Heat and Mass Transfer

, Volume 55, Issue 1, pp 133–148 | Cite as

Simulation of ferrofluid flow boiling in helical tubes using two-fluid model

  • M. Saedi
  • H. Aminfar
  • M. MohammadpourfardEmail author
  • R. Maroofiazar


In this paper, the effects of the variations of the coil pitch and coil diameter on ferrofluid flow boiling characteristics inside helical tubes have been investigated using two-fluid model and control volume technique. The effects of the non-uniform magnetic field on the ferrofluid flow boiling inside helical tubes have also been studied. The results indicated showed that decreasing the coil diameter enhances the heat transfer coefficient. This is due to the effect of centrifugal force which is increased by decreasing the coil diameter. Also, the results confirmed the dual role of the centrifugal force on heat transfer (increase) and vapor volume fraction (decrease) and at the same time remarkable increasing of locally void fraction on heated wall and raising possibility of occurrence of CHF. In addition, the improvement of surface wettability which is induced by nanoparticles sedimentation during the boiling process has been considered. Results showed the reduction of the void fraction. The application of a magnetic field at critical regions resulted in the bubble departure diameter and vapor volume fraction generation reduction. Consequently, the critical heat flux is increased.


Ferrofluid Two-fluid model Helical tubes Non-uniform transverse magnetic field Critical heat flux 



Interphase contact area(m−1.)


Pitch circle diameter(m)


Wall fraction influenced by nucleating bubbles


Specific heat capacity(J kg−1K−1)


Bubble mean diameter(m)


Bubble departure diameter (m)


Frequency (S−1)

\( \overrightarrow{f_D} \)

Drag force (N)

\( \overrightarrow{f_L} \)

Lift force (N)

\( \overrightarrow{f_W} \)

Wall lubrication force (N)

\( \overrightarrow{f_{TD}} \)

Turbulent dispersion force(N)

\( \overrightarrow{f_{VM}} \)

Virtual mass force (N)


Difference between specific enthalpies (J kg−1)


Liquid single-phase heat transfer coefficient (W m−2 K−1)

\( \overrightarrow{H} \)

Magnetic field vector (A m−1)


Magnetic field intensity component in x direction (A m−1)


Magnetic field intensity component in y direction (A m−1)


Electric intensity(=200 A)


Liquid thermal conductivity (W m−1 K−1)


Boltzmann constant(=1.3806503 × 10−23 J K−1)


Langevin function


Magnetization (A m−1)


Particle magnetic moment (A m2)


Active nucleation site density(m−2)


Coil Pitch(m)


Total heat flux (W m−2)


Quenching heat flux (W m−2)


Single-phase convection heat flux (W m−2)


Evaporation heat flux (W m−2)


Inner Diameter(m)




Velocity (m s−1)

Greek symbols


Void fraction


Density (kg m−3)


Liquid dynamic viscosity (kg m−1s−1)


Magnetic permeability in vacuum (=4π × 10−7 T m A−1)


Bohr magneton(=9.27 × 10−24 A m−2)


Langevin parameter














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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018
corrected publication August/2018

Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringUniversity of TabrizTabrizIran
  2. 2.Faculty of Chemical and Petroleum EngineeringUniversity of TabrizTabrizIran
  3. 3.Departement of Mechanical Engineering, Faculty of Mechanical EngineeringUniversity of MaraghehMaraghehIran

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