Neural Computing and Applications

, Volume 25, Issue 1, pp 171–178 | Cite as

Effect of magnetic field on Cu–water nanofluid heat transfer using GMDH-type neural network

  • M. Sheikholeslami
  • F. Bani Sheykholeslami
  • S. Khoshhal
  • H. Mola-Abasia
  • D. D. Ganji
  • Houman B. Rokni
Original Article


Heat transfer of Cu–water nanofluid over a stretching cylinder in the presence of magnetic field has been investigated. The group method of data handling (GMDH) type neural networks (NNs) is used to calculate Nusselt number formulation. Results indicate that GMDH-type NN in comparison with fourth-order Runge–Kutta integration scheme provides an effective means of efficiently recognizing the patterns in data and accurately predicting a performance. The effects of nanoparticle volume fraction, magnetic parameter and Reynolds number on Nusselt number are studied by sensitivity analyses. The results show that Nusselt number is an increasing function of Reynolds number and volume fraction of nanoparticles while it is a decreasing function of magnetic parameter. As volume fraction of nanoparticles increases, the effect of this parameter on Nusselt number also increases, but opposite behavior is obtained for magnetic parameter and Reynolds number.


GMDH Magnetohydrodynamic Stretching cylinder Nanofluid Heat transfer 

List of symbols

A1, A2, A3, A4

Constant parameters


Radius of cylinder


Coefficients of the quadratic polynomial equation


Positive constant


Skin friction coefficient


Dimensionless stream function


Thermal conductivity


Magnetic parameter


Mean square error


Mean absolute deviation


Nusselt number


Prandtl number


Heat transfer from the cylinder surface


Reynolds number


Absolute fraction of variance


Temperature of the nanofluid

u, v

Velocity components along the x and y directions, respectively

x, y

Cartesian coordinates along x and y axes, respectively

Greek symbols


Thermal diffusivity


Similarity variable


Similarity function for temperature




Nanoparticle volume fraction


Dynamic viscosity


Kinematic viscosity


Wall shear stress


Stream function


Electrical conductivity



Condition at the surface

Far field




Base fluid




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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • M. Sheikholeslami
    • 1
  • F. Bani Sheykholeslami
    • 2
  • S. Khoshhal
    • 2
  • H. Mola-Abasia
    • 3
  • D. D. Ganji
    • 1
  • Houman B. Rokni
    • 1
    • 4
  1. 1.Department of Mechanical EngineeringBabol University of TechnologyBabolIran
  2. 2.Department of Chemical EngineeringBabol University of TechnologyBabolIran
  3. 3.Department of Civil EngineeringBabol University of TechnologyBabolIran
  4. 4.Mechanical and Materials EngineeringUniversity of DenverDenverUSA

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