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


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.


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.



Average relative error


Absolute average relative error


Mean square error


Root Mean square error


Adaptive neuro fuzzy inference system


Fuzzy inference system


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


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


Specific heat (kJ kg−1 K−1)


Hydraulic diameter (m)

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

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


Thermal conductivity (W m−1 K−1)


Duct length (m)

Nu (exp)

Experimental average Nusselt number of Nanofluid

Nu (th)

Nanofluid Nusselt number calculated from Seider–Tate equation


Peclet number


Prandtl number


Heat flux (W)


Reynolds number


Bulk temperature (K)


Duct wall temperature (K)

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

Average fluid velocity (m s−1)

Greek letters


Viscosity (Pa s)


Nanofluid viscosity at duct wall temperature (Pa s)

\( \phi \)

Nanoparticle volume fraction (%)


Density (kg m−3)





Solid nanoparticles




  1. 1.
    Salehi H, Zeinali Heris S, Noie SH (2011) Experimental study of two-Phase closed thermosyphon with nanofluid and magnetic field effect. J Enhanc Heat Transf 18(3):261–269CrossRefGoogle Scholar
  2. 2.
    Zeinali Heris S, Nasr Esfahany M, Etemad SG (2007) Experimental investigation of convective heat transfer of Al2O3/water nanofluid in circular tube. Int J Heat Fluid Flow 28(2):203–210CrossRefGoogle Scholar
  3. 3.
    Zeinali Heris S, Nasr Esfahany M, Etemad SGh (2006) Investigation of CuO/water nanofluid laminar convective heat transfer through a circular tube. J Enhanc Heat Transf 13(4):279–289CrossRefGoogle Scholar
  4. 4.
    Nassan TH, Heris SZ, Noie SH (2010) A comparison of experimental heat transfer characteristics for Al2O3/water and CuO/water nanofluids in square cross-section duct. Int Commun Heat Mass Transf 37:924–928CrossRefGoogle Scholar
  5. 5.
    Fotukian SM, Nasr Esfahany M (2010) Experimental study of turbulent convective heat transfer and pressure drop of dilute CuO/water nanofluid inside a circular tube. Int Commun Heat Mass Transf 37:214–219CrossRefGoogle Scholar
  6. 6.
    Ghasemi B, Aminossadati SM (2009) Natural convection heat transfer in an inclined enclosure filled with a water–CuO nanofluid, numerical heat transfer. Part A Appl 55(8):807–823CrossRefGoogle Scholar
  7. 7.
    Xuan Y, Li Q (2003) Investigation on convective heat transfer and flow features of nanofluids. J Heat Transf 125:151–155CrossRefGoogle Scholar
  8. 8.
    Williams WC, Buongiorno J, Hu LW (2008) Experimental investigation of turbulent convective heat transfer and pressure loss of alumina/water and zirconia/water nanoparticle colloids (nanofluids) in horizontal tubes. J Heat Transf 130(4):42412–42419CrossRefGoogle Scholar
  9. 9.
    Ahn HS, Kim H, Jo H, Kang S, Chang W, Kim MH (2010) Experimental study of critical heat flux enhancement during forced convective flow boiling of nanofluid on a short heated surface. Int J Multiph Flow 36:375–384CrossRefGoogle Scholar
  10. 10.
    Kim SJ, McKrell T, Buongiorno J, Hu LW (2009) Experimental study of flow critical heat flux in alumina–water, zinc-oxide–water, and diamond–water nanofluids. J Heat Transf 131:043204-1Google Scholar
  11. 11.
    Salehi H, Zeinali Heris S, Koolivand Salooki M, Noei SH (2011) Designing a neural network for closed thermosyphon with nanofluid using a generic algorithm. Braz J Chem Eng 28:157–168CrossRefGoogle Scholar
  12. 12.
    Jang JSR (1993) ANFIS: adaptive network-based fuzzy inference system. IEEE Trans Syst Man Cybern Part C 23:665e85Google Scholar
  13. 13.
    Babuska R (1998) Fuzzy modeling for control. Kluwer, BostonCrossRefGoogle Scholar
  14. 14.
    Han Y, Zeng W, Zhao Y, Qi Y, Sun Y (2011) An ANFIS model for the prediction of flow stress of Ti600 alloy during hot deformation process. Comput Mater Sci 50:2273–2279CrossRefGoogle Scholar
  15. 15.
    Wang YM, Taha MS, Elhag TMS (2008) An adaptive neuro-fuzzy inference system for bridge risk assessment. Expert Syst Appl 34(3):3099–3106CrossRefGoogle Scholar
  16. 16.
    Meharrar A, Tioursi M, Hatti M, Boudghène Stambouli A (2011) A variable speed wind generator maximum power tracking based on adaptative neuro-fuzzy inference system. Expert Syst Appl 38:7659–7664CrossRefGoogle Scholar
  17. 17.
    Rahmanian B, Pakizeh M, Esfandyari M, Maskooki A (2011) A fuzzy inference system for modeling of zinc removal using micellar-enhanced ultra filtration. Sep Sci Technol 46:1–11CrossRefGoogle Scholar
  18. 18.
    Aliyari Shoorehdeli M, Teshnehlab M, KhakiSedigh A (2009) Training ANFIS as an identifier with intelligent hybrid stable learning algorithm based on particle swarm optimization and extended Kalman filter. Fuzzy Sets Syst 160:922–948zbMATHCrossRefGoogle Scholar
  19. 19.
    Maxwell JC (1881) A treatise on electricity and magnetism, vol 1. Clarendon Press, OxfordGoogle Scholar
  20. 20.
    Seider EN, Tate GE (1936) Heat transfer and pressure drop of liquid in tubes. Ind Eng Chem 28(12):1429–1435CrossRefGoogle Scholar
  21. 21.
    Drew DA, Passman SL (1999) Theory of multi component fluids, 1st edn. Springer, BerlinGoogle Scholar
  22. 22.
    Einstein A (1956) Investigation on theory of Brownian motion, 1st edn. Dover, New YorkGoogle Scholar
  23. 23.
    Yang HD (1962) Statistical treatment of experimental data. McGrow-Hill, New yorkGoogle Scholar

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

Personalised recommendations