Influence of Magnetic Wire Positions on free convection of Fe3O4-Water nanofluid in a Square Enclosure Utilizing with MAC Algorithm

Document Type : Research Paper


1 Department of Mathematics, Sreenivasa Institute of Technology and Management studies

2 Department of Applied Mathematics, Sri Padmavati Mahila Visvavidyalayam, Tirupati

3 Department of Applied Mathematics, Sri Padmavati Mahila Visvavidyalayam Tirupati.

4 Department of Mathematics, SAS VIT University, Vellore.

5 Department of Mathematics, Sir Vishveshwaraiah Institute of Science and Technology Madanapalle.


The augment of heat transfer and fluid of buoyancy-driven flow of Fe3O4-Water nanofluid in a square cavity under the influence of an external magnetic field is studied numerically. Cold temperature is applied on the side (vertical) walls and high temperature is imposed on the bottom wall while the top wall is kept at thermally insulated. The governing non-dimensional differential equations are solved using Marker and Cell (MAC) Algorithm. The developed MATLAB code is validated with previous literature and it gives good agreement. The effects of Rayleigh number Ra, Prandtl number Pr and Hartmann number Ha on the flow and heat transfer characteristics are analyzed. Results indicate that the temperature gradient is an increasing function of the buoyancy force. The heat transfer characteristics and flow behavior are presented in the form of streamlines and isotherms. The position of magnetic wire is played a vital role in controlling of heat transfer rate.


  1. E. Rosenzweig, Ferrohydrodynamics, Dover Publications, Mineola, New York, 1997.
  2. Odenbach, Colloidal Magnetic Fluids: Basics Development and Application of Ferrofluids, Springer, Berlin, Heidelberg, 2009.
  3. Abareshi, E.K. Goharshadi, S. MojtabaZebarjad, H. KhandanFadafan, A. Youssefi, Fabrication, characterization and measurement of thermal conductivity of Fe3O4 nanofluids, J. Magn. Magn. Mater. 322 (2010) 3895– 3901.
  4. Mitamura, S. Arioka, D. Sakota, K. Sekine, M. Azegami, Application of a magnetic fluid seal to rotary blood pumps, J. Phys.-Condens. Mater. 20 (2008) 204145.
  5. Nkurikiyimfura, Y. Wang, Z. Pan, Heat transfer enhancement by magnetic nanofluids - a review, Renewable Sustainable Energy Rev. 21 (2013) 548–561.
  6. Baranwal, T.S. Deshmukh, MR-fluid technology and its application-a review, Int. J.Emerging Technol. Adv. Eng. 2 (2012) 563–569.
  7. Yamaguchi, I. Kobori, Y. Uehata, K. Shimada, Natural convection of magnetic fluid in a rectangular box, J. Magn. Magn. Mater. 20 (1999) 264–267.
  8. Yamaguchi, Z. Zhang, S. Shuchi, K. Shimada, Heat transfer characteristics of magnetic fluid in a partitioned rectangular box, J. Magn. Magn. Mater. 252 (2002) 203–205.
  9. P. Bednarz, C. Lei, J.C. Patterson, H. Ozoe, Effects of atransverse orizontal magnetic field on natural convection of a paramagnetic fluid in a cube, Int. J. Therm. Sci. 48 (2009) 26–33.
  10. Li, Y. Xuan, Experimental investigation on heat transfer characteristics of magnetic fluid flow around a fine wire under the influence of an external magnetic field, Exp. Therm. Fluid Sci. 33 (2009) 591–596.
  11. N. Afifah, S. Syahrullail, N.A. Che Sidik, Natural convection of alumina-distilled water nanofluid in cylindrical enclosure: an experimental study, J. Adv. Res. FluidMech. Therm. Sci. 12 (1) (2015) 1–10.
  12. M'hamed, N.A. Sidik, M.F. Akhbar, R. Mamat, G. Najafi, Experimental study on thermal performance of MWCNT nanocoolant in PeroduaKelisa 1000 cc radiator system, Int. Communication Heat Mass Transf. 24 (May 2016).
  13. A. Che Sidik, O.A. Alawi, Computational investigations on heat transfer enhancement using nanorefrigerants, J. Adv. Res. Des. 1 (2014) 35–41.
  14. A. Khattak, A. Mukhtar, S. Kamran Afaq, Application of nano-fluids as coolant in heat exchangers: a review, J. Adv. Rev. Sci. Res. 22 (1) (2016) 1–11.
  15. S. Nor Azwadi, I.M. Adamu, M.M. Jamil, Preparation methods and thermal performance of hybrid nanofluids, J. Adv. Rev. Sci. Res. 24 (1) (2016) 13–23.
  16. K. Sinz, H.E. Woei, M.N. Khalis, S.I. Ali Abbas, Numerical study on turbulent force convective heat transfer of hybrid nanofluid, Ag/HEG in a circular channel with constant heat flux. (2016), J. Adv. Res. Fluid Mech. Therm. Sci. 24 (2016) 1–11.
  17. G. Jehad, G.A. Hashim, Numerical prediction of forced convective heat transfer and friction factor of turbulent nanofluid flow through straight channels, J. Adv. Res. Fluid Mech. Therm. Sci. 1 (2014) 1–10.
  18. K. Lee, The use of nanofluids in domestic water heat exchanger, J. Adv. Res. Appl. Mech. 3 (2014) 9–24.
  19. B. Abubakar, N.A. Che Sidik, Numerical prediction of laminar nanofluid flow in rectangular microchannel heat sink, J. Adv. Res. Fluid Mech. Therm. Sci. 7 (2015) 29–38.
  20. Khanafer K, Vafai K, Lightstone M. Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. International Journal of Heat and Mass Transfer 2003; 46: 3639–53.
  21. Jang SP, Choi SUS. Free convection in a rectangular cavity (Benard convection) with nanofluids, Proceedings of IMECE04. Anaheim, California, USA; 2004. pp. 1–7.
  22. Floriana D. Stoian and Sorin Holotescu, experimental study of natural convection enhancement using a Fe3O4-water based magnetic nanofluid, journal of Nanoscience and Nanotechnology, 12 (2012) 8211-8214.
  23. Gul A, Khan I, Shafie S, Khalid A, Khan A (2015) Heat Transfer in MHD Mixed Convection Flow of a Ferrofluid along a Vertical Channel. PLoS ONE 10(11): e0141213. doi:10.1371/journal.pone.0141213
  24. Nader Ben-Cheikh, Ali J. Chamkha, Brahim Ben-Beya, Taieb Lili, Natural convection of water - Based nanofluid in a square enclosure with non-uniform heating of bottom wall, Journal of Modern Physics, 2013, 4, 147-159.
  25. Omid Ghaffarpasand, Numerical study of MHD natural convection inside a sinusoidally heated lid-driven cavity filled with Fe3O4 -water nanofluid in the presence of Joule heating, Applied Mathematical Modelling 40 (2016) 9165–9182.
  26. Neshat Rahimpour, Mostafa Keshavarz Moraveji, Free convection of water–Fe3O4 nanofluid in an inclined cavity subjected to a magnetic field: CFD modeling, sensitivity analysis, Advanced Powder Technology 28 (2017) 1573–1584.
  27. Abedini, T. Armaghani, Ali J. Chamkha, MHD free convection heat transfer of a water– Fe3O4 nanofluid in a baffled C-shaped enclosure, Journal of Thermal Analysis and Calorimetry, (2019) 135: 685-695. 
  28. Keshavarz Moraveji, M,Hejazian M., Natural convection in a rectangular enclosure containing an oval-shaped heat source and filled with Fe3O4/water nanofluid. Int. Commun. Heat Mass Transf., 2013; 44:135–46.
  29. Rosensweig RE., Ferrohydrodynamics., London: Cambridge University Press; 1985.
  30. Hiegeister R, Andra W, Buske N, Hergt R, Hilger I, Richter U, et al. Application of magnetite ferrofluids for hyperthermia. J MagnMagn Mater 1999; 201:420–2.
  31. Nakatsuka K, Jeyadevan B, Neveu S, Koganezawa H. The magnetic fluid for heat transfer applications. J MagnMagn Mater 2002; 252:360–2.
  32. Shuchi S, Sakatani K, Yamaguchi H. An application of a binary mixture of magnetic fluid for heat transport devices. J MagnMagn Mater 2005; 289:257– 9.
  33. Sheikholeslami, D.D. Ganji, Free convection of Fe3O4-water nanofluid under the influence of an external magnetic source, J. Mol. Liq. 229 (2017) 530–540.
  34. Sheikholeslami, K. Vajravelu, Nanofluid flow and heat transfer in a cavity with variable magnetic field, Appl. Math. Comput. 298 (2017) 272–282.
  35. Mohsen Sheikholeslami, DavoodDomiriGanji, Numerical investigation of nanofluid transportation in a curved cavity in existence of magnetic source,Chem. Phys. Lett. 667 (2017) 307–316.
  36. Sheikholeslami, Numerical simulation of magnetic nanofluid natural convection in porous media, Phys. Lett. A 381 (2017) 494–503.
  37. Kandelousi M. Sheikholeslami, Effect of spatially variable magnetic field on ferrofluid flow and heat transfer considering constant heat flux boundary condition, Euro. Phys. J. Plus (2014) 129–248.
  38. Sheikholeslami, M.M. Rashidi, Effect of space dependent magnetic field on free convection of Fe3O4-water nanofluid, J. Taiw. Inst. Chem. Eng. 56 (2015) 6–15.
  39. Venkatadri, S. GouseMohiddin and M. Suryanarayana Reddy, Numerical Analysis of Unsteady MHD Mixed Convection Flow in a Lid-Driven Square Cavity with Central Heating on Left Vertical Wall, Applications of Fluid Dynamics, Lecture Notes in Mechanical Engineering, Chapter 26 (2018) 355-370.
  40. B MD Hidayathulla Khan, K Venkatadri, O. Anwar Be ́g, V.Ramachandra Prasad, B. Mallikarjuna. ”Natural Convection in a Square Cavity with Uniformly Heated and/or Insulated Walls Using Marker-and-Cell Method” International Journal of Applied and Computational Mathematics, 4 (2018) 61.
  41. Venkatadri K, GouseMohiddin S, Suryanarayana Reddy M., Hydromagneto quadratic natural convection on a lid-driven square cavity with isothermal and a non-isothermal bottom wall, Engineering Computations, 34( 8) ( 2017 ) 2463-2478.
  42. Venkatadri, S. GouseMohiddin, M. Suryanarayana Reddy, Mathematical modeling of unsteady MHD double-diffusive natural convection flow in a square cavity, Frontiers in Heat and Mass Transfer, 9 (2017) No.33.
  43. Tanmay Basak, S. Roy, A.R. Balakrishnan, Effects of thermal boundary conditions on natural convection flows within a square cavity, International Journal of Heat and Mass Transfer 49 (2006) 4525–4535.
  44. C. Wan, B. S. V. Patnaik, and G. W. Wei, A new benchmark quality solution for the buoyancy-driven cavity by discrete singular convolution, Numerical Heat Transfer, Part B, 2001,40, 199- 228.
  45. Hatami, J. Zhou, J. Geng, D. Jing, Variable magnetic field (VMF) effect on the heat transfer of a half-annulus cavity filled by Fe3O4-Water nanofluid under the constant heat flux, journal of Magnetism and Magnetic Materials, 451 (2018) 173-182.
Volume 51, Issue 2
December 2020
Pages 323-331
  • Receive Date: 09 September 2019
  • Accept Date: 18 December 2019