Theoretical Study of Convective Heat Transfer in Ternary ‎Nanofluid Flowing past a Stretching Sheet

Document Type : Research Paper


1 Department of Mathematics, CHRIST (Deemed to be University), Mysore Road, Bangalore, 560074, India

2 Department of Mathematics, CHRIST (Deemed to be University), Hosur Road, Bangalore, 560029, India

3 Department of Studies and Research in Mathematics, Kuvempu University, Shankarghatta, Shimogga, 577451, India‎

4 Faculty of Engineering, Kuwait College of Science and Technology, Doha District, 7th Ring Road, 35004, Kuwait


A new theoretical tri-hybrid nanofluid model for enhancing the heat transfer is presented in this article. This model explains the method to obtain a better heat conductor than the hybrid nanofluid. The tri-hybrid nanofluid is formed by suspending three types of nanoparticles with different physical and chemical bonds into a base fluid. In this study, the nanoparticles TiO2, Al2O3 and SiO2 are suspended into water thus forming the combination TiO2-SiO2-Al2O3-H2O. This combination helps in decomposing harmful substances, environmental purification and other appliances that requires cooling. The properties of tri-hybrid nanofluid such as Density, Viscosity, Thermal Conductivity, Electrical Conductivity and Specific Heat capacitance are defined mathematically in this article. The system of equations that governs the flow and temperature of the fluid are converted to ordinary differential equations and are solved using RKF-45 method. The results are discussed through graphs and it is observed that the tri-hybrid nanofluid has a better thermal conductivity than the hybrid nanofluid.


Main Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

[1] Sakiadis B.C., Boundary layer behaviour on continuous solid surface; I Boundary layer equations for two dimensional and axisymmetric flow, AIChE Journal, 7(1), 1961, 26-28.
[2] Tsou, F.K., Sparrow E.M., Glodstein R.J., Flow and heat transfer in the boundary layer on a continuous moving surface, International Journal of Heat and Mass Transfer, 10(2), 1967, 219-237.
[3] Rollins, D., Vajravelu, K., Heat transfer in a second order fluid over a continuous stretching surface, Acta Mechanica, 89(1), 1991, 167-178.
[4] Sharidan, S., Mahmood, T., Pop, I., Similarity solution for the unsteady boundary layer flow and heat transfer due to a stretching sheet, International Journal of Applied Mechanical Engineering, 11, 2006, 647-65.
[5] Puneeth, V., Manjunatha, S., Gireesha, B.J., Gorla, R.S.R., Magneto convective flow of casson nanofluid due to Stefan blowing in the presence of bio-active mixers, Proceedings of the Institution of the Mechanical Engineers, Part N: Journal of Nanomaterials, Nanoengineering and Nanosystems, 2021, DOI: 23977914211016692
[6] Abel, M.S., Khan, S.K., Prasad, K.V., Study of Visco-elastic fluid and heat transfer over a stretching sheet with variable viscosity, International Journal of Non-linear Mechanics, 37(1), 2002, 81-88.
[7] Elbashbeshy, E.M.A., Heat transfer over a stretching surface with variable surface heat flux, Journal of Physics D: Applied Physics, 31(16), 1998, 1951-1954.
[8] Elbashbeshy, E.M.A., Bazid, M.A.A., Heat transfer over an unsteady stretching surface, International Journal of Heat and Mass Transfer, 41(1), 2004, 1-4.
[9] Elbashbeshy, E.M.A., Aldawody, D.A., Effect of thermal radiation and magnetic field on unsteady mixed convection flow and heat transfer over a porous stretching surface, International Journal of Non-Linear Sciences, 9(4), 2010, 448-454.
[10] Grubka, L.J., Bobba, K.M., Heat transfer characteristics of a continuous stretching surface with variable temperature, International Journal of Heat and Mass Transfer, 107(1), 1985, 248-250.
[11] Fujishima, A., Honda, K., Electrochemical photolysis of water at a semiconductor electrode, Nature, 238(5358), 1972, 37-38.
[12] Bischoff, B.L., Anderson, M.A., Peptization process in the sol-gel preparation of porous anatase (TiO2), Chemistry of Materials, 7(10), 1995, 1772-1778.
[13] Hulteen, J., A general template based method for the preparation of nanomaterials, Journal of Materials Chemistry, 7(7), 1997, 1075-1087.
[14] Zhang, M., Bando, Y., Wada, K., Sol-gel template preparation of TiO2 nanotubes and nanorods, Journal of Materials Science Letters, 20(2), 2001, 167-170.
[15] Seo, D.S., Lee, J.K., Kim, H., Preparation of nanotube shaped TiO2 powder, Journal of Crystal Growth, 229(1-4), 2001, 428-432.
[16] Martin, C.R., Nanomaterials: a membrane based synthetic approach, Science, 266(5193), 1994, 1961-1966.
[17] Martin, C.R., Parthasarathy, R., Menon, V., Template synthesis of electronically conductive polymers preparation of thin films, Electrochemica Acta, 39(8-9), 1994, 1309-1313.
[18] Choi, S.U.S., Eastman, J.A., Enhancing the thermal conductivity of fluids with nanoparticles, Argonne National Lab 43 (ANL/MSD/CP-84938 CONF-951135-29), 1995, 99–105.
[19] Xuan, Y., Roetzel, W., Conceptions for heat transfer correlation of nanofluids, International Journal of Heat and Mass Transfer, 43(19), 2000, 3701–3707.
[20] Xuan, Y., Li, Q., Heat transfer enhancement of nanofluids, International Journal of Heat and Fluid Flow, 21(1), 2004, 58–64.
[21] Keblinskia, P., Phillpot, S., Choi, S.U.S., Eastman, J.A., Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids), International Journal of Heat and Mass Transfer, 45(4), 2002, 36–44.
[22] Keblinskia, P., Eastman, J.A., Cahill, D.G., Nanofluids for thermal transport, Materials Today, 8(6), 2005, 36–44.
[23] Mehryan, S.A.M., Ghalambaz, M., Gargari, L.S., Hajjar, A., Sheremet, M., Natural convection flow of a suspension containing nano-encapsulated phase change particles in an eccentric annulus, Journal of Energy Storage, 28, 2020, 101236.
[24] Ghalambaz, M., Groşan, T., Pop, I., Mixed convection boundary layer flow and heat transfer over a vertical plate embedded in a porous medium filled with a suspension of nano-encapsulated phase change materials, Journal of Molecular Liquids, 293, 2019, 111432.
[25] Ghalambaz, M., Mehryan, S.A.M., Hajjar, A., Veismoradi, A., Unsteady natural convection flow of a suspension comprising Nano-Encapsulated Phase Change Materials (NEPCMs) in a porous medium, Advanced Powder Technology, 31(3), 2020, 954-966.
[26] Hajjar, A., Mehryan, S.A.M., Ghalambaz, M., Time periodic natural convection heat transfer in a nano-encapsulated phase-change suspension, International Journal of Mechanical Sciences, 166, 2020, 105243.
[27] Hayat, T., Nadeem, S., Heat transfer enhancement with Ag-CuO/water hybrid nanofluid, Results in Physics, 7, 2017, 2317-2324.
[28] Tayebi, T., Chamkha, A.J., Entropy generation analysis due to MHD natural convection flow in a cavity occupied with hybrid nanofluid and equipped with a conducting hollow cylinder, Journal of Thermal analysis and Calorimetry, 139(3), 2020, 2165-2179.
[29] Ghalambaz, M., Doostani, A., Izadpahani, E., Chamkha, A.J., Conjugate natural convection flow of Ag-MgO/water hybrid nanofluid in a square cavity, Journal of Thermal Analysis and Calorimetry, 139(3), 2020, 2321-2336.
[30] Dogonchi, A.S., Nayak, M.K., Karimi, N., Chamkha, A.J., Ganji, D.D., Numerical simulation of hydrothermal features of Cu-H2O nanofluid natural convection within a porous annulus considering diverse configurations of heater, Journal of Thermal Analysis and Calorimetry, 141, 2020, 2109-2125.
[31] Manjunatha, S., Kuttan, B.A., Jayanthi, S., Chamkha A.J., Gireesha, B.J., Heat transfer enhancement in the boundary layer flow of hybrid nanofluids due to variable viscosity and natural convection, Heliyon, 5(4), 2019, e01469.
[32] Nihara, K., New design concept of structural ceramics-ceramic nano composites, Journal of Ceramics Society Japan, 99(1154), 1991, 974-982.
[33] Baheraei, M., Jamshidmofid M., Goodarz, M., Efficacy of a hybrid nanofluid in a new microchannel heat sink equipped with both secondary channels and ribs, Journal of Molecular Liquids, 273, 2019, 88-98.
[34] Baheraei, M., Mazaheri, N., Hossein, S.M., Zamani, H., Efficacy of a new graphene platinum nanofluid in tubes fitted with single and twin twisted tapes regarding counter and co-swirling flows for efficient use of energy, International Journal of Mechanical Sciences, 150, 2019, 290-303.
[35] Bahiraei, M., Heshmatian, S., Thermal performance and second law characteristics of two new microchannel heat sinks operated with hybrid nanofluid containing graphene-silver nanoparticles, Energy Conversations and Management, 168, 2018, 357-370.
[36] Bahiraei, M., Mazaheri, N., Application of a novel hybrid nanofluid containing graphene-platinum nanoparticles in a chaotic twisted geometry for utilization in miniature devices: thermal and energy efficacy considerations, International Journal of Mechanical Sciences, 138, 2018, 337-349.
[37] Han, B., Li, Z., Zhang, L., Zeng, S., Yu, X., Ou, J., Reactive powder concrete reinforced with nano SiO2-coated TiO2, Construction and Building Materials, 148, 2017, 104-112.
[38] Kuttan, B.A., Manjunatha, S., Jayanthy, S., Gireesha B.J., Archana, M., Effect of variable viscosity on Marangoni convective boundary layer flow of nanofluid in the presence of mixed convection, Journal of Nanofluids, 8(4), 2019.
[39] Manjunatha, S., Gireesha, B.J., Effects of variable viscosity and thermal conductivity on MHD flow and heat transfer of a dusty fluid, Ain Shams Engineering Journal, 7(1), 2016, 505-515.
[40] Puneeth, V., Manjunatha, S., Makinde, O. D., Gireesha, B. J., Bioconvection of a radiating hybrid nanofluid past a thin needle in the presence of heterogeneous–homogeneous chemical reaction, Journal of Heat Transfer, 2021, 143(4), 042502.
[41] Hamza, M.H., Sidik, N.A.C., Ken, T.L., Mamat, R., Najafi, G., Factors affecting the performance of hybrid nanofluids: a comprehensive review, International Journal of Heat and Mass Transfer, 115, 2017, 630-646.
[42] Khan, W.A., Pop, I., Boundary layer flow of a nanofluid past a stretching sheet, International Journal of Heat and Mass transfer, 53(11-12), 2010, 2477-2483.
[43] Ghalambaz, M., Sheremet, M.A., Mehryan, S.A.M., Kashkooli, F.M., Pop, I., Local thermal non-equilibrium analysis of conjugate free convection within a porous enclosure occupied with Ag–MgO hybrid nanofluid, Journal of Thermal Analysis and Calorimetry, 135(2), 2019, 1381-1398.
[44] Gorla, R.S.R., Sidwai, I., Free convection on a vertical surface with suction and blowing, Applied Scientific Research, 52(3), 1994, 247-257.