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Heat and Mass Transfer

, Volume 49, Issue 4, pp 575–583 | Cite as

Nero-fuzzy modeling of the convection heat transfer coefficient for the nanofluid

  • H. SalehiEmail author
  • S. Zeinali-Heris
  • M. Esfandyari
  • M. Koolivand
Original

Abstract

In this study, experiments were performed by six different volume fractions of Al2O3 nanoparticles in distilled water. Then, actual nanofluid Nusslet number compared by Adaptive neuro fuzzy inference system (ANFIS) predicted number in square cross-section duct in laminar flow under uniform heat flux condition. Statistical values, which quantify the degree of agreement between experimental observations and numerically calculated values, were found greater than 0.99 for all cases.

Keywords

Nusselt Number Fuzzy Inference System Peclet Number Adaptive Neuro Fuzzy Inference System Convective Heat Transfer Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Abbreviations

ARE

Average relative error

AARE

Absolute average relative error

MSE

Mean square error

RMSE

Root Mean square error

ANFIS

Adaptive neuro fuzzy inference system

FIS

Fuzzy inference system

CHF

Critical heat flux

List of symbols

X, Y, and Z

Linguistic variables

ai, bi, and ci

Parameter set

μA(x), and μB(x)

Membership function

A

Surface area of the square cross-section duct (m2)

Cp

Specific heat (kJ kg−1 K−1)

Dh

Hydraulic diameter (m)

\( \overline{\text{h}}_{\text{nf}} (\exp ) \)

Experimental average heat transfer coefficient of Nanofluid (W m−2 K−1)

K

Thermal conductivity (W m−1 K−1)

L

Duct length (m)

Nu (exp)

Experimental average Nusselt number of Nanofluid

Nu (th)

Nanofluid Nusselt number calculated from Seider–Tate equation

Pe

Peclet number

Pr

Prandtl number

Q

Heat flux (W)

Re

Reynolds number

Tb

Bulk temperature (K)

Tw

Duct wall temperature (K)

\( \overline{\text{U}} \)

Average fluid velocity (m s−1)

Greek letters

μ

Viscosity (Pa s)

μwnf

Nanofluid viscosity at duct wall temperature (Pa s)

\( \phi \)

Nanoparticle volume fraction (%)

ρ

Density (kg m−3)

Subscripts

nf

Nanofluid

s

Solid nanoparticles

w

Water

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • H. Salehi
    • 1
    Email author
  • S. Zeinali-Heris
    • 1
  • M. Esfandyari
    • 2
  • M. Koolivand
    • 3
  1. 1.Department of Chemical Engineering, Faculty of Engineering, Heat Pipe and Nanofluid Research CenterFerdowsi University of MashhadMashhadIran
  2. 2.Department of Chemical Engineering, Faculty of EngineeringFerdowsi University of MashhadMashhadIran
  3. 3.Petroleum DepartmentNational Iranian South Oil Field CompanyAhwazIran

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