Skip to main content
SpringerLink
Log in

Ferrofluid heat transfer treatment in the presence of variable magnetic field

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

In this paper, the Control Volume-based Finite Element Method (CVFEM) is applied to simulate Fe3O4 -water nanofluid mixed convection heat transfer in a lid-driven semi annulus in the presence of a non-uniform magnetic field. The calculations were performed for different governing parameters, namely, Richardson number, viscosity parameter, nanoparticle volume fraction, magnetic number and Hartmann number. Results show that the Nusselt number has a direct relationship with Richardson number and nanoparticle volume fraction, while it has a reverse relationship with Hartmann number and magnetic number. Also, it can be found that the Nusselt number increases by considering magnetic-field-dependent viscosity.

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

Similar content being viewed by others

Abbreviations

B :

Magnetic induction (= μ 0H) [T]

C p :

Specific heat at constant pressure [J/KgK]

Ec :

Eckert number (= (μ f α f )/[(ρC P ) f ΔT L 2])

Gr f :

Grashof number

H x , H y :

Components of the magnetic field intensity

H :

The magnetic field strength [T]

Ha :

Hartmann number \(\left( { = \mu _0 H_0 L\sqrt {\sigma _f /\mu _f } } \right)\)

Mn F :

Magnetic number arising from FHD (=μ 0 H 20 K′(T h − T c )/(ρ f U 2lid ))

M :

Magnetization \(\left( { = K'\bar H\left( {T'_c - T} \right)} \right)\)

Nu loc :

Local Nusselt number

Nu ave :

Average Nusselt number

Pr:

Prandtl number (= ν f /α f )

T :

Fluid temperature

T′ c :

Curie temperature [K]

u, v :

Velocity components in the x-direction and y-direction [m/s]

U, V :

Dimensionless velocity components in the X-direction and Y-direction [m/s]

x, y :

Space coordinates [m]

X, Y :

Dimensionless space coordinates [m]

r :

Non-dimensional radial distance [m]

k :

Thermal conductivity [W/m · k]

L :

Gap between inner and outer boundary of the enclosure L = r out − r in = r in

\(\vec g\) :

Gravitational acceleration vector [m/s2]

Ri :

Richardson number (= Gr/Re2)

ζ :

Angle measured from the lower right plane

α :

Thermal diffusivity [m2/s]

φ :

Volume fraction

γ′:

Magnetic field strength at the source

ε 1 :

Temperature number (= T 1/ΔT)

σ :

Electrical conductivity [(Ω · m)−1]

μ :

Dynamic viscosity [kg/ms]

μ 0 :

Magnetic permeability of vacuum (= 4π × 10−7 Tm/A)

ν :

Kinematic viscosity [m2/s]

ψ and Ψ :

Stream function and dimensionless stream function

Θ:

Dimensionless temperature

ρ :

Fluid density [Kg/m3]

β :

Thermal expansion coefficient [1/K]

c :

Cold

h :

Hot

ave:

Average

nf :

Nanofluid

f :

Base fluid

s :

Solid particles

in:

Inner

out :

Outer

References

  1. Mohammad Hossein Abolbashari, Navid Freidoonimehr, Foad Nazaria, Mohammad Mehdi Rashidi, Powder Technol. 267, 256 (2014).

    Article  Google Scholar 

  2. A. Malvandi, D.D. Ganji, Powder Technol. 263, 37 (2014).

    Article  Google Scholar 

  3. Tapas Ray Mahapatra, Dulal Pal, Sabyasachi Mondal, Int. Commun. Heat Mass Transfer 41, 47 (2013).

    Article  Google Scholar 

  4. Amir Houshang Mahmoudi, Ioan Pop, Mina Shahia, Farhad Talebi, Comp. Fluids 72, 46 (2013).

    Article  Google Scholar 

  5. Samir Kumar Nandy, Ioan Pop, Int. Commun. Heat Mass Transfer 53, 50 (2014).

    Article  Google Scholar 

  6. H.A. Mohammed, K. Narrein, Int. Commun. Heat Mass Transfer 39, 1375 (2012).

    Article  Google Scholar 

  7. R. Azizian, E. Doroodchi, T. McKrell, J. Buongiorno, L.W. Hu, B. Moghtaderi, Int. J. Heat Mass Transfer 68, 94 (2014).

    Article  Google Scholar 

  8. Fatih Selimefendigil, Hakan F. Oztop, Int. J. Heat Mass Transfer 71, 142 (2014).

    Article  Google Scholar 

  9. Mohsen Sheikholeslami Kandelousi, Eur. Phys. J. Plus 129, 248 (2014).

    Article  Google Scholar 

  10. C.E. Nanjundappa, I.S. Shivakumara, M. Ravisha, Int. Commun. Heat Mass Transfer 37, 1246 (2010).

    Article  Google Scholar 

  11. Mohsen Sheikholeslami, Mofid Gorji-Bandpy, Powder Technol. 256, 490 (2014).

    Article  Google Scholar 

  12. Mohsen Sheikholeslami, Mohammad Mehdi Rashidi, J. Taiwan Inst. Chem. Eng., DOI:10.1016/j.jtice.2015.03.035 (2015).

  13. Fatih Selimefendigil, Hakan F. Oztop, J. Taiwan Inst. Chem. Eng. 45, 2150 (2014).

    Article  Google Scholar 

  14. M. Hatami, M. Sheikholeslami, D.D. Ganji, J. Mol. Liq. 195, 230 (2014).

    Article  Google Scholar 

  15. Fatih Selimefendigil, Hakan F. Oztop, Int. J. Thermal Sci. 86, 258 (2014).

    Article  Google Scholar 

  16. Mohsen Sheikholeslami, Shirley Abelman, IEEE Trans. Nanotechnol. 14, 561 (2015) DOI:10.1109/TNANO.2015.2416318.

    Article  Google Scholar 

  17. Mohsen Sheikholeslami, Mofid Gorji Bandpy, Hamid Reza Ashorynejad, Phys. A: Stat. Mech. Appl. 432, 58 (2015).

    Article  Google Scholar 

  18. Mohsen Sheikholeslami, Davood Domiri Ganji, Comput. Methods Appl. Mech. Eng. 283, 651 (2015).

    Article  ADS  Google Scholar 

  19. Mohsen Sheikholeslami, M.T. Mustafa, Particuology, DOI:10.1016/j.partic.2014.09.004 (2015).

  20. Fatih Selimefendigil, Hakan F. Öztop, Int. J. Heat Mass Transfer 71, 142 (2014).

    Article  Google Scholar 

  21. Fatih Selimefendigil, Hakan F. Öztop, J. Magn. & Magn. Mater. 372, 122 (2014).

    Article  ADS  Google Scholar 

  22. M. Sheikholeslami, R. Ellahi, J. Z. Naturforsch. 70, 115 (2015).

    Google Scholar 

  23. M. Sheikholeslami, M. Hatami, G. Domairry, J. Taiwan Inst. Chem. Eng. 46, 43 (2015).

    Article  Google Scholar 

  24. Mohsen Sheikholeslami Kandelousi, Phys. Lett. A 378, 3331 (2014).

    Article  MATH  ADS  Google Scholar 

  25. Mohsen Sheikholeslami, Davood Domiri Ganji, Phys. A 417, 273 (2015).

    Article  Google Scholar 

  26. Mohsen Sheikholeslami, Mofid Gorji-Bandpy, Kuppalapalle Vajravelu, Int. J. Heat Mass Transfer 80, 16 (2015).

    Article  Google Scholar 

  27. M. Sheikholeslami, J. Braz. Soc. Mech. Sci. Eng., DOI:10.1007/s40430-014-0242-z (2014).

  28. M. Mustafa, S. Hina, T. Hayat, A. Alsaedi, Int. J. Heat Mass Transfer 55, 4871 (2012).

    Article  Google Scholar 

  29. M. Mustafaa, T. Hayat, I. Pop, S. Asghare, S. Obaidat, Int. J. Heat Mass Transfer 54, 5588 (2011).

    Article  Google Scholar 

  30. Mohsen Sheikholeslami, Davood Domiri Ganji, M. Younus Javed, R. Ellahi, J. Magn. & Magn. Mater. 374, 36 (2015).

    Article  ADS  Google Scholar 

  31. Mohsen Sheikholeslami, Shirley Abelman, Davood Domiri Ganji, Int. J. Heat Mass Transfer 79, 212 (2014).

    Article  Google Scholar 

  32. Mohsen Sheikholeslami, Davood Domiri Ganji, J. Braz. Soc. Mech. Sci. Eng. 37, 895 (2014).

    Article  Google Scholar 

  33. M. Sheikholeslami, M. Gorji-Bandpay, D.D. Ganji, Arab. J. Sci. Eng. 39, 5007 (2014).

    Article  Google Scholar 

  34. M. Sheikholeslami, D.D. Ganji, J. Appl. Fluid Mech. 7, 535 (2014).

    Google Scholar 

  35. S. Nadeem, Rashid Mehmood, Noreen Sher Akbar, J. Comput. Theor. Nanosci. 10, 2737 (2013).

    Article  Google Scholar 

  36. Mohsen Sheikholeslami, M. Hatami, M. Jafaryar, F. Farkhadnia, Davood Domiri Ganji, Mofid Gorji-Bandpy, Energy Build. 88, 361 (2015).

    Article  Google Scholar 

  37. N.S. Akbar, S. Nadeem, R.U. Haq, Ul Rizwan, Z.H. Khan, J. Comput. Theor. Nanosci. 11, 47 (2014).

    Article  Google Scholar 

  38. S.A. Shehzad, M. Qasim, A. Alsaedi, T. Hayat, M.S. Alhuthali, Eur. Phys. J. Plus 128, 7 (2013).

    Article  Google Scholar 

  39. S.A. Shehzad, F.E. Alsaadi, S.J. Monaquel, T. Hayat, Eur. Phys. J. Plus 128, 56 (2013).

    Article  Google Scholar 

  40. Mohsen Sheikholeslami, Mofid Gorji-Bandpy, Davood Domiri Ganji, Renew. Sustain. Energy Rev. 49, 444 (2015).

    Article  Google Scholar 

  41. Mohsen Sheikholeslami, Mofid Gorji Bandpy, R. Ellahi, A. Zeeshan, J. Magn. & Magn. Mater. 369, 69 (2014).

    Article  ADS  Google Scholar 

  42. M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Soheil Soleimani, Trans. Mech. Eng. 38, 217 (2014).

    Google Scholar 

  43. M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, J. Taiwan Inst. Chem. Eng. 45, 1204 (2014).

    Article  Google Scholar 

  44. Mohammad Hatami, Mohsen Sheikholeslami, M. Hosseini, Davood Domiri Ganji, J. Mol. Liq. 194, 251 (2014).

    Article  Google Scholar 

  45. M. Hatami, D.D. Ganji, Particuology 16, 206 (2014).

    Article  Google Scholar 

  46. M. Hatami, D.D. Ganji, Powder Technol. 258, 94 (2014).

    Article  Google Scholar 

  47. M. Hatami, D.D. Ganji, Int. J. Refrig. 40, 140 (2014).

    Article  Google Scholar 

  48. M. Hatami, M. Sheikholeslami, D.D. Ganji, Powder Technol. 253, 769 (2014).

    Article  Google Scholar 

  49. M. Sheikholeslami, E. Ellahi, Int. J. Heat Mass Transfer 89, 799 (2015).

    Article  Google Scholar 

  50. M. Sheikholeslami, D.D. Ganji, Sci. Iran. B 21, 203 (2014).

    Google Scholar 

  51. M. Sheikholeslami, D.D. Ganji, J. Mol. Liq. 194, 13 (2014).

    Article  Google Scholar 

  52. M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Powder Technol. 254, 82 (2014).

    Article  Google Scholar 

  53. M. Sheikholeslami, D.D. Ganji, Powder Technol. 253, 789 (2014).

    Article  Google Scholar 

  54. M. Sheikholeslami, M. Hatami, D.D. Ganji, J. Mol. Liq. 190, 112 (2014).

    Article  Google Scholar 

  55. M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Energy 60, 501 (2013).

    Article  Google Scholar 

  56. M. Sheikholeslami, M. Gorji Bandpy, R. Ellahi, Mohsan Hassan, Soheil Soleimani, J. Magn. & Magn. Mater. 349, 188 (2014).

    Article  ADS  Google Scholar 

  57. M. Sheikholeslami, F. Bani Sheykholeslami, S. Khoshhal, H. Mola-Abasi, D.D. Ganji, Houman B. Rokni, Neural. Comput. Appl. 25, 171 (2014).

    Article  Google Scholar 

  58. M. Sheikholeslami, M. Gorji-Bandpy, S.M. Seyyedi, D.D. Ganji, Houman B. Rokni, Soheil Soleimani, Powder Technol. 247, 87 (2013).

    Article  Google Scholar 

  59. M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Sci. Iran., Trans. B: Mech. Eng. 20, 1241 (2013).

    Google Scholar 

  60. M. Sheikholeslami, M. Hatami, D.D. Ganji, Powder Technol. 246, 327 (2013).

    Article  Google Scholar 

  61. M. Sheikholeslami, M. Gorji-Bandpy, G. Domairry, Appl. Math. Mech. 34, 1 (2013).

    Article  Google Scholar 

  62. M. Sheikholeslami, D.D. Ganji, H.R. Ashorynejad, Powder Technol. 239, 259 (2013).

    Article  Google Scholar 

  63. M. Sheikholeslami, D.D. Ganji, Powder Technol. 235, 873 (2013).

    Article  Google Scholar 

  64. H.R. Ashorynejad, M. Sheikholeslami, I. Pop, D.D. Ganji, Heat Mass Transfer 49, 427 (2013).

    Article  ADS  Google Scholar 

  65. Hamid Reza Ashorynejad, Abdulmajeed A. Mohamad, Mohsen Sheikholeslami, Int. J. Therm. Sci. 64, 240 (2013).

    Article  Google Scholar 

  66. M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Soheil Soleimani, S.M. Seyyedi, Int. Commun. Heat Mass Transfer 39, 1435 (2012).

    Article  Google Scholar 

  67. M. Sheikholeslami, M. Gorji-Bandpay, D.D. Ganji, Int. Commun. Heat Mass Transfer 39, 978 (2012).

    Article  Google Scholar 

  68. M. Sheikholeslami, D.D. Ganji, H.R. Ashorynejad, Houman B. Rokni, Appl. Math. Mech. 33, 1553 (2012).

    Article  MathSciNet  Google Scholar 

  69. Davood Domairry, Mohsen Sheikholeslami, Hamid Reza Ashorynejad, Rama Subba Reddy Gorla, Mostafa Khani, Proc. Inst. Mech. Eng. N: J. Nanoeng. Nanosyst. 225, 115 (2011) DOI:10.1177/1740349911433468.

    Article  Google Scholar 

  70. M. Sheikholeslami, H.R. Ashorynejad, D.D. Ganji, A. Yildirim, Sci. Iran. B 19, 437 (2012).

    Article  Google Scholar 

  71. M. Sheikholeslami, H.R. Ashorynejad, D.D. Ganji, A. Kolahdooz, Math. Probl. Eng. 2011, 258734 (2011) DOI:10.1155/2011/258734.

    Article  MathSciNet  Google Scholar 

  72. M. Sheikholeslami, D.D. Ganji, Houman B. Rokni, Int. J. Eng. Trans. 26, 653 (2013).

    Google Scholar 

  73. Mohsen Sheikholeslami, Davood Domairry Ganji, Hydrothermal Analysis in Engineering Using Control Volume Finite Element Method (Academic Press, 2015) ISBN: 9780128029503.

  74. Soheil Soleimani, M. Sheikholeslami, D.D. Ganji, M. Gorji-Bandpay, Int. Commun. Heat Mass Transfer 39, 565 (2012).

    Article  Google Scholar 

  75. M. Sheikholeslami, D.D. Ganji, Energy 75, 400 (2014).

    Article  Google Scholar 

  76. M. Sheikholeslami, M. Gorji-Bandpy, I. Pop, Soheil Soleimani, Int. J. Therm. Sci. 72, 147 (2013).

    Article  Google Scholar 

  77. Mohsen Sheikholeslami, Davood Domiri Ganji, Mohammad Mehdi Rashidi, J. Taiwan Inst. Chem. Eng. 47, 6 (2015).

    Article  Google Scholar 

  78. M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, P. Rana, Soheil Soleimani, Comp. Fluids 94, 147 (2014).

    Article  Google Scholar 

  79. M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Soheil Soleimani, J. Mol. Liq. 194, 179 (2014).

    Article  Google Scholar 

  80. M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Soheil Soleimani, J. Mol. Liq. 193, 174 (2014).

    Article  Google Scholar 

  81. M. Sheikholeslami, D.D. Ganji, M. Gorji-Bandpy, Soheil Soleimani, J. Taiwan Inst. Chem. Eng. 45, 795 (2014).

    Article  Google Scholar 

  82. M. Sheikholeslami, M. Gorji-Bandpy, Soheil Soleimani, Int. Commun. Heat Mass Transfer 47, 73 (2013).

    Article  Google Scholar 

  83. M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Soheil Soleimani, J. Taiwan Inst. Chem. Eng. 45, 40 (2014).

    Article  Google Scholar 

  84. M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Soheil Soleimani, Adv. Powder Technol. 24, 980 (2013).

    Article  Google Scholar 

  85. M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Soheil Soleimani, Neural. Comput. Appl. 24, 873 (2014).

    Article  Google Scholar 

  86. V. Loukopoulos, E. Tzirtzilakis, Int. J. Eng. Sci. 42, 571 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  87. K. Khanafer, K. Vafai, M. Lightstone, Int. J. Heat Mass Transfer 46, 3639 (2003).

    Article  MATH  Google Scholar 

  88. H. Aminfar, M. Mohammadpourfard, F. Mohseni, J. Magn. & Magn. Mater. 324, 830 (2012).

    Article  ADS  Google Scholar 

  89. G. De Vahl Davis, Int. J. Numer. Methods Fluids 3, 249 (1962).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Babol University of Technology, Babol, Islamic Republic of Iran

    M. Sheikholeslami

  2. Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Tongji University, Address: 4800 Cao An Rd., 201804, Jiading, Shanghai, China

    M. M. Rashidi

  3. ENN-Tongji Clean Energy Institute of Advanced Studies, Shanghai, China

    M. M. Rashidi

Authors
  1. M. Sheikholeslami
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. M. Rashidi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Sheikholeslami.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sheikholeslami, M., Rashidi, M.M. Ferrofluid heat transfer treatment in the presence of variable magnetic field. Eur. Phys. J. Plus 130, 115 (2015). https://doi.org/10.1140/epjp/i2015-15115-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2015-15115-4

Keywords

Search

Navigation