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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

Abstract

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.

Keywords

GMDH Magnetohydrodynamic Stretching cylinder Nanofluid Heat transfer 

List of symbols

A1, A2, A3, A4

Constant parameters

a

Radius of cylinder

ai

Coefficients of the quadratic polynomial equation

c

Positive constant

Cf

Skin friction coefficient

f

Dimensionless stream function

k

Thermal conductivity

M

Magnetic parameter

MS

Mean square error

MAD

Mean absolute deviation

Nu

Nusselt number

Pr

Prandtl number

qw

Heat transfer from the cylinder surface

Re

Reynolds number

R2

Absolute fraction of variance

T

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

α

Thermal diffusivity

η

Similarity variable

θ

Similarity function for temperature

ρ

Density

ϕ

Nanoparticle volume fraction

μ

Dynamic viscosity

υ

Kinematic viscosity

τw

Wall shear stress

ψ

Stream function

σ

Electrical conductivity

Subscripts

w

Condition at the surface

Far field

nf

Nanofluid

f

Base fluid

s

Nano-solid-particles

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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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