Fuzzy Set Theory (FST) offers a more practical framework for examining and simulating situations with ambiguous information because of the uncertainties present in real-life problems. The main goal of the present study is to create a model that uses triangular fuzzy numbers to analyze the impact of the fuzzy volume fraction of nanoparticles on the composite nanofluid flow. Fuzzy Set Theory is utilized to account for the ambiguity of the instances using a Williamson hybrid (Al2O3 and Cu/EO) nanofluid. The findings reveal that adding nanoparticles of copper (Cu), and alumina (Al2O3) significantly improves base fluid’s thermal conduction and stability. Employing the triangular fuzzy number (TFN), the percentage of nanomaterials affecting the thermophysical characteristics are considered as fuzzy parameters in order to compare the thermal profiles of composite nanofluids (Al2O3 + Cu/EO) and nanofluids (Cu/EO or Al2O3/EO). According to the fuzzy logic study, hybrid nanofluids are more effective at transferring heat than nanofluids. In order to overcome the drawbacks of basic neural networks, including sluggish convergence, underfitting, and overfitting, a hybrid strategy that combines the Levenberg–Marquardt (LM) algorithm and Bayesian Regularization (BR) is used to analyze preliminary data and obtain key physical characteristics. An outstanding overlap across projected and targeted values demonstrates how this novel strategy greatly enhances the model’s extrapolation, improves training, and produces strong and trustworthy predictions even with little data. Neural networks and the fuzzy method together offer a foundation for better decision-making when it comes to nanofluid concentration and optimization.
HayatTNadeemS.Heat transfer enhancement with Ag–CuO/water hybrid nanofluid. Results Phys2017; 7: 2317–2324.
2.
SharmaBKKumarAMishraNK, et al. Computational analysis of melting radiative heat transfer for solar Riga trough collectors of Jeffrey hybrid-nanofluid flow: a new stochastic approach. Case Stud Therm Eng2023; 52: 103658.
3.
ShahSZHAyubABhattiS, et al. Aspects of inclined magnetohydrodynamics and heat transfer in a non-Newtonian tri-hybrid bio-nanofluid flow past a wedge-shaped artery utilizing artificial neural network scheme. J Appl Math Mech2024; 104(12): e202400278.
4.
SureshSVenkitarajKSelvakumarP, et al. Effect of Al2O3–Cu/water hybrid nanofluid in heat transfer. Exp Therm Fluid Sci2012; 38: 54–60.
5.
KumarASharmaBKMuhammadT, et al. Optimization of thermal performance in hybrid nanofluids for parabolic trough solar collectors using Adams–Bashforth–Moulton method. Ain Shams Eng J2024; 15(12): 103106.
6.
GulTKhanABilalM, et al. Magnetic dipole impact on the hybrid nanofluid flow over an extending surface. Sci Rep2020; 10(1): 8474.
7.
AbbasNNadeemSSaleemA, et al. Models base study of inclined MHD of hybrid nanofluid flow over nonlinear stretching cylinder. Chin J Phys2021; 69: 109–117.
8.
WainiIIshakAGroşanT, et al. Mixed convection of a hybrid nanofluid flow along a vertical surface embedded in a porous medium. Int Commun Heat Mass Transf2020; 114: 104565.
9.
RamzanMBilalMChungJD.Radiative Williamson nanofluid flow over a convectively heated Riga plate with chemical reaction-a numerical approach. Chin J Phys2017; 55(4): 1663–1673.
10.
AyubAShahSZHSirisubtaweeS.Multifactorial analysis of ternary magnetized radiative nanofluid with waste discharge concentration and microorganism behavior: multi-hidden layer mechanism. Nano2025; 20: 2550003.
11.
ShahSAAAwanAU. Significance of magnetized Darcy-Forchheimer stratified rotating Williamson hybrid nanofluid flow: a case of 3D sheet. Int Commun Heat Mass Transf2022; 136: 106214.
12.
ShamshuddinMSalawuSShahzadF, et al. Thermal examination of chemical interaction and thermophoretic diffusion of Williamson fluid flow across Riga Plate surface with nonlinearity radiation flux. Numeri Heat Transf A Appl2024; 85(23): 4006–4020.
13.
SharmaPKSharmaBKSharmaM, et al. Influence of magnetohydrodynamics and chemical reactions on oscillatory free convective flow through a vertical channel in a rotating system with variable permeability. Mod Phys Lett B2025; 39(19): 2550050.
14.
AwaisMBilalSUr RehmanK, et al. Analysis on flow features of unsteady Williamson fluid inaugurated by melted wedge in the presence of heat generation–absorption: an extensive computational study. Can J Phys2019; 97(12): 1277–1287.
15.
KhanUZaibABakarSA, et al. Computational simulation of cross-flow of Williamson fluid over a porous shrinking/stretching surface comprising hybrid nanofluid and thermal radiation. AIMS Math2022; 7(4): 6489–6515.
16.
KulkarniMShankarH.Numerical investigation of mixed convective Williamson nanofluid flow over a stretching/shrinking wedge in the presence of chemical reaction parameter and liquid hydrogen diffusion. Numeri Heat Transf A Appl2025; 86(17): 5913–5926.
17.
MandalRKMaitiHNandySK.Bioconvective MHD flow of Williamson nanofluid past an expandable Riga wedge in the presence of activation energy, mass suction and velocity slip. Numeri Heat Transf A Appl2025; 86(2): 368–397.
18.
HamidA.Existence of dual solutions for wedge flow of magneto-Williamson nanofluid: a revised model. Alex Eng J2020; 59(3): 1525–1537.
19.
SharmaBKKumarAAlmohsenB, et al. Computational analysis of radiative heat transfer due to rotating tube in parabolic trough solar collectors with Darcy Forchheimer porous medium. Case Stud Therm Eng2023; 51: 103642.
20.
HussainMLubnaAAshrafM, et al. Ohmically dissipated MHD mixed convective flow of Williamson fluid over a penetrable stretching convective wedge with thermal radiations. Numeri Heat Transf B Fundamentals2024; 85(8): 1026–1040.
21.
HussainMAshrafMRanjhaQA, et al. Exploration of Newtonian heating, viscous dissipation effects on MHD mixed convection flow of Williamson fluid against radially stretched penetrable wedge: a numerical study. J Comput Biophys Chem2023; 22(3): 335–346. https://doi.org/10.1142/S2737416523400082
22.
DawarAShahZTassaddiqA, et al. A convective flow of Williamson nanofluid through cone and wedge with non-isothermal and non-isosolutal conditions: a revised Buongiorno model. Case Stud Therm Eng2021; 24: 100869. https://doi.org/10.1016/j.csite.2021.100869
23.
HussainMJahanSRanjhaQA, et al. Suction/blowing impact on magneto-hydrodynamic mixed convection flow of Williamson fluid through stretching porous wedge with viscous dissipation and internal heat generation/absorption. Results Eng2022; 16: 100709. https://doi.org/10.1016/j.rineng.2022.100709
24.
Ur RehmanMIChenHHamidA, et al. Chemical reactive process of unsteady bioconvective magneto Williamson nanofluid flow across wedge with nonlinearly thermal radiation: Darcy–Forchheimer model. Numeri Heat Transf B Fundamentals2023; 84(4): 432–448. https://doi.org/10.1080/10407790.2023.2211228
25.
MuhammadTWaqasHKhanSA, et al. Melting heat transfer in bioconvective transport of Williamson nanofluid over a wedge with exponential space and thermal-dependent heat source. Waves Random Complex Media2024; 34(5): 4463–4493. https://doi.org/10.1080/17455030.2021.1991601
26.
AhmadIAzizSAliN, et al. Significance of bioconvection in flow of Williamson nano-material confined by a porous radioactive Riga surface with convective Nield constrains. Numer Methods Partial Differ Equ2024; 40(2): e22735. https://doi.org/10.1002/num.22735
27.
ZulqarnainRMNadeemMSiddiqueI, et al. Heat transfer analysis of Maxwell tri-hybridized nanofluid through Riga wedge with fuzzy volume fraction. Sci Rep2023; 13(1): 18238.
28.
NadeemMSiddiqueIBilalM, et al. Numerical study of MHD Prandtl Eyring fuzzy hybrid nanofluid flow over a wedge. Numeri Heat Transf A Appl2024; 85(24): 4328–4344.
29.
KezzarMDibAAyubA, et al. Duan Rach approach solution of MHD flow of ternary hybrid Casson magnetized nanofluid in converging/diverging geometry with velocity slip effects. Numeri Heat Transf A Appl. Epub ahead of print 12June2024. DOI: 10.1080/10407782.2024.2360654.
30.
NadeemMSiddiqueIRiazZ, et al. Numerical study of unsteady tangent hyperbolic fuzzy hybrid nanofluid over an exponentially stretching surface. Sci Rep2023; 13(1): 15551.
31.
SajidTGariAAJamshedW, et al. Case study of autocatalysis reactions on tetra hybrid binary nanofluid flow via Riga wedge: biofuel thermal application. Case Stud Therm Eng2023; 47: 103058.
32.
AyubAShahSZHIqbalZ, et al. Streamlines and neural intelligent scheme for thermal transport to infinite shear rate for ternary hybrid nanofluid subject to homogeneous-heterogeneous reactions. Case Stud Therm Eng2024; 61: 104961.
33.
KhanSDarveshALiuS, et al. Characteristics and thermal repercussions of the trihybrid temperature-dependent viscosity model of Carreau nanofluid over catalysed and heated surface in the Magnetized and radiative domain. Int J Ambient Energy2025; 46(1): 2473529.
34.
AlhadriMRazaJYashkunU, et al. Response surface methodology (RSM) and artificial neural network (ANN) simulations for thermal flow hybrid nanofluid flow with Darcy-Forchheimer effects. J Indian Chem Soc2022; 99(8): 100607.
35.
Richa SharmaBKAlmohsenB, et al. Intelligent neuro-computational modelling for MHD nanofluid flow through a curved stretching sheet with entropy optimization: Koo–Kleinstreuer–Li approach. J Comput Des Eng2024; 11(5): 164–183.
36.
ShahSZHWahabHAAhmadS, et al. Numerical investigation of ternary hybrid non-Newtonian nanofluids and heat transport over an inclined shrinking sheet utilizing artificial neural network. Adv Math Phys2024; 2024(1): 4133538.
37.
KantiPKSharmaKSaidZ, et al. Experimental investigation on thermal conductivity of fly ash nanofluid and fly ash-Cu hybrid nanofluid: prediction and optimization via ANN and MGGP model. Particulate Sci Technol2022; 40(2): 182–195.
38.
SouayehBHaiderAAyubA, et al. Intelligent neuron based interpretation of carreau trihybrid nanofluid model with streamline analysis: configuration of distinct geometries. J Radiat Res Appl Sci2024; 17(4): 101154.
39.
AyubAIqbalZShahSZH, et al. Neural intelligent approach for heat transfer applications of trihybrid cross bio-nanofluid over wedge geometry. Mod Phys Lett B2025; 39(10): 2450439.
40.
ChuY-MIbrahimMSaeedT, et al. Examining rheological behavior of MWCNT-TiO2/5W40 hybrid nanofluid based on experiments and RSM/ANN modeling. J Mol Liq2021; 333: 115969.
41.
KumarASharmaBKAlmohsenB, et al. Artificial neural network analysis of Jeffrey hybrid nanofluid with gyrotactic microorganisms for optimizing solar thermal collector efficiency. Sci Rep2025; 15(1): 4729.
42.
AyubADarveshAShahSZH, et al. Magnetized and quadratic convection based thermal transport in ternary radiative bio-nanofluid via intelligent neural networks: two hidden layers mechanism. Results Phys2024; 65: 107973.
43.
DarveshAMaizFMSouayehB, et al. ANN-based two hidden layers computational procedure for analysis of heat transport dynamics in polymer-based trihybrid Carreau nanofluid flow over needle geometry. Hybrid Adv2025; 9: 100396.
44.
RameshKWarkeAKotechaK, et al. Numerical and artificial neural network modelling of magnetorheological radiative hybrid nanofluid flow with Joule heating effects. J Magn Magn Mater2023; 570: 170552.
45.
DarveshASuksamranJSirisubtaweeS.Computational insights into nanoscale heat dynamics of chemically reactive and magnetized carreau hybrid bio-nanofluid using a multilayer supervised neural computing scheme. Int J Numer Methods Fluids2025; 97(6): 940–965.
46.
DarveshAMaizFMSouayehB, et al. Advanced ANN computational procedure for thermal transport prediction in polymer-based ternary radiative Carreau nanofluid with extreme shear rates over bullet surface. Appl Rheol2025; 35(1): 20240029.
47.
HeWRuhaniBToghraieD, et al. Using of artificial neural networks (ANNs) to predict the thermal conductivity of zinc oxide–silver (50%–50%)/water hybrid Newtonian nanofluid. Int Commun Heat Mass Transf2020; 116: 104645. https://doi.org/10.1016/j.icheatmasstransfer.2020.104645
48.
HussainSMMahatRKatbarNM, et al. Artificial neural network modeling of mixed convection viscoelastic hybrid nanofluid across a circular cylinder with radiation effect: case study. Case Stud Therm Eng2023; 50: 103487. https://doi.org/10.1016/j.csite.2023.103487
49.
SharmaBKSharmaPMishraNK, et al. Darcy-Forchheimer hybrid nanofluid flow over the rotating Riga disk in the presence of chemical reaction: artificial neural network approach. Alex Eng J2023; 76: 101–130. https://doi.org/10.1016/j.aej.2023.06.014
50.
AbadJMNAlizadehRFattahiA, et al. Analysis of transport processes in a reacting flow of hybrid nanofluid around a bluff-body embedded in porous media using artificial neural network and particle swarm optimization. J Mol Liq2020; 313: 113492. https://doi.org/10.1016/j.molliq.2020.113492
51.
UysalCKorkmazME.Estimation of entropy generation for Ag-MgO/water hybrid nanofluid flow through rectangular minichannel by using artificial neural network. Politeknik Dergisi2019; 22(1): 41–51. https://doi.org/10.2339/politeknik.417756
52.
RajputSVermaAKBhattacharyyaK, et al. Unsteady nonlinear mixed convective flow of nanofluid over a wedge: Buongiorno model. Waves Random Complex Media2024; 34(5): 4059–4073.
53.
RawatSKUpretiHKumarM.Comparative study of mixed convective MHD Cu-water nanofluid flow over a cone and wedge using modified Buongiorno’s model in presence of thermal radiation and chemical reaction via Cattaneo-Christov double diffusion model. J Appl Comput Mech2021; 7(3): 1383–1402.
54.
NadeemMSiddiqueIAwrejcewiczJ, et al. Numerical analysis of a second-grade fuzzy hybrid nanofluid flow and heat transfer over a permeable stretching/shrinking sheet. Sci Rep2022; 12(1): 1631.
55.
ZulqarnainRMNadeemMSiddiqueI, et al. Impacts of entropy generation in second-grade fuzzy hybrid nanofluids on exponentially permeable stretching/shrinking surface. Sci Rep2023; 13(1): 22132.
56.
VermaLMeherRHammouchZ, et al. Effect of heat transfer on hybrid nanofluid flow in converging/diverging channel using fuzzy volume fraction. Sci Rep2022; 12(1): 20845.
57.
HussainSM.Numerical assessment of a sutterby hybrid nanofluid over a stretching sheet with a particle shape factor. Waves Random Complex Media. Epub ahead of print 10January2023. DOI: 10.1080/17455030.2023.2166148.
58.
AlgehyneEASaeedAArifM, et al. Gyrotactic microorganism hybrid nanofluid over a Riga plate subject to activation energy and heat source: numerical approach. Sci Rep2023; 13(1): 13675.
59.
KumariMTakharHSNathG.Mixed convection flow over a vertical wedge embedded in a highly porous medium. Heat Mass Transf2001; 37(2): 139–146.
