Stability Scrutinization of Time Depending Flow of a Ternary Hybrid Nanofluid Past a Shrinking Sheet with Wall Mass Suction Effect


  • Farah Nadzirah Jamrus ᵃDepartment of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia; ᵇCollege of Computing, Informatics, and Mathematics, Universiti Teknologi MARA Cawangan Melaka Kampus Jasin, 77300, Merlimau, Melaka, Malaysia
  • Anuar Ishak Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia
  • Iskandar Waini Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, 76100 Durian Tunggal, Melaka, Malaysia



Nanofluid, heat transfer, dual solutions, stability analysis


The dynamics of unsteady flow of a ternary hybrid nanofluid on a stretching/shrinking sheet with wall mass suction is numerically analysed. In this study, a mixture of Al2O3, Cu, and TiO2 is employed as additives in water, which serves as the base fluid. The equations governed the problem are simplified into a collection of ODEs by adopting the similarity transformation. Maintaining the flow on a shrinking sheet is reliant on the essential aspect of suction. Furthermore, augmenting the strength of suction amplifies the thermal conductivity process of the flow. Additionally, this study unveils dual solutions existing within a defined range of parameters. It has been determined that one solution exhibits long-term stability, whereas the other solution is deemed unstable through the stability analysis conducted.


S. U. S. Choi and J. A. Eastman. (1995). Enhancing thermal conductivity of fluids with nanoparticles. Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, FED 231/MD 66, 99-105.

A. Gavili and T. Isfahani. (2020). Experimental investigation of transient heat transfer coefficient in natural convection with Al2O3-nanofluids. Heat and Mass Transfer, 56(3), 901-911.

R. Mohebbi and M. M. Rashidi. (2017). Numerical simulation of natural convection heat transfer of a nanofluid in an L-shaped enclosure with a heating obstacle. J Taiwan Inst Chem Eng., 72, 70-84.

M. Turkyilmazoglu. (2020). Single phase nanofluids in fluid mechanics and their hydrodynamic linear stability analysis. Comput Methods Programs Biomed., 187, 105171.

Hayat and S. Nadeem. (2017). Heat transfer enhancement with Ag-CuO/water hybrid nanofluid. Results Phys., 7, 2317-2324.

A. I. Ramadhan, W. H. Azmi, and R. Mamat. (2021). Experimental investigation of thermo-physical properties of tri-hybrid nanoparticles in water-ethylene glycol mixture. Walailak Journal of Science and Technology (WJST), 18(8).

L. S. Sundar, K. V. V. Chandra Mouli, Z. Said, and A. C. M. Sousa. (2021). Heat transfer and second law analysis of ethylene glycol-based ternary hybrid nanofluid under laminar flow. J Therm Sci Eng Appl., 13(5).

A. Dezfulizadeh, A. Aghaei, A. H. Joshaghani, and M. M. Najafizadeh. (2021). An experimental study on dynamic viscosity and thermal conductivity of water-Cu-SiO2-MWCNT ternary hybrid nanofluid and the development of practical correlations. Powder Technol., 389, 215-234.

W. Ahmed et al. (2021). Heat transfer growth of sonochemically synthesized novel mixed metal oxide ZnO+Al2O3+TiO2/DW based ternary hybrid nanofluids in a square flow conduit. Renewable and Sustainable Energy Reviews, 145, 111025.

J. Mohammed Zayan et al. (2023). Synthesis and characterization of novel ternary-hybrid nanoparticles as thermal additives. Materials, 16(1).

T. Elnaqeeb, I. L. Animasaun, and N. A. Shah. (2021). Ternary-hybrid nanofluids: significance of suction and dual-stretching on three-dimensional flow of water conveying nanoparticles with various shapes and densities. Zeitschrift für Naturforschung A, 76(3), 231-243.

K. A. M. Alharbi et al. (2022). Computational valuation of darcy ternary-hybrid nanofluid flow across an extending cylinder with induction effects. Micromachines (Basel), 13(4), 588.

J. K. Madhukesh, I. E. Sarris, B. C. Prasannakumara, and A. Abdulrahman. (2023). Investigation of thermal performance of ternary hybrid nanofluid flow in a permeable inclined cylinder/plate. Energies (Basel), 16(6), 2630.

M. K. Sarangi, D. N. Thatoi, M. K. Nayak, J. Prakash, K. Ramesh, and M. Azam. (2022). Rotational flow and thermal behavior of ternary hybrid nanomaterials at small and high Prandtl numbers. International Communications in Heat and Mass Transfer, 138, 106337.

I. L. Animasaun, S.-J. Yook, T. Muhammad, and A. Mathew. (2022). Dynamics of ternary-hybrid nanofluid subject to magnetic flux density and heat source or sink on a convectively heated surface. Surfaces and Interfaces, 28, 101654.

Z. Mahmood, Z. Iqbal, M. A. Alyami, B. Alqahtani, M. F. Yassen, and U. Khan. (2022). Influence of suction and heat source on MHD stagnation point flow of ternary hybrid nanofluid over convectively heated stretching/shrinking cylinder. Advances in Mechanical Engineering, 14(9), 168781322211262.

Z. Mahmood, N. A. Ahammad, S. E. Alhazmi, U. Khan, and M. Z. Bani-Fwaz. (2022). Ternary hybrid nanofluid near a stretching/ shrinking sheet with heat generation/ absorption and velocity slip on unsteady stagnation point flow. Int J Mod Phys B, 36(29).

A. Mohammadi, M. H. Ahmadi, M. Bidi, F. Joda, A. Valero, and S. Uson. (2017). Exergy analysis of a combined cooling, heating and power system integrated with wind turbine and compressed air energy storage system. Energy Convers Manag., 131, 69-78.

B.C. Sakiadis. (1961). Boundary-layer behavior on continuous solid surfaces: I. Boundary-layer equations for two-dimensional and axisymmetric flow. AIChE Journal, 7(1), 26-28.

L. J. Crane. (1970). Flow past a stretching plate. Zeitschrift für angewandte Mathematik und Physik ZAMP, 21(4), 645-647.

S. Goldstein. (1965). On backward boundary layers and flow in converging passages. J Fluid Mech., 21(01), 33.

M. Miklavčič and C. Wang. (2006). Viscous flow due to a shrinking sheet. Q Appl Math, 64(2), 283-290. Apr

U. Halima, D. AM, and A. Sammani. (2023). Effects of injection/suction on unsteady mhd natural convective radiative flow of heat mass transfer in a plumb frequency. Saudi Journal of Engineering and Technology, 8(07), 171-180. Jul

H. Chanson. (2004). Unsteady open channel flows: 2. Applications. Hydraulics of Open Channel Flow, 318-370.

F. T. Smith. (1986). Steady and unsteady boundary-layer separation. Annu Rev Fluid Mech., 18(1), 197-220.

W. R. Sears and D. P. Telionis. (1975). Boundary-Layer Separation in Unsteady Flow. SIAM J Appl Math, 28(1), 215-235.

T. G. Fang, J. Zhang, and S.-S. Yao. (2009). Viscous flow over an unsteady shrinking sheet with mass transfer. Chinese Physics Letters, 26(1), 014703. Jan

A. M. Rohni, S. Ahmad, and I. Pop. (2012). Flow and heat transfer over an unsteady shrinking sheet with suction in nanofluids. Int J Heat Mass Transf., 55(7-8), 1888-1895.

P. S. Reddy, P. Sreedevi, and A. J. Chamkha. (2023). Hybrid nanofluid heat and mass transfer characteristics over a stretching/shrinking sheet with slip effects. Journal of Nanofluids, 12(1), 251-260.

G. Murtaza, L. Bonik, E. Em. Tzirtzilakis, and M. Ferdows. (2023). Finite difference simulation on biomagnetic fluid flow and heat transfer with gold nanoparticles towards a shrinking sheet in the presence of a magnetic dipole. IOCMA 2023, Basel Switzerland: MDPI. 18.

R. I. Yahaya, N. Md Arifin, S. S. P. Mohamed Isa, and M. M. Rashidi. (2021). Magnetohydrodynamics boundary layer flow of micropolar fluid over an exponentially shrinking sheet with thermal radiation: Triple solutions and stability analysis. Math Methods Appl Sci., 44(13), 10578-10608.

J. H. Merkin. (1986). On dual solutions occurring in mixed convection in a porous medium. J Eng Math., 20(2), 171-179.

P. D. Weidman, D. G. Kubitschek, and A. M. J. Davis. (2006). The effect of transpiration on self-similar boundary layer flow over moving surfaces. Int J Eng Sci., 44(11-12), 730-737.

A. Ishak. (2014). Flow and heat transfer over a shrinking sheet: a stability analysis. International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, 8, 902-906.

L. A. Lund, Z. Omar, and I. Khan. (2019). Steady incompressible magnetohydrodynamics Casson boundary layer flow past a permeable vertical and exponentially shrinking sheet: A stability analysis. Heat Transfer-Asian Research, 48(8), 3538-3556.

R. I. Yahaya, N. M. Arifin, R. Nazar, and I. Pop. (2020). Flow and heat transfer past a permeable stretching/shrinking sheet in Cu−Al2O3/water hybrid nanofluid. Int J Numer Methods Heat Fluid Flow, 30(3), 1197-1222.

I. Waini, A. Ishak, and I. Pop. (2019). Unsteady flow and heat transfer past a stretching/shrinking sheet in a hybrid nanofluid. Int J Heat Mass Transf., 136, 288-297.

N. Safwa Khashi'ie, N. C. Roșca, A. V. Roșca, and I. Pop. (2023). Dual solutions on MHD radiative three-dimensional bidirectional nanofluid flow over a non-linearly permeable shrinking sheet. Alexandria Engineering Journal, 71, 401-411.

G. Rasool, X. Wang, U. Yashkun, L. A. Lund, and H. Shahzad. (2023). Numerical treatment of hybrid water based nanofluid flow with effect of dissipation and Joule heating over a shrinking surface: Stability analysis. J Magn Magn Mater., 571, 170587.

Z. Xuan, Y. Zhai, M. Ma, Y. Li, and H. Wang. (2021). Thermo-economic performance and sensitivity analysis of ternary hybrid nanofluids. J Mol Liq., 323, 114889.

S. Manjunatha, V. Puneeth, B. J. Gireesha, and A. J. Chamkha. (2022). Theoretical study of convective heat transfer in ternary nanofluid flowing past a stretching sheet. Journal of Applied and Computational Mechanics, 8(4), 1279-1286.

J. Raza. (2018). Similarity solutions of boundary layer flows in a channel filled by non-newtonian fluids. Universiti Utara Malaysia, Changlun, Malaysia.

C. Y. Wang. (1989). Free convection on a vertical stretching surface. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 69(11), 418-420.

R. S. R. Gorla and I. Sidawi. (1994). Free convection on a vertical stretching surface with suction and blowing. Applied Scientific Research, 52(3), 247-257.

P. Priyadharshini, M. V. Archana, N. A. Shah, and M. H. Alshehri. (2023). ternary hybrid nanofluid flow emerging on a symmetrically stretching sheet optimization with machine learning prediction scheme. Symmetry (Basel), 15(6), 1225.

Iskandar Waini, Farah Nadzirah Jamrus, Abdul Rahman Mohd Kasim, Anuar Ishak, and Ioan Pop. (2023). Homogeneous-heterogeneous reactions on Al2O3-Cu hybrid nanofluid flow over a shrinking sheet. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 102(1), 85-97.

N. C. Roy, A. Hossain, and I. Pop. (2022). Flow and heat transfer of MHD dusty hybrid nanofluids over a shrinking sheet. Chinese Journal of Physics, 77, 1342-1356.

S. S. U. Devi and S. P. A. Devi. (2017). Heat transfer enhancement of Cu−Al2O3/water hybrid nanofluid flow over a stretching sheet. Journal of the Nigerian Mathematical Society, 36(2), 419-433. 85056632790&partnerID=40&md5=a194e2bee97b97967acf94f36023af87.

A. Ishak. (2010). Aliran lapisan sempadan bersebelahan plat tegak dengan suhu permukaan malar (boundary layer flow adjacent to a vertical plate with constant surface temperature). Sains Malaysiana, 39(6),1035-1039.