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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
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
Mohammad Hossein Abolbashari, Navid Freidoonimehr, Foad Nazaria, Mohammad Mehdi Rashidi, Powder Technol. 267, 256 (2014).
A. Malvandi, D.D. Ganji, Powder Technol. 263, 37 (2014).
Tapas Ray Mahapatra, Dulal Pal, Sabyasachi Mondal, Int. Commun. Heat Mass Transfer 41, 47 (2013).
Amir Houshang Mahmoudi, Ioan Pop, Mina Shahia, Farhad Talebi, Comp. Fluids 72, 46 (2013).
Samir Kumar Nandy, Ioan Pop, Int. Commun. Heat Mass Transfer 53, 50 (2014).
H.A. Mohammed, K. Narrein, Int. Commun. Heat Mass Transfer 39, 1375 (2012).
R. Azizian, E. Doroodchi, T. McKrell, J. Buongiorno, L.W. Hu, B. Moghtaderi, Int. J. Heat Mass Transfer 68, 94 (2014).
Fatih Selimefendigil, Hakan F. Oztop, Int. J. Heat Mass Transfer 71, 142 (2014).
Mohsen Sheikholeslami Kandelousi, Eur. Phys. J. Plus 129, 248 (2014).
C.E. Nanjundappa, I.S. Shivakumara, M. Ravisha, Int. Commun. Heat Mass Transfer 37, 1246 (2010).
Mohsen Sheikholeslami, Mofid Gorji-Bandpy, Powder Technol. 256, 490 (2014).
Mohsen Sheikholeslami, Mohammad Mehdi Rashidi, J. Taiwan Inst. Chem. Eng., DOI:10.1016/j.jtice.2015.03.035 (2015).
Fatih Selimefendigil, Hakan F. Oztop, J. Taiwan Inst. Chem. Eng. 45, 2150 (2014).
M. Hatami, M. Sheikholeslami, D.D. Ganji, J. Mol. Liq. 195, 230 (2014).
Fatih Selimefendigil, Hakan F. Oztop, Int. J. Thermal Sci. 86, 258 (2014).
Mohsen Sheikholeslami, Shirley Abelman, IEEE Trans. Nanotechnol. 14, 561 (2015) DOI:10.1109/TNANO.2015.2416318.
Mohsen Sheikholeslami, Mofid Gorji Bandpy, Hamid Reza Ashorynejad, Phys. A: Stat. Mech. Appl. 432, 58 (2015).
Mohsen Sheikholeslami, Davood Domiri Ganji, Comput. Methods Appl. Mech. Eng. 283, 651 (2015).
Mohsen Sheikholeslami, M.T. Mustafa, Particuology, DOI:10.1016/j.partic.2014.09.004 (2015).
Fatih Selimefendigil, Hakan F. Öztop, Int. J. Heat Mass Transfer 71, 142 (2014).
Fatih Selimefendigil, Hakan F. Öztop, J. Magn. & Magn. Mater. 372, 122 (2014).
M. Sheikholeslami, R. Ellahi, J. Z. Naturforsch. 70, 115 (2015).
M. Sheikholeslami, M. Hatami, G. Domairry, J. Taiwan Inst. Chem. Eng. 46, 43 (2015).
Mohsen Sheikholeslami Kandelousi, Phys. Lett. A 378, 3331 (2014).
Mohsen Sheikholeslami, Davood Domiri Ganji, Phys. A 417, 273 (2015).
Mohsen Sheikholeslami, Mofid Gorji-Bandpy, Kuppalapalle Vajravelu, Int. J. Heat Mass Transfer 80, 16 (2015).
M. Sheikholeslami, J. Braz. Soc. Mech. Sci. Eng., DOI:10.1007/s40430-014-0242-z (2014).
M. Mustafa, S. Hina, T. Hayat, A. Alsaedi, Int. J. Heat Mass Transfer 55, 4871 (2012).
M. Mustafaa, T. Hayat, I. Pop, S. Asghare, S. Obaidat, Int. J. Heat Mass Transfer 54, 5588 (2011).
Mohsen Sheikholeslami, Davood Domiri Ganji, M. Younus Javed, R. Ellahi, J. Magn. & Magn. Mater. 374, 36 (2015).
Mohsen Sheikholeslami, Shirley Abelman, Davood Domiri Ganji, Int. J. Heat Mass Transfer 79, 212 (2014).
Mohsen Sheikholeslami, Davood Domiri Ganji, J. Braz. Soc. Mech. Sci. Eng. 37, 895 (2014).
M. Sheikholeslami, M. Gorji-Bandpay, D.D. Ganji, Arab. J. Sci. Eng. 39, 5007 (2014).
M. Sheikholeslami, D.D. Ganji, J. Appl. Fluid Mech. 7, 535 (2014).
S. Nadeem, Rashid Mehmood, Noreen Sher Akbar, J. Comput. Theor. Nanosci. 10, 2737 (2013).
Mohsen Sheikholeslami, M. Hatami, M. Jafaryar, F. Farkhadnia, Davood Domiri Ganji, Mofid Gorji-Bandpy, Energy Build. 88, 361 (2015).
N.S. Akbar, S. Nadeem, R.U. Haq, Ul Rizwan, Z.H. Khan, J. Comput. Theor. Nanosci. 11, 47 (2014).
S.A. Shehzad, M. Qasim, A. Alsaedi, T. Hayat, M.S. Alhuthali, Eur. Phys. J. Plus 128, 7 (2013).
S.A. Shehzad, F.E. Alsaadi, S.J. Monaquel, T. Hayat, Eur. Phys. J. Plus 128, 56 (2013).
Mohsen Sheikholeslami, Mofid Gorji-Bandpy, Davood Domiri Ganji, Renew. Sustain. Energy Rev. 49, 444 (2015).
Mohsen Sheikholeslami, Mofid Gorji Bandpy, R. Ellahi, A. Zeeshan, J. Magn. & Magn. Mater. 369, 69 (2014).
M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Soheil Soleimani, Trans. Mech. Eng. 38, 217 (2014).
M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, J. Taiwan Inst. Chem. Eng. 45, 1204 (2014).
Mohammad Hatami, Mohsen Sheikholeslami, M. Hosseini, Davood Domiri Ganji, J. Mol. Liq. 194, 251 (2014).
M. Hatami, D.D. Ganji, Particuology 16, 206 (2014).
M. Hatami, D.D. Ganji, Powder Technol. 258, 94 (2014).
M. Hatami, D.D. Ganji, Int. J. Refrig. 40, 140 (2014).
M. Hatami, M. Sheikholeslami, D.D. Ganji, Powder Technol. 253, 769 (2014).
M. Sheikholeslami, E. Ellahi, Int. J. Heat Mass Transfer 89, 799 (2015).
M. Sheikholeslami, D.D. Ganji, Sci. Iran. B 21, 203 (2014).
M. Sheikholeslami, D.D. Ganji, J. Mol. Liq. 194, 13 (2014).
M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Powder Technol. 254, 82 (2014).
M. Sheikholeslami, D.D. Ganji, Powder Technol. 253, 789 (2014).
M. Sheikholeslami, M. Hatami, D.D. Ganji, J. Mol. Liq. 190, 112 (2014).
M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Energy 60, 501 (2013).
M. Sheikholeslami, M. Gorji Bandpy, R. Ellahi, Mohsan Hassan, Soheil Soleimani, J. Magn. & Magn. Mater. 349, 188 (2014).
M. Sheikholeslami, F. Bani Sheykholeslami, S. Khoshhal, H. Mola-Abasi, D.D. Ganji, Houman B. Rokni, Neural. Comput. Appl. 25, 171 (2014).
M. Sheikholeslami, M. Gorji-Bandpy, S.M. Seyyedi, D.D. Ganji, Houman B. Rokni, Soheil Soleimani, Powder Technol. 247, 87 (2013).
M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Sci. Iran., Trans. B: Mech. Eng. 20, 1241 (2013).
M. Sheikholeslami, M. Hatami, D.D. Ganji, Powder Technol. 246, 327 (2013).
M. Sheikholeslami, M. Gorji-Bandpy, G. Domairry, Appl. Math. Mech. 34, 1 (2013).
M. Sheikholeslami, D.D. Ganji, H.R. Ashorynejad, Powder Technol. 239, 259 (2013).
M. Sheikholeslami, D.D. Ganji, Powder Technol. 235, 873 (2013).
H.R. Ashorynejad, M. Sheikholeslami, I. Pop, D.D. Ganji, Heat Mass Transfer 49, 427 (2013).
Hamid Reza Ashorynejad, Abdulmajeed A. Mohamad, Mohsen Sheikholeslami, Int. J. Therm. Sci. 64, 240 (2013).
M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Soheil Soleimani, S.M. Seyyedi, Int. Commun. Heat Mass Transfer 39, 1435 (2012).
M. Sheikholeslami, M. Gorji-Bandpay, D.D. Ganji, Int. Commun. Heat Mass Transfer 39, 978 (2012).
M. Sheikholeslami, D.D. Ganji, H.R. Ashorynejad, Houman B. Rokni, Appl. Math. Mech. 33, 1553 (2012).
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.
M. Sheikholeslami, H.R. Ashorynejad, D.D. Ganji, A. Yildirim, Sci. Iran. B 19, 437 (2012).
M. Sheikholeslami, H.R. Ashorynejad, D.D. Ganji, A. Kolahdooz, Math. Probl. Eng. 2011, 258734 (2011) DOI:10.1155/2011/258734.
M. Sheikholeslami, D.D. Ganji, Houman B. Rokni, Int. J. Eng. Trans. 26, 653 (2013).
Mohsen Sheikholeslami, Davood Domairry Ganji, Hydrothermal Analysis in Engineering Using Control Volume Finite Element Method (Academic Press, 2015) ISBN: 9780128029503.
Soheil Soleimani, M. Sheikholeslami, D.D. Ganji, M. Gorji-Bandpay, Int. Commun. Heat Mass Transfer 39, 565 (2012).
M. Sheikholeslami, D.D. Ganji, Energy 75, 400 (2014).
M. Sheikholeslami, M. Gorji-Bandpy, I. Pop, Soheil Soleimani, Int. J. Therm. Sci. 72, 147 (2013).
Mohsen Sheikholeslami, Davood Domiri Ganji, Mohammad Mehdi Rashidi, J. Taiwan Inst. Chem. Eng. 47, 6 (2015).
M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, P. Rana, Soheil Soleimani, Comp. Fluids 94, 147 (2014).
M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Soheil Soleimani, J. Mol. Liq. 194, 179 (2014).
M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Soheil Soleimani, J. Mol. Liq. 193, 174 (2014).
M. Sheikholeslami, D.D. Ganji, M. Gorji-Bandpy, Soheil Soleimani, J. Taiwan Inst. Chem. Eng. 45, 795 (2014).
M. Sheikholeslami, M. Gorji-Bandpy, Soheil Soleimani, Int. Commun. Heat Mass Transfer 47, 73 (2013).
M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Soheil Soleimani, J. Taiwan Inst. Chem. Eng. 45, 40 (2014).
M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Soheil Soleimani, Adv. Powder Technol. 24, 980 (2013).
M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Soheil Soleimani, Neural. Comput. Appl. 24, 873 (2014).
V. Loukopoulos, E. Tzirtzilakis, Int. J. Eng. Sci. 42, 571 (2004).
K. Khanafer, K. Vafai, M. Lightstone, Int. J. Heat Mass Transfer 46, 3639 (2003).
H. Aminfar, M. Mohammadpourfard, F. Mohseni, J. Magn. & Magn. Mater. 324, 830 (2012).
G. De Vahl Davis, Int. J. Numer. Methods Fluids 3, 249 (1962).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
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
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2015-15115-4