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


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














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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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  • CNT nanofluid
  • Natural convection
  • Cavity
  • Volume fraction influence
  • Non-Newtonian effect