Skip Navigation Links
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


Thermal Stratification Effects on Electromagnetic Ferrofluid Flow over an Unsteady Stretching Sheet

Discontinuity, Nonlinearity, and Complexity 11(4) (2022) 613--627 | DOI:10.5890/DNC.2022.12.004

V. Loganayagi, Peri K. Kameswaran, K. Hemalatha

Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, India

Department of Mathematics, V.R. Siddartha Engineering College, Vijayawada 520007, India

Download Full Text PDF

 

Abstract

The concern of the present article is to look at the impacts of thermal stratification and heat transfer on two dimensional, laminar, incompressible nanofluid flow over an unsteady stretching sheet.~The influence of thermal stratification added to the energy equation and temperature boundary condition.~The nanoparticles sorted out here are Barium, and Zinc Ferrite.~The base liquid as taken as water.~The governing system of equations is reduced in the system of nonlinear differential equations and solved numerically.~The influence of the thermal stratification parameter, electric field parameter on temperature, skin-friction, heat transfer rates has examined.~The comparison made with the available outcomes in the literature and present outcomes is adequate concurrence with the literature's findings for different estimations.~A bit of the results shows that with an increase in thermal stratification parameter temperature profile decreases; subsequently, heat transfer rate increases.~We also conclude an increase in the nanoparticle volume fraction that the heat transfer rate increases from Barium to Zinc ferrite.

References

  1. [1]  Raj, K. and Moskowitz, R. (1990), Commercial applications of ferrofluids, Journal of Magnetism and Magnetic Materials, 85(1-3), 233-245.
  2. [2]  Hussain, S., Oztop, H.F., Qureshi, M.A., and Abu-Hamdeh, N. (2020), Magnetohydrodynamic flow and heat transfer of ferrofluid in a channel with non-symmetric cavities, J. Therm Anal Calorim, 140, 811-823.
  3. [3]  Muhammad, N., Nadeem, S., and Mustafa, M.T. (2019), Impact of magnetic dipole on a thermally stratified ferrofluid past a stretchable surface, Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 233(2), 177-183.
  4. [4]  Khan, H., Haneef, M., Shah, Z., Islam, S., Khan, W., and Muhammad, S. (2018), The combined magneto hydrodynamic and electric field effect on an unsteady Maxwell nanofluid flow over a stretching surface under the influence of variable heat and thermal radiation, Appl. Sci., 8(2), 160.
  5. [5]  EL-Kabeir, S.M.M., EL-Zahar, E.R., Modather, M., Gorla, R.S.R., and Rashad, A.M. (2019), Unsteady MHD slip flow of a ferrofluid over an impulsively stretched vertical surface, AIP Advances, 9, 045112.
  6. [6]  Tarakaramu, N. and Satya Narayana, P.V. (2017), Unsteady MHD nanofluid flow over a stretching sheet with chemical reaction, IOP Conf. Ser.: Mater. Sci. Eng., 263(6), 062030.
  7. [7]  Vinod Kumar, G., Varma, S.V.K., and Kumar, R.V.M.S.S.K. (2019), Unsteady three-dimensional MHD Nanofluid flow over a stretching sheet with variable wall thickness and slip effects, International Journal of Applied Mechanics and Engineering, 24(3), 709-724.
  8. [8]  Daba, M. and Devaraj, P. (2016), Unsteady boundary layer flow of a nanofluid over a stretching sheet with variable fluid properties in the presence of thermal radiation, Thermophys. Aeromech., 23, 403-413.
  9. [9]  Ali, R., Salleh, Z., and Gul, T. (2019), The impact of the magnetic field and viscous dissipation on the thin film unsteady flow of GO-EG/GO-W nanofluids, J. Phys.: Conf. Ser., 1336(1), 012031.
  10. [10]  Khan, Z.H., Khan, W.A., Qasim, M., and Shah, I.A. (2014), MHD stagnation point ferrofluid flow and heat transfer toward a stretching sheet, IEEE Transactions on Nanotechnology, 13(1), 35-40.
  11. [11]  Sha, Z., Dawar, A., Alzahrani, E.O., Kumam, P., Jabar Khan, A., and Islam, S. (2019), Hall effect on couple stress 3D nanofluid flow over an exponentially stretched surface with cattaneo christov heat flux model, IEEE Access, 7, 64844-64855.
  12. [12]  Abraham, A. and Rani Titus, L.S. (2011), Boundary layer flow of ferrofluid over a stretching sheet in the presence of heat source/sink, Mapana J Sci., 10(1), 14-24.
  13. [13]  Aliy, G. and Kishan, N. (2018), Effect of electric field on MHD flow and heat transfer characteristics of williamson nanofluid over a heated surface with variable thickness. OHAM Solution, Journal of Advances in Mathematics and Computer Science, 30(1), 1-23.
  14. [14]  Daniel, Y.S., Aziz, Z.A., Ismail, Z., and Salah, F. (2018), Impact of thermal radiation on electrical MHD flow of nanofluid over nonlinear stretching sheet with variable thickness, Alexandria Engineering Journal, 57(3), 2187-2197.
  15. [15]  Chakrabarti, A. and Gupta, A.S. (1979), Hydromagnetic flow and heat transfer over a stretching sheet, Quarterly of Applied Mathematics, 37(1), 73-78.
  16. [16]  Muhammad, N., Nadeem, S., and Haq, R.U. (2017), Heat transport phenomenon in the ferromagnetic fluid over a stretching sheet with thermal stratification, Results in Physics, 7, 854-861.
  17. [17]  Rosmila, A.B., Kandasamy, R., and Muhaimin, I. (2012), Lie symmetry group transformation for MHD natural convection flow of nanofluid over linearly porous stretching sheet in presence of thermal stratification, Appl. Math. Mech.-Engl. Ed., 33(5), 593-604.
  18. [18]  Mukhopadhyay, S. (2013), MHD boundary layer flow and heat transfer over an exponentially stretching sheet embedded in a thermally stratified medium, Alexandria Engineering Journal, 52(3), 259-265.
  19. [19]  Alarifi, I.M., Abokhalil, A.G., Osman, M., Lund, L.A., Ayed, M.B., Belmabrouk, H., and Tlili, I. (2019), MHD flow and heat transfer over vertical stretching sheet with heat sink or source effect, Symmetry, 11(3), 297.
  20. [20]  Daniel, Y.S., Aziz, Z.A., Ismail, Z., and Salah, F. (2018), Thermal stratification effects on MHD radiative flow of nanofluid over nonlinear stretching sheet with variable thickness, Journal of Computational Design and Engineering, 5(2), 232-242.
  21. [21]  Nadeem, S., Raishad, I., Muhammad, N., and Mustafa, M.T. (2017), Mathematical analysis of ferromagnetic fluid embedded in a porous medium, Results in Physics, 7, 2361-2368.
  22. [22]  Sheikholeslami, M., Shah, Z., Tassaddiq, A., Shafee, A., and Khan, I. (2019), Application of electric field for augmentation of ferrofluid heat transfer in an enclosure including double moving walls, IEEE Access, 7, 21048-21056.
  23. [23]  Khan, U., Abbasi, A., Ahmed, N., and Mohyud-Din, S.T. (2017), Flow of magneto-nanofluid over a thermally stratified bi-directional stretching sheet in the presence of Ohmic heating: A numerical study of particle shapes, Engineering Computations, 34(8), 2499-2513.
  24. [24]  Sharma, R., Ishak, A., and Pop, I. (2013), Partial slip flow and heat transfer over a stretching sheet in a nanofluid, Mathematical Problems in Engineering, 724547, 1-7.
  25. [25]  Khan, I., Malik, M.Y., Hussain, A., and Salahuddin, T. (2017), Effect of homogenous-heterogeneous reactions on MHD prandtl fluid flow over a stretching sheet, Results in Physics, 7, 4226-4231.
  26. [26]  Nayak, M.K., Shaw, S., and Chamkha, A.J. (2019), 3D MHD Free convective stretched flow of a radiative nanofluid inspired by variable magnetic field, Arabian Journal for Science and Engineering, 44, 1269-1282.
  27. [27]  Shaw, S., Sen, S.S., Nayak, M.K., and Makinde, O.D. (2019), Boundary layer non-linear convection flow of Sisko-Nanofluid with melting heat transfer over an inclined permeable electromagnetic sheet, Journal of Nanofluids, 8(5), 917-928.
  28. [28]  Brinkman, H.C. (1952), The viscosity of concentrated suspensions and solution, J. Chem. Phys., 20(4), 571-581.
  29. [29]  Maxwell Garnett, J.C. (1904), Colours in metal glasses and in metallic films, Philos, Trans. R. Soc. Lond. A, 203, 385-420.
  30. [30]  Guerin, C.A., Mallet, P., and Sentenac, A. (2006), Effective-medium theory for finite-size aggregates, J. Opt. Soc. Am. A, 23(2), 349-358.
  31. [31]  Daniel, Y.S., Abdul Aziz, Z., Ismail, Z., and Salah, F. (2018), Electrical unsteady MHD natural convection flow of nanofluid with thermal stratification and heat generation/absorption, MATEMATIKA, 34(2), 393-417.
  32. [32]  Ibrahim, W. and Shankar, B. (2013), MHD boundary layer flow and heat transfer of a nanofluid past a permeable stretching sheet with velocity, thermal and solutal slip boundary conditions, Computers $\&$ Fluids, 75, 1-10.