MHD Flow and Heat Transfer of a Ternary Hybrid Ferrofluid Over a Stretching/Shrinking Porous Sheet with the Effects of Brownian Diffusion and Thermophoresis

  • Michael I. Kopp Institute for Single Cristals, Nat. Academy of Science Ukraine, Kharkіv, Ukraine https://orcid.org/0000-0001-7457-3272
  • Volodymyr V. Yanovsky Institute for Single Cristals, Nat. Academy of Science Ukraine, Kharkiv,Ukraine; V.N. Karazin Kharkiv National University, 4, Kharkiv, Ukraine https://orcid.org/0000-0003-0461-749X
  • Thippeswamy Anusha Department of Mathematics, Shivagangotri, Davangere University, Davangere, India https://orcid.org/0000-0003-0950-6481
  • Ulavathi S. Mahabaleshwar Department of Mathematics, Shivagangotri, Davangere University, Davangere, India https://orcid.org/0000-0003-1380-6057
Keywords: ternary hybrid ferrofluid, stretching/shrinking, heat and mass transfer, mass transpiration, magnetic field

Abstract

In this paper, the magnetohydrodynamic (MHD) flow of a ternary hybrid ferrofluid over a stretching/shrinking porous sheet in the presence of radiation and mass transpiration is studied. The ternary hybrid nanofluid is formed by suspending three types of nanoparticles for enhancing heat transfer. The nanoparticles of copper, (Cu) iron oxide (Fe3O4), and cobalt ferrite (CoFe2O4) are suspended in water in this study, producing in the combination Cu-Fe3O4-CoFe2O4-H2O. Brownian motion and thermophoresis are integrated into the ternary hybrid ferrofluid model. Similarity transformations convert the governing partial differential equations into ordinary differential equations. The boundary value problem (BVP) is used in the Maple computer software to solve transformed equations numerically. The computed results for relevant parameters such as velocity profile, temperature profile, skin friction coefficient, local Nusselt and Sherwood numbers are visually shown and explained in detail.

Downloads

Download data is not yet available.

References

J. C. Maxwell, A Treatise on Electricity and Magnetism (Clarendon, Oxford, 1873)

S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, in: Development and applications of Non-Newtonian flows, edited by D.A. Signier and H.P. Wang, Vol. 66, (ASME, New York, 1995) pp. 99-105.

B.C. Sakiadis, “Boundary layer behaviour on continuous solid surfaces: I. boundary layer equations for two-dimensional and axisymmetric flow”, AIChE J. 7, 26-28 (1961). https://doi.org/10.1002/aic.690070108

B.C. Sakiadis, “Boundary layer behaviour on continuous solid surfaces: II. the boundary layer on a continuous flat surface”, AIChE J. 7, 221-225 (1961), https://doi.org/10.1002/aic.690070211

L.J. Crane, “Flow past a Stretching Plate”, Z. Angrew. Math. Phys. 21, 645-647 (1970). https://doi.org/10.1007/BF01587695

E.H. Aly, and I. Pop, “MHD flow and heat transfer near stagnation point over a stretching/shrinking surface with partial slip and viscous dissipation: Hybrid nanofluid versus nanofluid”, Powder Technol. 367, 192-205 (2020). https://doi.org/10.1016/j.powtec.2020.03.030

U. Khan, A. Shafiq, A. Zaib, and D. Baleanu, “Hybrid nanofluid on mixed convective radiative flow from an irregular variably thick moving surface with convex and concave effects”, Case stud. Therm. Eng. 21, 100660 (2020). https://doi.org/10.1016/j.csite.2020.100660

A. Jamaludin, K. Naganthran, R. Nazar, and I. Pop, “MHD mixed convection stagnation-point flow of Cu-Al2O3/water hybrid nanofluid over a permeable stretching/shrinking surface with heat source/sink”, Euro. J. Mech. B/Fluids, 84, 71-80 (2020). https://doi.org/10.1016/j.euromechflu.2020.05.017

U.S. Mahabaleshwar, A.B. Vishalakshi, and H.I. Andersson, “Hybrid nanofluid flow past a stretching/shrinking sheet with thermal radiation and mass transpiration”, Chinese Jour. Phys. 75, 152-168 (2022). https://doi.org/10.1016/J.CJPH.2021.12.014

T. Anush, U.S. Mahabaleshwar, and Y. Sheikhnejad, “An MHD of Nanofluid Flow Over a Porous Stretching/Shrinking Plate with Mass Transpiration and Brinkman Ratio”, Transp. Porous Med. 142, 333-352 (2021). https://doi.org/10.1007/s11242-021-01695-y

K.E. Aslani, U.S. Mahabaleshwar, J. Singh, I.E. Sarris, “Combined effect of radiation and inclined MHD flow of a micro polar fluid over a porous stretching/shrinking sheet with mass transpiration”, Int. J. Appl. Comput. Math. 7, 1-21 (2021). https://doi.org/10.1007/s40819-021-00987-7

U.S. Mahabaleshwar, K.N. Sneha, and H.N. Haung, “An effect of MHD and radiation on CNTs-water based nanofluids due to a stretching sheet in a Newtonian fluid”, Case Stud. Therm. Eng. 28, 101462 (2021). https: //doi.org/10.1016/j.csite.2021.101462

R.E. Rosensweig, Ferrohydrodynamics, (Cambridge University Press, Cambridge, 1985)

Y.M. Chu, S. Bilal, and M.R. Hajizadeh, “Hybrid ferrofluid along with MWCNT for augmentation of thermal behavior of fluid during natural convection in a cavity”, Math. Methods Appl. Sci. 2020, 1-12 (2020). https://doi.org/10.1002/mma.6937

K.A. Kumar, N. Sandeep, V. Sugunamma, and I.L. Animasaun, “Effect of irregular heat source/sink on the radiative thin film flow of MHD hybrid ferrofluid”, J. Therm. Anal. Calorim. 139, 2145-2153 (2020). https://doi.org/10.1007/s10973-019-08628-4

I. Tlili, M.T. Mustafa, K.A. Kumar, and N. Sandeep, “Effect of asymmetrical heat rise/fall on the film flow of magnetohydrodynamic hybrid ferrofluid”, Sci. Rep. 10, 6677 (2020). https://doi.org/10.1038/s41598-020-63708-y

N.S. Anuar, N. Bachok, and I. Pop, “Influence of MHD Hybrid Ferrofluid Flow on Exponentially Stretching/Shrinking Surface with Heat Source/Sink under Stagnation Point Region”, Mathematics, 9, 2932 (2021). https://doi.org/10.3390/math9222932

L.A. Lund, Z. Omar, J. Raza, and I. Khan, “Magnetohydrodynamic flow of Cu-Fe3O4/H2O hybrid nanofluid with effect of viscous dissipation: Dual similarity solutions”, J. Therm. Anal. Calorim. 143, 915-927 (2021). https://doi.org/10.1007/s10973-020-09602-1

L.S. Sundar, K.V.V.C. Mouli, Z. Said, and A.C.M. Sousa, “Heat transfer and second law analysis of ethylene glycol-based ternary hybrid nanofluid under laminar flow”, J. Therm. Sci. Eng Appl. 13, 1-15 (2021). https://doi.org/10.1115/1.4050228

U. Khan, and Z. Mahmood, “MHD Stagnation Point Flow of Ternary Hybrid Nanofluid Flow over a Stretching/Shrinking Cylinder with Suction and Ohmic Heating”, Preprint, (2022). https://www.authorea.com/doi/full/10.22541/au.164873383.38887373

G.K. Ramesh, J.K. Madhukesh, S.A. Shehzad, and A. Rauf, “Ternary nanofluid with heat source/sink and porous medium effects in stretchable convergent/divergent channel”, Proc. Inst. Mech. Eng. E: J. Process Mech. Eng. 2022, 1-10 (2022). https://doi.org/10.1177/09544089221081344

I.L. Animasaun, S.J. Yook, T. Muhammad, and A. Mathew, “Dynamics of ternary-hybrid nanofluid subject to magnetic flux density and heat source or sink on a convectively heated surface”, Surf. Interfaces 28, 101654 (2022). https://doi.org/10.1016/j.surfin.2021.101654

S. Manjunatha, V. Puneeth, B.J. Gireesha, and A.J. Chamkha, “Theoretical Study of Convective Heat Transfer in Ternary Nanofluid Flowing past a Stretching Sheet.” J. Appl. Comput. Mech. 8, 1279-1286 (2022). https://doi.org/10.22055/JACM.2021.37698.3067

N.L. Aleng, N. Bachok, and N.M. Arifin, “Flow and Heat Transfer of a Nanofluid over an Exponentially Shrinking Sheet”, Indian J. Sci. Technol. 8, 1-6 (2015). https://doi.org/10.17485/ijst/2015/v8i31/87246

J. Raza, A.M. Rohni, Z. Omar, and M. Awais, “Rheology of the Cu-H2O nanofluid in porous channel with heat transfer: Multiple solutions” Phys. E: Low-Dimens. Syst. Nanostructures, 86, 248-252 (2017). https://doi.org/10.1016/j.physe.2016.10.038

B. Takabi, and S. Salehi, “Augmentation of the heat transfer performance of a sinusoidal corrugated enclosure by employing hybrid nanofluid.” Adv. Mech. Eng. 6, 147059 (2014). https://doi.org/10.1155/2014/147059

R.S.R. Gorla, S. Siddiqa, M.A. Mansour, A.M. Rashad, and T. Salah, “Heat source/sink effects on a hybrid nanofluid-filled porous cavity”, J. Thermophys. Heat Transf. 31, 847-857 (2017). https://doi.org/10.2514/1.T5085

E. Magyari, and A.J. Chamkha, “Exact analytical results for the thermosolutal mhd marangoni boundary layers”, Int. J. Therm. Sci. 47, 848-857 (2008). https://doi.org/10.1016/j.ijthermalsci.2007.07.004

P.G. Siddheshwar, and U.S. Mahabaleswar, “Effects of radiation and heat source on MHD flow of a viscoelastic liquid and heat transfer over a stretching sheet”, Int. J. Non-Linear Mech. 40, 807-820 (2005). https://doi.org/10.1016/j.ijnonlinmec.2004.04.006

A. Alam, D.N.K. Marwat, and A. Ali, “Flow of nano-fluid over a sheet of variable thickness with non-uniform stretching (shrinking) and porous velocities”, Adv. Mech. Eng. 13, 1-16 (2021). https://doi.org/10.1177/16878140211012913

Published
2023-03-02
Cited
How to Cite
Kopp, M. I., Yanovsky, V. V., Anusha, T., & Mahabaleshwar, U. S. (2023). MHD Flow and Heat Transfer of a Ternary Hybrid Ferrofluid Over a Stretching/Shrinking Porous Sheet with the Effects of Brownian Diffusion and Thermophoresis. East European Journal of Physics, (1), 7-18. https://doi.org/10.26565/2312-4334-2023-1-01