This study analyzes entropy generation in a ternary hybrid nanofluid flow over an exponentially stretching sheet, incorporating quadratic thermal radiation, Cattaneo-Christov heat flux, and chemical reaction parameters. After converting the governing equations to a collection of ordinary differential equations, the bvp4c solver was used to find solutions. For three different shape factors—platelet, cylinder, and brick—the outcomes are displayed. The friction factor is found to be positively correlated with the volume percentage of titanium dioxide and negatively correlated with the magnetic field parameter (Mn). The friction factor decreases at a rate of 0.18023 for the platelet shape, 0.1802 for the cylindrical shape, and 0.18016 for the brick shape at 0.5≤Mn≤4. It is noted that the rise in heat transmission rate is accompanied by the rise in radiation parameter (Rd). It has been found that when 0.1≤Rd≤2.5, the Nusselt number increases by 0.246750723, 0.248424079, and 0.251223958 for platelet, cylinder, and brick shapes respectively. An escalation in the Sherwood number is noticed with an increase in the chemical reaction parameter (Cn). There is a noticeable increase of 0.167544801, 0.16785809, and 0.168374083 in the Sherwood number for platelet, cylinder, and brick shapes, respectively at 0.1≤Cn≤0.7.
StraughanB.Thermal convection with the Cattaneo–Christov model. Int J Heat Mass Transf2010; 53(1–3): 95–98.
2.
MustafaM.Cattaneo-Christov heat flux model for rotating flow and heat transfer of upper-convected Maxwell fluid. Aip Adv2015; 5(4): 47109.
3.
WaqasMHayatTFarooqM, et al. Cattaneo-Christov heat flux model for flow of variable thermal conductivity generalized Burgers fluid. J Mole Liq2016; 220: 642–648.
4.
AbbasiFMShehzadSA.Heat transfer analysis for three-dimensional flow of Maxwell fluid with temperature dependent thermal conductivity: application of Cattaneo-Christov heat flux model. J Mole Liq2016; 220: 848–854.
5.
DogonchiASGanjiDD.Effect of Cattaneo–Christov heat flux on buoyancy MHD nanofluid flow and heat transfer over a stretching sheet in the presence of Joule heating and thermal radiation impacts. Ind J Phys2018; 92(6): 757–766.
6.
IbrahimWHindebuB.Magnetohydrodynamic (MHD) boundary layer flow of Eyring-Powell nanofluid past stretching cylinder with Cattaneo-Christov heat flux model. Nonlinear Eng2019; 8(1): 303–317.
7.
UllahKSAliNHayatT, et al. Heat transfer analysis based on Cattaneo-Christov heat flux model and convective boundary conditions for flow over an oscillatory stretching surface. Therm Sci2019; 23(2 Part A): 443–455.
8.
KhanUAhmadSHayyatA, et al. On the Cattaneo–Christov heat flux model and OHAM analysis for three different types of nanofluids. Appl Sci2020; 10(3): 886.
9.
RawatSKKumarM.Cattaneo–Christov heat flux model in flow of copper water nanofluid through a stretching/shrinking sheet on stagnation point in presence of heat generation/absorption and activation energy. Int J Appl Comput Math2020; 6: 112.
10.
TassaddiqA.Impact of Cattaneo-Christov heat flux model on MHD hybrid nano-micropolar fluid flow and heat transfer with viscous and joule dissipation effects. Sci Rep2021; 11(1): 67.
11.
AliLLiuXAliB, et al. Finite element analysis of unsteady MHD Blasius and Sakiadis flow with radiation and thermal convection using Cattaneo-Christov heat flux model. Phys Scripta2021; 96(12): 125219.
12.
Naveen KumarRSuresh GoudJSrilathaP, et al. Cattaneo–Christov heat flux model for nanofluid flow over a curved stretching sheet: an application of Stefan blowing. Heat Transf2022; 51(6): 4977–4991.
13.
YaseenMRawatSKKumarM.Cattaneo–Christov heat flux model in Darcy–Forchheimer radiative flow of MoS2–SiO2/kerosene oil between two parallel rotating disks. J Therm Anal Calorimet2022; 147(19): 10865–10887.
14.
KhattakSAhmedMAbrarMN, et al. Numerical simulation of Cattaneo–Christov heat flux model in a porous media past a stretching sheet. Waves Random Complex Media2022; 35(1): 1230–1249.
15.
YusufTAAshrafMBMaboodF.Cattaneo–Christov heat flux model for three-dimensional magnetohydrodynamic flow of an Eyring Powell fluid over an exponentially stretching surface with convective boundary condition. Num Methods Partial Diff Eq2023; 39(1): 242–253.
16.
JakeerSBala Anki ReddyP, et al. Entropy generation and Melting heat transfer on the Ferrohydrodynamic flow of Fe3O4-Ag/blood hybrid nanofluid with Cattaneo-Christov heat flux model. Waves Random Complex Media. Epub ahead of print 9January2023. DOI: 10.1080/17455030.2022.2164808
17.
GowdaRPKumarRNKumarR, et al. Three-dimensional coupled flow and heat transfer in non-Newtonian magnetic nanofluid: an application of Cattaneo-Christov heat flux model. J Magnetism Magnet Mater2023; 567: 170329.
18.
LathaKBReddyMGTripathiD, et al. Computation of stagnation coating flow of electro-conductive ternary Williamson hybrid GO-AU-Co3O4/EO nanofluid with a Cattaneo–Christov heat flux model and magnetic induction. Sci Rep2023; 13(1): 10972.
19.
ShahFZhangDLinlinG.Non-similar analysis of two-phase hybrid nano-fluid flow with Cattaneo-Christov heat flux model: a computational study. Eng Appl Comput Fluid Mech2024; 18(1): 2380800.
20.
KumarPVidhyaKGAlmeidaF, et al. Optimization using response surface methodology for Eyring-Powell fluid flow with Cattaneo-Christov heat flux and cross diffusion effects. Int J Thermofl2025; 25: 100981.
21.
SarkarSGangulySDalalA.Analysis of entropy generation during mixed convective heat transfer of nanofluids past a square cylinder in vertically upward flow. J Heat Transf2012; 134(12): 122501.
22.
OztopHFAl-SalemK.A review on entropy generation in natural and mixed convection heat transfer for energy systems. Renew Sustain Energy Rev2012; 16(1): 911–920.
23.
ChinyokaTMakindeOD.Analysis of entropy generation rate in an unsteady porous channel flow with Navier slip and convective cooling. Entropy2013; 15(6): 2081–2099.
24.
SaqibMAliFKhanI, et al. Entropy generation in different types of fractionalized nanofluids. Arab J Sci Eng2019; 44(1): 531–540.
25.
SiavashiMYousofvandRRezanejadS.Nanofluid and porous fins effect on natural convection and entropy generation of flow inside a cavity. Adv Powder Technol2018; 29(1): 142–156.
26.
PordanjaniAHVahediSMAghakhaniS, et al. Effect of magnetic field on mixed convection and entropy generation of hybrid nanofluid in an inclined enclosure: sensitivity analysis and optimization. Europ Phys J Plus2019; 134: 412.
27.
KhanNSShahQBhaumikA, et al. Entropy generation in bioconvection nanofluid flow between two stretchable rotating disks. Sci Rep2020; 10(1): 4448.
28.
MuhammadRKhanMIJameelM, et al. Fully developed Darcy-Forchheimer mixed convective flow over a curved surface with activation energy and entropy generation. Comput Methods Prog Biomed2020; 188: 105298.
29.
HouEHussainARehmanA, et al. Entropy generation and induced magnetic field in pseudoplastic nanofluid flow near a stagnant point. Sci Rep2021; 11(1): 23736.
30.
ShoaibMKausarMNisarKS, et al. The design of intelligent networks for entropy generation in Ree-Eyring dissipative fluid flow system along quartic autocatalysis chemical reactions. Int Commun Heat Mass Transf2022; 133: 105971.
31.
MarzouguiSMebarek-OudinaFMagherbiM, et al. Entropy generation and heat transport of Cu–water nanoliquid in porous lid-driven cavity through magnetic field. Int J Num Methods Heat Fluid Flow2022; 32(6): 2047–2069.
32.
AcharyaNMaitySKunduPK.Entropy generation optimization of unsteady radiative hybrid nanofluid flow over a slippery spinning disk. Proc IMechE, Part C: J Mechanical Engineering Science2022; 236(11): 6007–6024.
33.
MountrichasPZhaoWRandevaMS, et al. Entropy generation of CuO-water nanofluid in a cavity with an intruded rectangular fin. Energies2023; 16(2): 912.
34.
KhanMIQayyumSChuYM, et al. Numerical simulation and modeling of entropy generation in Marangoni convective flow of nanofluid with activation energy. Num Methods Partial Diff Eq2023; 39(6): 4421–4431.
35.
MannaNKBiswasNMandalDK, et al. Impacts of heater-cooler position and Lorentz force on heat transfer and entropy generation of hybrid nanofluid convection in quarter-circular cavity. Int J Num Methods Heat Fluid Flow2023; 33(3): 1249–1286.
36.
Abdel-wahedMSAhmedSIMekheimerKS, et al. Entropy generation analysis of a micropolar fluid in a corrugated channel with convective and slip conditions. Case Stud Therm Eng2024; 57: 104283.
37.
MajeedAHMahmoodRLiuD, et al. Numerical simulations of entropy generation and thermal fluid flow in a wavy enclosure: a Newton-Pardiso solver-based study. Int Commun Heat Mass Transf2025; 162: 108569.
38.
ChamkhaAJPopI.Effect of thermophoresis particle deposition in free convection boundary layer from a vertical flat plate embedded in a porous medium. Int Commun Heat Mass Transf2004; 31(3): 421–430.
39.
GorlaRSChamkhaARashadAM.Mixed convective boundary layer flow over a vertical wedge embedded in a porous medium saturated with a nanofluid. In: 2010 3rd international conference on thermal issues in emerging technologies theory and applications (TKETA 2010), Cairo, Egypt. 19–22 December 2010, pp.445–451. New York, NY: IEEE.
40.
GangadharKKumariMAChamkhaAJ.EMHD flow of radiative second-grade nanofluid over a Riga Plate due to convective heating: revised Buongiorno’s nanofluid model. Arab J Sci Eng2022; 47(7): 8093–8103.
41.
KrishnaMVAnandPVChamkhaAJ.Heat and mass transfer on free convective flow of amicropolar fluid through a porous surface with inclined magnetic field and Hall effects. Special Top Rev Porous Med Int J2019; 10(3): 1–21.
42.
KrishnaMVAhamadNAChamkhaAJ.Hall and ion slip impacts on unsteady MHD convective rotating flow of heat generating/absorbing second grade fluid. Alexandr Eng J2021; 60(1): 845–858.
43.
NadeemSAhmedZSaleemS.Carbon nanotubes effects in magneto nanofluid flow over a curved stretching surface with variable viscosity. Microsys Technol2019; 25: 2881–2888.
44.
Purna Chandar RaoDThiagarajanSSrinivasa KumarV. Significance of quadratic thermal radiation on the bioconvective flow of Ree-Eyring fluid through an inclined plate with viscous dissipation and chemical reaction: non-Fourier heat flux model. Int J Ambient Energy2022; 43(1): 6436–6448.
45.
ManjunathaSPuneethVGireeshaBJ, et al. Theoretical study of convective heat transfer in ternary nanofluid flowing past a stretching sheet. J Appl Comput Mech2022; 8(4): 1279–1286.
46.
SheikholeslamiMRokniHB.Magnetic nanofluid natural convection in the presence of thermal radiation considering variable viscosity. Europ Phys J Plus2017; 132: 1–2.
47.
AlharbiKAAhmedAEOuld SidiM, et al. Computational valuation of Darcy ternary-hybrid nanofluid flow across an extending cylinder with induction effects. Micromachines2022; 13(4): 588.
48.
JamaludinANazarRNaganthranK, et al. Mixed convection hybrid nanofluid flow over an exponentially accelerating surface in a porous media. Neur Comput Appl2021; 33(22): 15719–15729.
49.
BidinBNazarR.Numerical solution of the boundary layer flow over an exponentially stretching sheet with thermal radiation. Europ J Sci Res2009; 33(4): 710–717.
50.
MukhopadhyayS.Slip effects on MHD boundary layer flow over an exponentially stretching sheet with suction/blowing and thermal radiation. Ain Shams Eng J2013; 4(3): 485–491.
