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Natural convection of CNT water-based nanofluids in a differentially heated square cavity

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The present paper deals with the prediction of average Nusselt number in a differentially heated square cavity filled with Newtonian and non-Newtonian CNT nanofluids. Based on thermophysical properties which were experimentally evaluated, available correlations are used for estimating the Nusselt number and heat transfer coefficient of natural convection of CNT nanofluids with volume fractions in a range of 0.0055–0.418%. The effects of surfactant, average temperature of nanofluids within the cavity, driving temperature of cavity walls on Nusselt number are investigated and discussed. A peculiar attention is devoted to the non-Newtonian nature of CNT nanofluids in the analysis. It is found in particular that Nusselt number of nanofluids is lowered by nanoparticle content increase related to non-Newtonian behavior of nanofluids and temperature increase.

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ρ :

Density (kg m−3)

k :

Thermal conductivity (W m−1 K−1)

μ :

Viscosity (Pa s)

\(\dot{\gamma }\) :

Shear rate (s−1)

τ :

Shear stress (Pa)

η :

Consistency (Pa sn)

n :

Flow index behavior (–)

C p :

Specific heat (J kg−1 K−1)

β :

Thermal expansion coefficient (K−1)

ϕ :

Nanoparticle volume fraction


Nusselt number


Rayleigh number


Prandtl number

L :

Length and height of the enclosure (m)

g :

Gravity (m s−2)


Carbon nanotubes


Sodium dodecyl benzene sulfonate


Base fluid














  1. Haddad Z, Öztop HF, Abu-Nada E, Mataoui A. A review on natural convective heat transfer of nanofluids. Renew Sust Energy Rev. 2012;16:5363–78.

    Article  CAS  Google Scholar 

  2. Öztop HF, Estellé P, Yan W-M, Al-Salem K, Orfi J, Mahian O. A brief review of natural convection in enclosures under localized heating with and without nanofluids. Int Commun Heat Mass Transfer. 2015;60:37–44.

    Article  Google Scholar 

  3. Öztop HF, Abu-Nada E. Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. Int J Heat Fluid Flow. 2008;29:1326–36.

    Article  Google Scholar 

  4. Abouali O, Ahmadi G. Computer simulations of natural convection of single phase nanofluids in simple enclosures: a critical review. Appl Thermal Eng. 2012;36:1–13.

    Article  CAS  Google Scholar 

  5. Ho CJ, Chen MW, Li ZW. Numerical simulation of natural convection of nanofluid in square enclosure: effects due to uncertainties of viscosity and thermal conductivity. Int J Heat Mass Transfer. 2008;51:4506–16.

    Article  CAS  Google Scholar 

  6. Abouali O, Falahat Pisheh A. Numerical investigation of natural convection of Al2O3 nanofluid in vertical annuli. Heat Mass Transfer. 2009;46:15–23.

    Article  CAS  Google Scholar 

  7. Hwang KS, Lee JH, Jang JP. Buoyancy-driven heat transfer of water-based Al2O3 nanofluids in a rectangular cavity. Int J Heat Mass Transfer. 2007;50:4003–10.

    Article  CAS  Google Scholar 

  8. Murshed SMS, Nieto de Castro CA. Superior thermal features of carbon nanotubes-based nanofluids—a review. Renew Sust Energy Rev. 2014;37:155–67.

    Article  CAS  Google Scholar 

  9. Shanbedi M, Heris ZS, Maskooki A. Experimental investigation of stability and thermophysical properties of carbon nanotubes suspension in the presence of different surfactants. J Therm Anal Calorim. 2015;120:1193–201.

    Article  CAS  Google Scholar 

  10. Shamaeil M, Firouzi M, Fakhar A. The effects of temperature and volume fraction on the thermal conductivity of functionalized DWCNTs/ethylene glycol nanofluid. J Therm Anal Calorim. 2016;126:1455.

    Article  CAS  Google Scholar 

  11. Estellé P, Halelfadl S, Maré T. Thermal conductivity of CNT water based nanofluids: experimental trends and models overview. J Thermal Eng. 2015;1(2):381–90.

    Article  Google Scholar 

  12. Halelfadl S, Estellé P, Aladag B, Doner N, Maré T. Viscosity of carbon nanotubes water-based nanofluids: influence of concentration and temperature. Int J Thermal Sci. 2013;71:111–7.

    Article  CAS  Google Scholar 

  13. Estellé P. Comment on “Viscosity measurements of multi-walled carbon nanotubes-based high temperature nanofluids”. Mat Lett. 2015;138:162–3.

    Article  Google Scholar 

  14. Li Y, Suzuki S, Inagaki T, Yamauchi N. Carbon-nanotube nanofluid thermophysical properties and heat transfer by natural convection. J Phys Conf Ser. 2014;557:012051.

    Article  Google Scholar 

  15. Esfe MH, Arani AAA, Yan W-M, Ehteram H, Aghaei A, Afrand M. Natural convection in a trapezoidal enclosure filled with carbon nanotube-EG-water nanofluid. Int J Heat Mass Transfer. 2016;92:76–82.

    Article  Google Scholar 

  16. Halelfadl S, Adham AM, Mohd-Ghazali N, Maré T, Estellé P, Ahmad R. Optimization of thermal performance and pressure drop of a rectangular microchannel heat sink using aqueous carbon nanotubes based nanofluid. App Thermal Eng. 2014;62(2):492–9.

    Article  CAS  Google Scholar 

  17. Halelfadl S, Maré T, Estellé P. Efficiency of carbon nanotubes water based nanofluids as coolants. Exp Thermal Fluid Sci. 2014;53:104–10.

    Article  CAS  Google Scholar 

  18. O’Hanley H, Buangiorno J, McKrell T, Hu LW. Measurement and model validation of nanofluid specific heat capacity with differential scanning calorimetry. Adv Mech Eng. 2012. doi:10.1155/2012/181079.

    Google Scholar 

  19. Khanafer K, Vafai K, Lightstone M. Buoyency-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Int J Heat Mass Transfer. 2003;46:3639–53.

    Article  CAS  Google Scholar 

  20. Deng L, Young RJ, Kinloch IA, Sun R, Zhang G, Noé L, Monthioux M. Coefficient of thermal expansion of carbon nanotubes measured by Raman spectroscopy. Appl Phys Lett. 2014;104:051907.

    Article  Google Scholar 

  21. Turan O, Sachdeva A, Chakraborty N, Poole RJ. Laminar natural convection of power-law fluids in a square enclosure with differentially heated side walls subjected to constant temperatures. J Non-Newt Fluids Mech. 2011;166:1049–63.

    Article  CAS  Google Scholar 

  22. Berkovsky BM, Polevikov VK. Numerical study of problems on high-intensive free convection. In: Spalding DB, Afgan H, editors. Heat transfer and turbulent buoyant convection. Washington: Hemisphere; 1977. p. 443–55.

    Google Scholar 

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Correspondence to Patrice Estellé.

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Estellé, P., Mahian, O., Maré, T. et al. Natural convection of CNT water-based nanofluids in a differentially heated square cavity. J Therm Anal Calorim 128, 1765–1770 (2017).

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