","first-page":"1054","DOI":"10.1016\/j.ijheatmasstransfer.2017.06.135","article-title":"Entropy generation analysis in MHD mixed convection of hybrid nanofluid in an open cavity with a horizontal channel containing an adiabatic obstacle","volume":"114","author":"Hussain","year":"2017","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"766","DOI":"10.1016\/j.ijheatmasstransfer.2016.05.142","article-title":"Magnetohydrodynamic (MHD) mixed convection flow of micropolar liquid due to nonlinear stretched sheet with convective condition","volume":"102","author":"Waqas","year":"2016","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.jmmm.2016.01.025","article-title":"Streaming potential and heat transfer of nanofluids in microchannels in the presence of magnetic field","volume":"407","author":"Zhao","year":"2016","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1441","DOI":"10.1016\/j.applthermaleng.2016.05.039","article-title":"Numerical investigation of the effect of magnetic field on the onset of nanofluid convection","volume":"103","author":"Yadav","year":"2016","journal-title":"Appl. Therm. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Chamkha, A., Rashad, E., El-Zahar, H.A., and EL-Mky, H.A. (2019). Analytical and numerical investigation of Fe3O4\u2013water nanofluid flow over a moveable plane in a parallel stream with high suction. Energies, 12.","DOI":"10.3390\/en12010198"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"045112","DOI":"10.1063\/1.5088610","article-title":"Unsteady MHD slip flow of a ferrofluid over an impulsively stretched vertical surface","volume":"9","author":"Modather","year":"2019","journal-title":"AIP Adv."},{"key":"ref_15","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. Angew. Math. Phys."},{"key":"ref_16","first-page":"227","article-title":"Unsteady MHD radiative flow and heat transfer of a dusty nanofluid over an exponentially stretching surface","volume":"19","author":"Sandeep","year":"2016","journal-title":"Eng. Sci. Technol. Int. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2159","DOI":"10.1016\/j.apt.2017.05.022","article-title":"MHD 3D free convective flow of nanofluid over an exponentially stretching sheet with chemical reaction","volume":"28","author":"Nayak","year":"2017","journal-title":"Adv. Powder Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1016\/j.rinp.2017.12.038","article-title":"Flow of 3D Eyring-Powell fluid by utilizing Cattaneo-Christov heat flux model and chemical processes over an exponentially stretching surface","volume":"8","author":"Hayat","year":"2018","journal-title":"Results Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1552","DOI":"10.1016\/j.cjph.2017.05.006","article-title":"Heat transfer analysis for three-dimensional stagnation-point flow over an exponentially stretching surface","volume":"55","author":"Rehman","year":"2017","journal-title":"Chin. J. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1088\/0022-3727\/32\/5\/012","article-title":"Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface","volume":"32","author":"Magyari","year":"1999","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"095005","DOI":"10.1088\/2399-6528\/ab31e2","article-title":"The impact of variable fluid properties on hydromagnetic boundary layer and heat transfer flows over an exponentially stretching sheet","volume":"3","author":"Mushtaq","year":"2019","journal-title":"J. Phys. Commun."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"408528","DOI":"10.1155\/2012\/408528","article-title":"MHD mixed convective boundary layer flow of a nanofluid through a porous medium due to an exponentially stretching sheet","volume":"2012","author":"Ferdows","year":"2012","journal-title":"Math. Probl. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Rahman, A.N.H., Bachok, N., and Rosali, H. (2019). Numerical Solutions of Mhd Stagnation-Point Flow over an Exponentially Stretching\/Shrinking Sheet in a Nanofluid, IOP Publishing.","DOI":"10.1088\/1742-6596\/1366\/1\/012012"},{"key":"ref_24","first-page":"407","article-title":"Die Grenzschicht an einem in den gleichformigen Flussigkeitsstrom eingetauchten geraden Kreiszylinder","volume":"326","author":"Hiemenz","year":"1911","journal-title":"Dinglers Polytech. J."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1002\/zamm.19360160304","article-title":"Der Einflu\u03b2 gro\u03b2er Z\u00e4higkeit bei der Str\u00f6mung um den Zylinder und um die Kugel","volume":"16","author":"Homann","year":"1936","journal-title":"Z. Angew. Math. Mech."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1016\/j.ijnonlinmec.2007.12.021","article-title":"Stagnation flow towards a shrinking sheet","volume":"43","author":"Wang","year":"2008","journal-title":"Int. J. Non-Linear Mech."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.compfluid.2011.01.040","article-title":"Melting heat transfer in boundary layer stagnation-point flow towards a stretching\/shrinking sheet in a micropolar fluid","volume":"47","author":"Yacob","year":"2011","journal-title":"Comput. Fluids"},{"key":"ref_28","first-page":"499","article-title":"On the homotopy analysis method for nonlinear problems","volume":"147","author":"Liao","year":"2004","journal-title":"Appl. Math. Comput."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"015223","DOI":"10.1063\/1.5083972","article-title":"Darcy Forchheimer nanofluid thin film flow of SWCNTs and heat transfer analysis over an unsteady stretching sheet","volume":"9","author":"Nasir","year":"2019","journal-title":"AIP Adv."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.rinp.2017.12.013","article-title":"Multiple slips effects on MHD SA-Al2O3 and SA-Cu non-Newtonian nanofluids flow over a stretching cylinder in porous medium with radiation and chemical reaction","volume":"8","author":"Tlili","year":"2018","journal-title":"Results Phys."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Khan, N.S., Shah, Z., Islam, S., Khan, I., Alkanhal, T.A., and Tlili, I. (2019). Entropy generation in MHD mixed convection non-Newtonian second-grade nanoliquid thin film flow through a porous medium with chemical reaction and stratification. Entropy, 21.","DOI":"10.3390\/e21020139"},{"key":"ref_32","first-page":"139","article-title":"An asymptotic method with applications to nonlinear coupled partial differential equations","volume":"50","author":"Fiza","year":"2018","journal-title":"Punjab Univ. J. Math."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1166\/jctn.2014.3402","article-title":"On the numerical solution of thermal shock problem for generalized magneto-thermoelasticity for an infinitely long annular cylinder with variable thermal conductivity","volume":"11","author":"Abbas","year":"2014","journal-title":"J. Comput. Theor. Nanosci."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Li, C., Guo, H., He, T., and Tian, X. (2022). Thermally nonlinear non-Fourier piezoelectric thermoelasticity problems with temperature-dependent elastic constants and thermal conductivity and nonlinear finite element analysis. Waves Random Complex Media, 1\u201338.","DOI":"10.1080\/17455030.2022.2075953"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1385","DOI":"10.1016\/j.cnsns.2008.04.006","article-title":"Finite element analysis of hydromagnetic flow and heat transfer of a heat generation fluid over a surface embedded in a non-Darcian porous medium in the presence of chemical reaction","volume":"14","author":"Mohamed","year":"2009","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2531","DOI":"10.1080\/15376494.2020.1870780","article-title":"Finite element analysis of coupled phase-field and thermoelasticity equations at large strains for martensitic phase transformations based on implicit and explicit time discretization schemes","volume":"29","author":"Rahbar","year":"2022","journal-title":"Mech. Adv. Mater. Struct."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/10\/2136\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:53:30Z","timestamp":1760144010000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/10\/2136"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,13]]},"references-count":36,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["sym14102136"],"URL":"https:\/\/doi.org\/10.3390\/sym14102136","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,13]]}}}