Comprehending the behaviour of ternary hybrid nanofluids with the influence of couple stress effects on a flat plate will provide vital insights for the development of more effective heat exchangers and cooling systems. In this investigation, we analyzed the impact of various factors, including couple stress and cross-diffusion parameters (Dufour and Soret), on a ternary hybrid nanofluid flow across a convectively heated flat plate. The analysis takes into account non-Fourier heat flux and irreversibility. The governing equations are converted into a set of ordinary differential equations using appropriate similarity transformations, and then the bvp4c solver is used to find solutions. Outcomes are provided for two instances, that is, nanofluid () and ternary hybrid nanofluid The fluid velocity is found to be negatively correlated with the couple stress parameter rises () which is one of the major findings in this study. Within the range of it is seen that the friction factor exhibits a gradual increase with a rate of 0.02878 (in the case of nanofluid flow) and 0.038083 (in the case of ternary hybrid nanofluid flow). Additionally, when the Dufour number is between 0 and 0.6, the Nusselt number exhibits a discernible decrease of 0.27678 (in the case of nanofluid flow) and 0.26428 (in the case of ternary hybrid nanofluid flow). Furthermore, at (the Sherwood number), the Sherwood number drops at a rate of 0.0786 (in the case of nanofluid flow) and 0.05592 (in the case of ternary hybrid nanofluid flow). It has been observed that an increase in the chemical reaction parameter lowers the fluid concentration. It is observed that the Sherwood number increases at a rate of 0.037654 (in the case of nanofluid flow) and 0.037661 (in the case of ternary hybrid nanofluid flow) when .
AdesanyaSOMakindeOD. Effects of couple stresses on entropy generation rate in a porous channel with convective heating. Comput Appl Math2015; 34: 293–307.
2.
RatchagarNPBalakrishnanVVasanthakumariR. Effect of Hall current in oscillatory flow of a couple stress fluid in an inclined channel. Ann Pure Appl Math2018; 16: 151–169.
3.
ReddyGJKumarMKethireddyB, et al.Colloidal study of unsteady magnetohydrodynamic couple stress fluid flow over an isothermal vertical flat plate with entropy heat generation. J Mol Liq2018; 252: 169–179.
4.
ShaZDawarAAlzahraniEO, et al.Hall effect on couple stress 3D nanofluid flow over an exponentially stretched surface with Cattaneo Christov heat flux model. IEEE Access2019; 7: 64844–64855.
5.
ZeeshanAEllahiRMaboodF, et al.Numerical study on bi-phase coupled stress fluid in the presence of Hafnium and metallic nanoparticles over an inclined plane. Int J Numer Method H2019; 29: 2854–2869.
6.
MaboodFYusufTABognárG. Features of entropy optimization on MHD couple stress nanofluid slip flow with melting heat transfer and nonlinear thermal radiation. Sci Rep2020; 10: 19163.
7.
SohailMAliUAl-MdallalQ, et al.Theoretical and numerical investigation of entropy for the variable thermophysical characteristics of couple stress material: applications to optimization. Alex Eng J2020; 59: 4365–4375.
8.
SivaTKumbhakarBJangiliS, et al.Unsteady electro-osmotic flow of couple stress fluid in a rotating microchannel: an analytical solution. Phys Fluids2020; 32: 102013.
9.
TarakaramuNSatya NarayanaPVHarish BabuD, et al.Joule heating and dissipation effects on magnetohydrodynamic couple stress nanofluid flow over a bidirectional stretching surface. Int J Heat Technol2021; 39: 205–212.
10.
Satya NarayanaPVTarakaramuNSarojammaG, et al.Numerical simulation of nonlinear thermal radiation on the 3D flow of a couple stress Casson nanofluid due to a stretching sheet. J Therm Sci Eng Appl2021; 13: 021028.
11.
SnehaKNVanithaGPMahabaleshwarUS, et al.Effect of couple stress and mass transpiration on ternary hybrid nanoliquid over a stretching/shrinking sheet with heat transfer. Micromachines2022; 13: 1694.
12.
AhmadSHaqSUAliF, et al.Time fractional analysis of channel flow of couple stress Casson fluid using Fick’s and Fourier’s laws. Sci Rep2022; 12: 2956.
13.
MahmudKRanaSAl-ZubaidiA, et al.Interaction of Lorentz force with cross swimming microbes in couple stress nano fluid past a porous Riga plate. Int J Heat Mass Transf2022; 138: 106347.
14.
MaheshRMahabaleshwarUSVinay KumarPN, et al.Impact of radiation on the MHD couple stress hybrid nanofluid flow over a porous sheet with viscous dissipation. Results Eng2023; 17: 100905.
15.
ArifMKumamPSeangwattanaT, et al.A fractional model of magnetohydrodynamics Oldroyd-B fluid with couple stresses, heat and mass transfer: a comparison among non-Newtonian fluid models. Heliyon2023; 9: e17642.
16.
PostelnicuA. Influence of a magnetic field on heat and mass transfer by natural convection from vertical surfaces in porous media considering Soret and Dufour effects. Int J Heat Mass Transf2004; 47: 1467–1472.
17.
HayatTShehzadSAAlsaediA. Soret and Dufour effects on magnetohydrodynamic (MHD) flow of Casson fluid. Appl Math Mech2012; 33: 1301–1312.
18.
MahdyA. Heat transfer and flow of a Casson fluid due to a stretching cylinder with the Soret and Dufour effects. J Eng Phys Thermophys2015; 88: 928–936.
19.
ZhaoJZhengLZhangX, et al.Convection heat and mass transfer of fractional MHD Maxwell fluid in a porous medium with Soret and Dufour effects. Int J Heat Mass Transf2016; 103: 203–210.
20.
KasmaniMRSivasankaranSBhuvaneswariM, et al.Analytical and numerical study on convection of nanofluid past a moving wedge with Soret and Dufour effects. Int J Numer Method H2017; 27: 2333–2354.
21.
QayyumSHayatTKhanMI, et al.Optimization of entropy generation and dissipative nonlinear radiative Von Karman's swirling flow with Soret and Dufour effects. J Mol Liq2018; 262: 261–274.
22.
PatilPMKumbarwadiN. Effects of MHD mixed convection with non-uniform heat source/sink and cross-diffusion over exponentially stretching sheet. Int J Numer Method H. 2018; 28: 1238–1255.
23.
RajuCSKNeerajaGDineshPA, et al.MHD Casson fluid in a suspension of convective conditions and cross diffusion across a surface of paraboloid of revolution. Alex Eng J2018; 57: 3615–3622.
24.
Bilal AshrafMHayatTShehzadSA, et al.Thermophoresis and MHD mixed convection three-dimensional flow of viscoelastic fluid with Soret and Dufour effects. Neural Comput Appl2019; 31: 249–261.
25.
AliAIqbalFKhan MarwatDN, et al.Soret and Dufour effects between two rectangular plane walls with heat source/sink. Heat Transf Res2020; 49: 614–625.
26.
GautamAKVermaAKBhattacharyyaK, et al.Soret and Dufour effects on MHD boundary layer flow of non-Newtonian Carreau fluid with mixed convective heat and mass transfer over a moving vertical plate. Pramana2020; 94: 1–10.
27.
RasoolGShafiqABaleanuD. Consequences of Soret–Dufour effects, thermal radiation, and binary chemical reaction on Darcy Forchheimer flow of nanofluids. Symmetry2020; 12: 1421.
28.
ShaheenNAlshehriMHMRamzanM, et al.Soret and Dufour effects on a Casson nanofluid flow past a deformable cylinder with variable characteristics and Arrhenius activation energy. Sci Rep2021; 11: 19282.
29.
JawadMSaeedAKhanA, et al.Analytical study of MHD mixed convection flow for Maxwell nanofluid with variable thermal conductivity and Soret and Dufour effects. AIP Adv2021; 11: 035215.
30.
KathyayaniG. MHD Mixed convection jeffrey fluid near a stagnation-point flow of induced magnetic field and linear/non-linear vertical stretching sheet with chemical reaction in the presence of thermal radiation and suction or injection. Turk J Comp Math E2021; 12: 2453–2464.
31.
KuneRNaikHSReddyBS, et al.Role of nanoparticles and heat source/sink on MHD flow of Cu-H2O nanofluid flow past a vertical plate with Soret and Dufour effects. Math Comput Appl2022; 27: 102.
32.
ArifUNawazMSalmiA. Numerical study of simultaneous transport of heat and mass transfer in Maxwell hybrid nanofluid in the presence of Soret and Dufour effects. Phys Scr2022; 97: 025207.
33.
BiswalMMSwainKDashGC, et al.Study of radiative magneto-non-Newtonian fluid flow over a nonlinearly elongating sheet with Soret and Dufour effects. Numer Heat Transf; A: Appl2023; 83: 331–342.
34.
VijayNSharmaK. Magnetohydrodynamic hybrid nanofluid flow over a decelerating rotating disk with Soret and Dufour effects. Multidiscip Model Mater Struct2023; 19: 253–276.
35.
Ul-HaqSAshrafMB. Entropy analysis in MHD convective flow of Carreau fluid over a curved stretching surface with soret and dufour effects. Numer Heat Transf; A: Appl2024: 85 : 1780–1799.
36.
RajuSSRRenuka DeviRLVAsogwaKK, et al.Falkner–Skan slip flow of non-Newtonian fluid over a moving and nonlinearly radiated wedge with variable heat source/sink and viscous dissipation. Int J Mod Phys B2024: 382450004.
37.
PatilPMRoySPopI. Unsteady mixed convection flow over a vertical stretching sheet in a parallel free stream with variable wall temperature. Int J Heat Mass Transf2010; 53: 4741–4748.
38.
PatilPMChamkhaAJ. Heat and mass transfer from mixed convection flow of polar fluid along a plate in porous media with chemical reaction. Int J Numer Method H2013; 23: 899–926.
39.
PatilPMMomoniatERoyS. Influence of convective boundary condition on double diffusive mixed convection from a permeable vertical surface. Int J Heat Mass Transf2014; 70: 313–321.
40.
Rushi KumarBSravan KumarTKumarAG. Thermal diffusion and radiation effects on unsteady free convection flow in the presence of magnetic field fixed relative to the fluid or to the plate. Front Heat Mass Transf2015; 6: –9.
41.
PatilPMLathaDNRoyS, et al.Non-similar solutions of mixed convection flow from an exponentially stretching surface. Ain Shams Eng J2017; 8: 697–705.
42.
LathaRRushi KumarBMakindeOD. Effects of heat dissipation on the peristaltic flow of Jeffery and Newtonian fluid through an asymmetric channel with porous medium. Defect Diffus2018; 387: 218–243.
43.
PatilPMShashikantA. Unsteady mixed convection along a permeable exponentially stretching surface: influence of velocity slip and thermal jump. Int J Numer Method H2018; 28: 1994–2011.
44.
PatilPMShivanandappaHDHiremathPS, et al.Influence of applied magnetic field on mixed convective nanofluid flow past an exponentially stretching surface with roughness. J Braz Soc Mech Sci Eng2019; 41: 62.
45.
KumaranGSivarajRSubramanyam ReddyA, et al.Hydromagnetic forced convective flow of Carreau nanofluid over a wedge/plate/stagnation of the plate. Eur Phys J: Spec Top2019; 228: 2647–2659.
46.
PatilPMShashikantAHiremathPS. Effects of surface roughness on mixed convection nanoliquid flow over slender cylinder with liquid hydrogen diffusion. Int J Hydrogen Energy2019; 44: 11121–11133.
47.
PatilPMShashikantAMomoniatE. Analysis of sodium chloride and sucrose diffusions in mixed convective nanoliquid flow. Ain Shams Eng J2021; 12: 2117–2124.
48.
GomathyGRushi KumarB. Impacts of nanoparticle shapes on Ag-water nanofluid thin film flow through a porous medium with thermal radiation and ohmic heating. J Therm Anal Calorim2023: 1–19. DOI: 10.1007/s10973-023-12609-z.
49.
PatilPMGoudarBPatilM, et al.Bioconvective periodic MHD Eyring-Powell fluid flow around a rotating cone: influence of multiple diffusions and oxytactic microorganisms. Alex Eng J2023; 81: 636–655.
50.
MohanaCMRushi KumarB. Shape effects of Darcy–Forchheimer unsteady three-dimensional CdTe-C/H2O hybrid nanofluid flow over a stretching sheet with convective heat transfer. Phys Fluids2023; 35: 092002.
51.
PatilPMGoudarBMomoniatE. Magnetized bioconvective micropolar nanofluid flow over a wedge in the presence of oxytactic microorganisms. Case Stud Therm Eng2023; 49: 103284.
52.
PatilPMBenawadiSMomoniatE. Thermal analysis of bioconvective nanofluid flow over a sphere in presence of multiple diffusions and a periodic magnetic field. Case Stud Therm Eng2023; 51: 103569.
53.
PadmajaKRushi KumarB. Viscous dissipation and chemical reaction effects on MHD nanofluid flow over a vertical plate in a rotating system. ZAMM Z fur Angew Math Mech2023; 103: e202200471.
54.
PatilPMGoudarBSheremetMA. Tangent hyperbolic ternary hybrid nanofluid flow over a rough-yawed cylinder due to impulsive motion. J Taibah Univ SCI2023; 17: 2199664.
55.
PatilPMBenawadiSMuttannavarVT. Mixed bioconvective flow of Williamson nanofluid over a rough vertical cone. Arab J Sci Eng2023; 48: 2917–2928.
56.
RaoDPCThiagarajanSSrinivas KumarV. Significance of Dufour and Soret effects on the non-Darcy flow of cross fluid by a tilted plate with radiation and chemical reaction: a Cattaneo–Christov heat flux model. Heat Transf2022; 51: 1585–1600.
57.
ManjunathaSPuneethVGireeshaBJ, et al.Theoretical study of convective heat transfer in ternary nanofluid flowing past a stretching sheet. J Appl Comput Mech2022; 8: 1279–1286.
58.
MakindeOD. Effects of viscous dissipation and Newtonian heating on boundary-layer flow of nanofluids over a flat plate. Int J Numer Method H2013; 23: 1291–1303.
59.
KayaA. Effects of conjugate heat transfer on steady MHD mixed convective heat transfer flow over a thin vertical plate embedded in a porous medium with high porosity. Math Probl Eng2012; 2012: 1–19.
60.
KhademiRRazminiaAShiryaevVI. Conjugate-mixed convection of nanofluid flow over an inclined flat plate in porous media. Appl Math Comput2020; 366: 124761.
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