Skip to main content
SpringerLink
Log in

Flow and Thermal Fields of a Ferrofluid in Rectangular Enclosures with Two Heated Fins Under Effects of a Variable Electromagnetic Force-Dependent Viscosity

  • Research Article-Mechanical Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

Ferroconvective flow and thermal fields of Fe3O4–H2O ferrofluid that has a variable dynamic viscosity resulting from two heated fins within a rectangular enclosure have been examined. The dynamic viscosity is assumed as a function of a variable magnetic field that is produced from a magnetic wire below the bottom wall of the domain. The governing equations are formulated based on the principles of magnetohydrodynamic and the ferrohydrodynamics. The control volume solver is applied to solve the dimensionless system of the governing equations. The controlling parameters in this study are the Hartmann number Ha, the magnetic number Mn, the height of the fins H and the nanoparticles volume fraction ϕ. The obtained results revealed that the average Nusselt number is supported by 36.09% at ϕ = 0%, 35.83% at ϕ = 2%, 34.29% at ϕ = 5% and 48.15% at ϕ = 10% when height of the fins H is growing from 0 to 0.5. Also, as Ha is increased from 0 to 50, there is a reduction by 50% in values of the stream function obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Abbreviations

B :

Magnetic induction

c p :

Specific heat at constant pressure

Ec:

Eckert number

g :

Gravity acceleration

H :

Magnetic field strength

Ha:

Hartmann number

K :

Pyromagnetic coefficient

k :

Thermal conductivity

L :

Length

M :

Magnetization

Mn:

Magnetic number arising from FHD for the base fluid

Nu:

Nusselt number

P :

Pressure

Pr:

Prandtl number

Ra:

Rayleigh number

t :

Time

T :

Temperature

(u, v):

Velocity components in the x and y direction

(\( \bar{x}, \bar{y} \)):

Dimensional Cartesian coordinates

(x, y):

Dimensionless Cartesian coordinates

α :

Thermal diffusivity

β :

Coefficient of thermal expansion

σ :

Electrical conductivity

ϕ :

Volume fraction

δ :

Linear measure of the viscosity variations with the applied magnetic field

μ :

Dynamic viscosity

μ 0 :

Magnetic permeability of vacuum

μ f1 :

Viscosity of the ferrofluid

θ :

Dimensionless temperature

ρ :

Density

ω :

Dimensionless vorticity

c:

Cold

f:

Fluid

ff:

Ferrofluid

h:

Hot

P:

Nanoparticle

References

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

    Google Scholar 

  2. Hiegeister, R.; Andra, W.; Buske, N.; Hergt, R.; Hilger, I.; Richter, U.; Kaiser, W.: Application of magnetite ferrofluids for hyperthermia. J. Magn. Magn. Mater. 201, 420–422 (1999)

    Article  Google Scholar 

  3. Nakatsuka, K.; Jeyadevan, B.; Neveu, S.; Koganezawa, H.: The magnetic fluid for heat transfer applications. J. Magn. Magn. Mater. 252, 360–362 (2002)

    Article  Google Scholar 

  4. Aminfar, H.; Mohammadpourfard, M.; Ahangar Zonouzi, S.: Numerical study of the ferrofluid flow and heat transfer through a rectangular duct in the presence of a non-uniform transverse magnetic field. J. Magn. Magn. Mater. 327, 31–42 (2013)

    Article  Google Scholar 

  5. Sheikholeslami, M.; Abelman, S.: Numerical study of the effect of magnetic field on Fe3O4–water ferrofluid convection with thermal radiation. Eng. Comput. 35, 1855–1872 (2018)

    Article  Google Scholar 

  6. Asadi, A.; HosseinNezhad, A.; Sarhaddi, F.; Keykha, T.: Laminar ferrofluid heat transfer in presence of non-uniform magnetic field in a channel with sinusoidal wall: a numerical study. J. Magn. Magn. Mater. 471, 56–63 (2019)

    Article  Google Scholar 

  7. Gibanov, N.; Sheremet, M.; Oztop, H.; Al-Salem, K.: MHD natural convection and entropy generation in an open cavity having different horizontal porous blocks saturated with a ferrofluid. J. Magn. Magn. Mater. 452, 193–204 (2018)

    Article  Google Scholar 

  8. Astanina, M.; Sheremet, M.; Oztop, H.; Abu-Hamdeh, N.: MHD natural convection and entropy generation of ferrofluid in an open trapezoidal cavity partially filled with a porous medium. Int. J. Mech. Sci. 136, 493–502 (2018)

    Article  Google Scholar 

  9. Vaidyanathan, G.; Sekar, R.; Vasanthakumari, R.; Ramanathan, A.: The effect of magnetic field dependent viscosity on ferroconvection in a rotating sparsely distributed porous medium. J. Magn. Magn. Mater. 250, 65–76 (2002)

    Article  Google Scholar 

  10. Ramanathan, A.; Suresh, G.: Effect of magnetic field dependent viscosity and anisotropy of porous medium on ferroconvection. Int. J. Eng. Sci. 42, 411–425 (2004)

    Article  Google Scholar 

  11. Sunil, D.; Sharma, R.: The effect of magnetic field dependent viscosity on thermosolutal convection in a ferromagnetic fluid saturating a porous medium. Transp. Porous Media 60, 251–274 (2005)

    Article  MathSciNet  Google Scholar 

  12. Sunil, A.; Sharma, R.: The effect of magnetic field dependent viscosity on thermosolutal convection in ferromagnetic fluid. Appl. Math. Comput. 163, 1197–1214 (2005)

    MathSciNet  MATH  Google Scholar 

  13. Sunil, A.; Sharma, D.; Kumar, P.: Effect of magnetic field–dependent viscosity on thermal convection in a ferromagnetic fluid. Chem. Eng. Commun 195, 571–583 (2008)

    Article  Google Scholar 

  14. Sunil, A.; Sharma, R.; Shandil, U.: Gupta, Effect of magnetic field dependent viscosity and rotation on ferroconvection saturating a porous medium in the presence of dust particles. Int. Commun. Heat Mass Transf. 32, 1387–1399 (2005)

    Article  Google Scholar 

  15. Sunil, A.; Sharma, P.: Kumar, Effect of magnetic field dependent viscosity and rotation on ferroconvection in the presence of dust particles. Appl. Math. Comput. 182, 82–88 (2006)

    MathSciNet  MATH  Google Scholar 

  16. Ramn, P.; Bhandari, A.; Sharma, K.: Effect of magnetic field-dependent viscosity on revolving ferrofluid. J. Magn. Magn. Mater. 322, 3476–3480 (2010)

    Article  Google Scholar 

  17. Sheikholeslami, M.; Rashidi, M.; Hayat, T.; Ganji, D.: Free convection of magnetic nanofluid considering MFD viscosity effect. J. Mol. Liq. 218, 393–399 (2016)

    Article  Google Scholar 

  18. Kandelousi, M.S.: Effect of spatially variable magnetic field on ferrofluid flow and heat transfer considering constant heat flux boundary condition. Eur. Phys. J. Plus 129, 248–260 (2014)

    Article  Google Scholar 

  19. Sheikholeslami, M.; Rashidi, M.: Ferrofluid heat transfer treatment in the presence of variable magnetic field. Eur. Phys. J. Plus 130, 115–127 (2015)

    Article  Google Scholar 

  20. Sheikholeslamia, M.; Chamkha, A.: Flow and convective heat transfer of a ferro-nanofluid in a double-sided lid-driven cavity with a wavy wall in the presence of a variable magnetic field. Numer. Heat Transf. Part A 69, 1186–1200 (2016)

    Article  Google Scholar 

  21. Sheikholeslami, M.; Vajravelu, K.: Nanofluid flow and heat transfer in a cavity with variable magnetic field. Appl. Math. Comput. 298, 272–282 (2017)

    MathSciNet  MATH  Google Scholar 

  22. Gibanov, N.; Sheremet, M.; Oztop, H.; Nusier, O.: Convective heat transfer of ferrofluid in a lid-driven cavity with a heat-conducting solid backward step under the effect of a variable magnetic field. Numer. Heat Transf. Part A 72, 54–67 (2017)

    Article  Google Scholar 

  23. Hatami, M.; Zhou, J.; Geng, J.; Jing, D.: Variable magnetic field (VMF) effect on the heat transfer of a half annulus cavity filled by Fe3O4–water nanofluid under constant heat flux. J. Magn. Magn. Mater. 451, 173–182 (2018)

    Article  Google Scholar 

  24. Sheikholeslami, M.; Rashidi, M.; Ganji, D.: Numerical investigation of magnetic nanofluid forced convective heat transfer in existence of variable magnetic field using two phase model. J. Mol. Liq. 212, 117–126 (2015)

    Article  Google Scholar 

  25. Wankhade, P.A.; Kundu, B.; Das, R.: Establishment of non-fourier heat conduction model for an accurate transient thermal response in wet fins. Int. J. Heat Mass Transf. 126, 911–923 (2018)

    Article  Google Scholar 

  26. Das, R.; Kundu, B.: Direct and inverse approaches for analysis and optimization of fins under sensible and latent heat load. Int. J. Heat Mass Transf. 124, 331–343 (2018)

    Article  Google Scholar 

  27. Kundu, B.; Das, R.; Wankhade, P.A.; Lee, K.-S.: Heat transfer improvement of a wet fin under transient response with a unique design arrangement aspect. Int. J. Heat Mass Transf. 127, 1239–1251 (2018)

    Article  Google Scholar 

  28. Das, R.: A simplex search method for a conductive–convective fin with variable conductivity. Int. J. Heat Mass Transf. 54(23), 5001–5009 (2011)

    Article  Google Scholar 

  29. Das, R.; Kundu, B.: Forward and inverse nonlinear heat transfer analysis for optimization of a constructal t-shape fin under dry and wet conditions. Int. J. Heat Mass Transf. 137, 461–475 (2019)

    Article  Google Scholar 

  30. Hatami, M.: Numerical study of nanofluids natural convection in a rectangular cavity including heated fins. J. Mol. Liq. 233, 1–8 (2017)

    Article  Google Scholar 

  31. Ahmed, S.E.; Mansour, M.A.; Hussein, A.K.; Mallikarjuna, B.; Almeshaal, M.A.; Kolsi, L.: MHD mixed convection in an inclined cavity containing adiabatic obstacle and filled with cu–water nanofluid in the presence of the heat generation and partial slip. J. Ther. Anal. Calorim. 139, 1443–1460 (2019)

    Article  Google Scholar 

  32. Ahmed, S.E.; Rashed, Z.Z.: MHD natural convection in a heat generating porous medium-filled wavy enclosures using buongiorno’s nanofluid model. Case Stud. Ther. Eng. 14, 100430 (2019)

    Article  Google Scholar 

  33. Rashed, Z.Z.; Ahmed, S.E.; Sheremet, M.: MHD buoyancy flow of nanofluids over an inclined plate immersed in uniform porous medium in the presence of solar radiation. J. Mech. 35(4), 563–576 (2019). https://doi.org/10.1017/jmech.2018.40

    Article  Google Scholar 

  34. Hussain, S.; Ahmed, S.E.: Unsteady MHD forced convection over a backward facing step including a rotating cylinder utilizing fe3o4-water ferrofluid. J. Magn. Magn. Mater. 484, 356–366 (2019)

    Article  Google Scholar 

  35. Rashad, A.M.; Gorla, R.S.R.; Mansour, M.A.; Ahmed, S.E.: Magnetohydrodynamic effect on natural convection in a cavity filled with a porous medium saturated with nanofluid. J. Porous Media 20(4), 363–379 (2017)

    Article  Google Scholar 

  36. Mahdy, A.; Ahmed, S.E.: Unsteady MHD convective flow of non-newtonian casson fluid in the stagnation region of an impulsively rotating sphere. J. Aerosp. Eng. 30(5), 04017036 (2017)

    Article  Google Scholar 

  37. Ahmed, S.E., Mansour, M.A., Rashad, A.M., Salah, T.: MHD natural convection from two heating modes in fined triangular enclosures filled with porous media using nanofluids. J. Ther. Anal. Calorim. 139, 3133–3149 (2020)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, Faculty of Science and Arts, Jouf University, Qurayyat, Saudi Arabia

    Z. Z. Rashed

Authors
  1. Z. Z. Rashed
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Z. Z. Rashed.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rashed, Z.Z. Flow and Thermal Fields of a Ferrofluid in Rectangular Enclosures with Two Heated Fins Under Effects of a Variable Electromagnetic Force-Dependent Viscosity. Arab J Sci Eng 45, 5459–5469 (2020). https://doi.org/10.1007/s13369-020-04440-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-020-04440-7

Keywords

Search

Navigation