Despite extensive research on nanofluids and magnetohydrodynamic (MHD) flows, the simultaneous investigation of melting heat transfer, thermal radiation, and ternary hybrid nanofluid (THNF) on inclined surfaces remains unexplored, presenting a significant gap in thermal management literature. This work addresses this gap by examining the combined effects of melting phenomena, MHD, and mixed convection in a THNF composed of copper (Cu), aluminum oxide (), and titanium dioxide (TiO2) nanoparticles flowing over an inclined surface. Similarity transformations and numerical solution via the Keller box method are employed to solve the governing equations, incorporating mixed convection and thermal radiation effects. Key results demonstrate a substantial enhancement in the local Nusselt number of THNF by ∼19% due to the melting phenomenon, accompanied by a 6% increase in the skin friction coefficient. The skin friction coefficient increases on the stretching sheet but decreases on the shrinking sheet. Furthermore, the melting parameter leads to a significant decrease in temperature profiles (around 18%), whereas the inclination parameter causes a minor increase (∼3%) for both stretching and shrinking scenarios. Notably, the analysis confirms that THNF demonstrates superior thermal performance compared to conventional hybrid and single-component nanofluids. These results provide actionable insights for designing nanoengineered thermal management systems applicable to solar thermal collectors, battery cooling systems, and advanced heat exchangers, directly supporting the development of efficient and sustainable energy technologies.
SunthrayuthPAbdelmohsenSARekhaM, et al. Impact of nanoparticle aggregation on heat transfer phenomena of second grade nanofluid flow over melting surface subject to homogeneous-heterogeneous reactions. Case Stud Therm Eng2022; 32: 101897.
2.
KhanSAHayatTAlsaediA, et al. Heat and mass transfer enhancement in nonlinear mixed convective flow: Buongiorno model and melting heat phenomenon. Int Commun Heat Mass Transf2024; 153: 107330.
3.
EpsteinMChoD.Melting heat transfer in steady laminar flow over a flat plate. J Heat Transf1976; 98(3): 531–533.
4.
HafeezALiuDKhalidA, et al. Melting heat transfer features in a B Dewadt flow of hybrid nanofluid (Cu–Al2O3/water) by a stretching stationary disk. Case Stud Therm Eng2024; 59: 104554.
5.
RozenfeldTHayatRKozakY, et al. Enhanced melting for transient thermal management. In: Proceedings of the ASME 2015 international technical conference and exhibition on packaging and integration of electronic and photonic microsystems and ASME 2015 12th international conference on nanochannels, microchannels, and minichannels - InterPACKICNMM2015, San Francisco, CA, USA, 6–9 July 2015, p. 1–6, vol. 56888.
6.
RashidFLAl-ObaidiMADulaimiA, et al. Recent advances on the applications of phase change materials in cold thermal energy storage: a critical review. J Compos Sci2023; 7(8): 338.
7.
HyderALimYKhanI, et al. Thermal behavior of MHD stagnation ternary nanofluid over a melting surface with joule heating. Malays J Math Sci2025; 19(2): 361–381.
8.
SakakiniTJKoelnJP. Switched moving boundary modeling of phase change thermal energy storage systems. In: 2023 IEEE conference on control technology and applications (CCTA), pp.941–947. New York: IEEE.
9.
LuoXLiaoS.Numerical study on melting heat transfer in dendritic heat exchangers. Energies2018; 11(10): 2504.
10.
KhanRJBhuiyanMZHAhmedDH.Investigation of heat transfer of a building wall in the presence of phase change material (PCM). Energy Built Environ2020; 1(2): 199–206.
11.
AlkasasbehHT.Modeling the flow of Casson nanofluid on a stretching sheet with heat transfer: a study of electric MHD and Darcy–Forchheimer effects. Partial Differ Equ Appl Math2025; 13: 101109.
12.
HanYYangYMallickT, et al. Nanoparticles to enhance melting performance of phase change materials for thermal energy storage. Nanomaterials2022; 12(11): 1864.
13.
KhalidAHafeezAAlFarhanAMM. Dual solution of melting heat transfer efficiency in radiative hybrid (Cu–Al2O3/water) nanofluid flow. Case Stud Therm Eng2023; 50: 103428.
14.
AlkasasbehHTAl FaqihFMAlizadehA, et al. Computational modeling of hybrid micropolar nanofluid flow over a solid sphere. J Magn Magn Mater2023; 569: 170444.
15.
RagaviMSreenivasuluPPoornimaT.Magnetohydrodynamic hybrid nanofluid flow with Cattaneo–Christov heat flux: thermal performance and entropy analysis. Multiscale Multidiscip Model Exp Des2025; 8(3): 167.
16.
GoudJSSrilathaPKumarRV, et al. Role of ternary hybrid nanofluid in the thermal distribution of a dovetail fin with the internal generation of heat. Case Stud Therm Eng2022; 35: 102113.
17.
HyderALimYJKhanI, et al. Heat transfer mechanisms in ternary TiO2–Al2O3–Cu/water-based nanofluids at stagnation phase change surfaces. J Appl Comput Mech2025; 11(3): 770–786.
18.
NoreenSFarooqUWaqasH, et al. Comparative study of ternary hybrid nanofluids with role of thermal radiation and Cattaneo–Christov heat flux between double rotating disks. Sci Rep2023; 13(1): 7795.
19.
AdunHKavazDDagbasiM.Review of ternary hybrid nanofluid: synthesis, stability, thermophysical properties, heat transfer applications, and environmental effects. J Clean Prod2021; 328: 129525.
20.
AlqarniMMemonAAMemonMA, et al. Numerical investigation of heat transfer and fluid flow characteristics of ternary nanofluids through convergent and divergent channels. Nanoscale Adv2023; 5(24): 6897–6912.
21.
OuadaMKezzarMTalbiN, et al. Heat transfer characteristics of moving longitudinal porous fin wetted with ternary (Cu–Al2O3–TiO2) hybrid nanofluid: ADM solution. Eur Phys J Plus2023; 138(9): 1–12.
22.
GargJPoudelBChiesaM, et al. Enhanced thermal conductivity and viscosity of copper nanoparticles in ethylene glycol nanofluid. J Appl Phys2008; 103(7): 074301.
23.
PrakashASatsangiSMittalS, et al. Investigation on Al2O3 nanoparticles for nanofluid applications – a review. IOP Conf Ser Mater Sci Eng2018; 377: 012175.
24.
KusriniEPutraNSiswahyuA, et al. Effects of sequence preparation of titanium dioxide–water nanofluid using cetyltrimethylammonium bromide surfactant and TiO2 nanoparticles for enhancement of thermal conductivity. Int J Technol2019; 10(7): 1453–1464.
25.
Bilal HafeezMKrawczukMJamshedW, et al. Thermal energy development in magnetohydrodynamic flow utilizing titanium dioxide, copper oxide and aluminum oxide nanoparticles: thermal dispersion and heat generating formularization. Front Energy Res2022; 10: 1000796.
26.
BhattadAAtgurVRaoBN, et al. Review on mono and hybrid nanofluids: preparation, properties, investigation, and applications in IC engines and heat transfer. Energies2023; 16(7): 3189.
27.
AzmiHMIsaSSPMArifinNM.The boundary layer flow, heat and mass transfer beyond an exponentially stretching/shrinking inclined sheet. CFD Lett2020; 12(8): 98–107.
28.
RafiqueKAlotaibiHNofalTA, et al. Numerical solutions of micropolar nanofluid over an inclined surface using Keller box analysis. J Math2020; 2020(1): 6617652.
29.
MadhukeshJKSarrisIEPrasannakumaraBC, et al. Investigation of thermal performance of ternary hybrid nanofluid flow in a permeable inclined cylinder/plate. Energies2023; 16(6): 2630.
30.
JangidSAlessaNMehtaR, et al. Numerical study of Cattaneo–Christov heat flux on water-based Carreau fluid flow over an inclined shrinking sheet with ternary nanoparticles. Symmetry2022; 14(12): 2605.
31.
UsharaniPReddyBR.Ternary hybrid nanofluid flow through an inclined shrinking sheet when Soret, Dufour and quadratic thermal radiation are significant: an irreversibility analysis with various shape factors. Int J Ambient Energy2024; 45(1): 2372681.
32.
SwainBKKarS.Dissipative MHD flow of ternary-hybrid nanofluid over an inclined stretching sheet with heat source and mass flux due to temperature gradient. ZAMM J Appl Math Mech2024; 104(4): e202200360.
33.
JamrusFNWainiIKhanU, et al. Effects of magnetohydrodynamics and velocity slip on mixed convective flow of thermally stratified ternary hybrid nanofluid over a stretching/shrinking sheet. Case Stud Therm Eng2024; 55(66): 104161.
34.
KanwalSShahSAABariqA, et al. Insight into the dynamics of heat and mass transfer in nanofluid flow with linear/nonlinear mixed convection, thermal radiation, and activation energy effects over the rotating disk. Sci Rep2023; 13(1): 23031.
35.
JhaBKSamailaG.Thermal radiation effect on boundary layer over a flat plate having convective surface boundary condition. SN Appl Sci2020; 2(3): 381.
36.
KumariPSIbrahimSMKumarPV, et al. Numerical analysis of micropolar nanofluid flow near a stagnation point over an inclined stretching surface. Power Eng Eng Thermophys2025; 4(1): 30–41.
37.
MahmoodZKhanU.Unsteady three-dimensional nodal stagnation point flow of polymer-based ternary-hybrid nanofluid past a stretching surface with suction and heat source. Sci Prog2023; 106(1): 00368504231152741.
38.
LiYMajeedAIjazN, et al. Melting thermal transportation in bioconvection Casson nanofluid flow over a nonlinear surface with motile microorganism: application in bioprocessing thermal engineering. Case Stud Therm Eng2023; 49: 103285.
39.
YangHMajeedAAl-KhaledK, et al. Significance of melting heat transfer and Brownian motion on flow of Powell–Eyring fluid conveying nano-sized particles with improved energy systems. Lubricants2023; 11(1): 32.
40.
DadheechAParmarAOlkhaA.Inclined MHD and radiative Maxwell slip fluid flow and heat transfer due to permeable melting surface with a non-linear heat source. Int J Appl Comput Math2021; 7(3): 89.
41.
KayalvizhiJVijaya KumarA.Entropy analysis of EMHD hybrid nanofluid stagnation point flow over a porous stretching sheet with melting heat transfer in the presence of thermal radiation. Energies2022; 15(21): 8317.
42.
RameshGKMadhukeshJShahNA, et al. Flow of hybrid CNTs past a rotating sphere subjected to thermal radiation and thermophoretic particle deposition. Alex Eng J2023; 64: 969–979.
43.
KellerHB.A new difference scheme for parabolic problems. In: HubbardB (ed.) Numerical solution of partial differential equations – II. Elsevier, 1971. pp.327–350.
44.
Al-ShibaniFIsmailAMAbdullahF.The implicit Keller box method for the one dimensional time fractional diffusion equation. J Appl Math Bioinform2012; 2(3): 69.
45.
VinothKumarBPoornimaTSreenivasuluP, et al. Effect of inclined Lorentzian force on radiated nanoflow Williamson model under asymmetric energy source/sink: Keller box method. APL Mater2024; 12: 041106.
46.
Vinoth KumarBSreenivasuluPPoornimaT. Optimizing the thermal efficiency and drug delivery to narrowing arteries with silver–gold nanoparticles: a numerical study. J Comput Appl Math2026; 471: 116723.
47.
ShinwariWHayatTAbbasZ, et al. A numerical study on the flow of water-based ternary hybrid nanomaterials on a stretchable curved sheet. Nanoscale Adv2023; 5(22): 6249–6261.
48.
SinghBSoodS.Hybrid nanofluids preparation, thermo-physical properties, and applications: a review. Hybrid Adv2024; 6: 100192.
49.
MaboodFYusufTBognárG.Features of entropy optimization on MHD couple stress nanofluid slip flow with melting heat transfer and nonlinear thermal radiation. Sci Rep2020; 10(1): 19163.
50.
SheikhMAbbasZ.Homogeneous–heterogeneous reactions in stagnation point flow of Casson fluid due to a stretching/shrinking sheet with uniform suction and slip effects. Ain Shams Eng J2017; 8(3): 467–474.
51.
ChoudharyPChoudharySJatK, et al. Significances of melting heat transfer and bioconvection phenomena in nanofluid flow over three different geometries. Int J Thermofluids2024; 24: 100855.
52.
ZaimiKIshakAPopI.Flow past a permeable stretching/shrinking sheet in a nanofluid using two-phase model. PLoS One2014; 9(11): e111743.
53.
YahayaRIArifinNMNazarR, et al. Flow and heat transfer past a permeable stretching/shrinking sheet in Cu–Al2O3/water hybrid nanofluid. Int J Numer Methods Heat Fluid Flow2019; 30(3): 1197–1222.
54.
MaboodFDasK.Outlining the impact of melting on MHD Casson fluid flow past a stretching sheet in a porous medium with radiation. Heliyon2019; 5(2): e01216.
55.
AbidGA.Effect of inclination angle on natural convection from inclined plate with variable viscosity and thermal conductivity. Univ Thi-Qar J Eng Sci2016; 7(1): 28–46.
56.
NaqviSMRSWaqasHYasminS, et al. Numerical simulations of hybrid nanofluid flow with thermal radiation and entropy generation effects. Case Stud Therm Eng2022; 40: 102479.
57.
BrozzesiZLiDLeeA.Exploring the potential of phase change material for thermal energy storage in building envelopes. J Energy Power Technol2023; 5(3): 1–21.
58.
OlkhaAChoudharyR.Investigation of melting heat transfer in viscous nanofluid flow including micro-organisms and entropy generation due to an inclined exponentially stretching sheet. J Nanofluids2024; 13(2): 446–463.
59.
SharmaSDadheechAParmarA, et al. Mhd micro polar fluid flow over a stretching surface with melting and slip effect. Sci Rep2023; 13(1): 10715.
60.
ShaikhGMMemonAAMemonMA, et al. Numerical study of flow behavior and heat transfer of ternary water-based nanofluids in the presence of suction/injection, stretching/shrinking sheet. J Therm Eng2024; 10(4): 1021–1043.
61.
VaratharajKTamizharasiRVajraveluK.Ternary hybrid nanofluid flow and heat transfer at a permeable stretching sheet with slip boundary conditions. Eur Phy J Spec Top2024; 234: 2293–2316.
62.
SoidSKBBakarFNANorzawaryNHA, et al. Stagnation-point flow and heat transfer over an exponentially stretching/shrinking inclined plate in a micropolar fluid. J Adv Res Numer Heat Transf2024; 16(1): 17–34.
63.
KitetuVMOnyangoTKwanzaJ, et al. Analysis of the effect of stretching parameter and time parameter on MHD nanofluid flow in the presence of suction. Glob J Pure Appl Math2019; 15: 637–648.
64.
SandeepNSulochanaCKumarBR.MHD boundary layer flow and heat transfer past a stretching/shrinking sheet in a nanofluid. J Nanofluids2015; 4(4): 512–517.
65.
MahabaleshwarUVinay KumarPSheremetM.Magnetohydrodynamics flow of a nanofluid driven by a stretching/shrinking sheet with suction. SpringerPlus2016; 5: 1–9.
66.
ChenHHePShenM, et al. Thermal analysis and entropy generation of Darcy–Forchheimer ternary nanofluid flow: a comparative study. Case Stud Therm Eng2023; 43: 102795.
67.
RamzanMKumamPLoneSA, et al. A theoretical analysis of the ternary hybrid nanofluid flows over a non-isothermal and non-isosolutal multiple geometries. Heliyon2023; 9(4): e14875.
68.
NathRSDekaRK.A numerical study on the MHD ternary hybrid nanofluid (Cu–Al2O3–TiO2/H2O) in presence of thermal stratification and radiation across a vertically stretching cylinder in a porous medium. East Eur J Phys2024; 1: 232–242.
69.
RafiqueKMahmoodZKhanU, et al. Investigation of thermal stratification with velocity slip and variable viscosity on MHD flow of Al2O3–Cu–TiO2/H2O nanofluid over disk. Case Stud Therm Eng2023; 49: 103292.
70.
WangC.Stagnation flow towards a shrinking sheet. Int J Non-Linear Mech2008; 43(5): 377–382.
71.
WahidNSArifinNMPopI, et al. Mhd stagnation-point flow of nanofluid due to a shrinking sheet with melting, viscous dissipation and joule heating effects. Alex Eng J2022; 61(12): 12661–12672.
72.
Al NuwairanMHafeezAKhalidA, et al. Multiple solutions of melting heat transfer of MHD hybrid based nanofluid flow influenced by heat generation/absorption. Case Stud Therm Eng2022; 35: 101988.
73.
BachokNIshakAPopI.Melting heat transfer in boundary layer stagnation-point flow towards a stretching/shrinking sheet. Phys Lett A2010; 374(40): 4075–4079.
