MHD free convection heat transfer of a water–Fe3O4 nanofluid in a baffled C-shaped enclosure

  • A. Abedini
  • T. Armaghani
  • Ali J. Chamkha


In this paper, the effect of a baffle on free convection heat transfer of a water–Fe3O4 nanofluid in a C-shaped enclosure in the presence of a magnetic field is investigated numerically. The enclosure is subjected to a constant magnetic field. The vertical wall on the left side is maintained at a constant hot temperature of Th, and the right one is kept at a constant cold temperature of Tc. The rest of the walls are insulated. The governing equations are discretized by the control volume method and solved simultaneously by the SIMPLE algorithm. The numerical results show very good agreement with other published works. The results indicate that by increasing the enclosure’s aspect ratio, the Nusselt number is increased. It is also found that the volume fraction of nanoparticles can be raised in order to achieve increased cooling in the enclosure. By increasing the aspect ratio, the effect of the nanoparticles on the enhancement of the Nusselt number is more pronounced. Also, the maximum effect of the baffle on the heat transfer is seen at the bottom of the hot wall. Generally, increasing the baffle length produces increases in the Nusselt number. The maximum cooling level is occurred for AR = 0.7 and Bf = 0.2.


Magnetic field Nanofluid Free convection C-shaped enclosure Baffle 

List of symbols


Baffle length


Aspect ratio, H/L


Magnetic field strength, T


Dimensionless baffle length, a/L


Specific heat at constant pressure (J kg-K−1)


Gravitational acceleration (m s−2)


Length of heat source (m)


Hartmann number, \(B_{0} L\sqrt {\sigma_{\text{f}} /\rho_{\text{f}} \nu_{\text{f}} }\)


Thermal conductivity (Wm−1 K−1)


Length of cavity (m)


Local Nusselt number


Average Nusselt number of heat source


Fluid pressure (Pa)


Dimensionless pressure, \(pH/\rho_{\text{nf}} \alpha_{\text{f}}^{2}\)


Prandtl number, \(\nu_{\text{f}} /\alpha_{\text{f}}\)


Rayleigh number, \(g\beta_{\text{f}} \left( {T_{\text{h}} - T_{\text{c}} } \right)H^{3} /\alpha_{\text{f}} \vartheta_{\text{f}}\)


Temperature (K)


Cold wall temperature (K)


Heated wall temperature (K)

u, v

Velocity components in the x, y directions (m s−1)

U, V

Dimensionless velocity components, \(u/v_{0} ,v/v_{0}\)

x, y

Cartesian coordinates (m)

X, Y

Dimensionless coordinates, x/L, y/L

Greek symbols


Thermal diffusivity, k/ρcp (m2 s−1)


Thermal expansion coefficient (K−1)


Solid volume fraction


Effective electrical conductivity (μS cm−1)


Boltzmann constant (J K−1)


Dimensionless temperature, \(\left( {T - T_{\text{c}} } \right)/\left( {T_{\text{h}} - T_{\text{c}} } \right)\)


Dynamic viscosity (N s m2)


Kinematic viscosity (m2 s−1)


Density (kg m−3)







Pure fluid


Hot wall








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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Department of Engineering, Semnan BranchIslamic Azad UniversitySemnanIran
  2. 2.Department of Engineering, Mahdishahr BranchIslamic Azad UniversityMahdishahrIran
  3. 3.Mechanical Engineering Department, Prince Sultan Endowment for Energy and EnvironmentPrince Mohammad Bin Fahd UniversityAl-KhobarSaudi Arabia
  4. 4.RAK Research and Innovation CenterAmerican University of Ras Al KhaimahRas al-KhaimahUnited Arab Emirates

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