# A thermal conductivity model for nanofluids including effect of the temperature-dependent interfacial layer

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## Abstract

The interfacial layer of nanoparticles has been recently shown to have an effect on the thermal conductivity of nanofluids. There is, however, still no thermal conductivity model that includes the effects of temperature and nanoparticle size variations on the thickness and consequently on the thermal conductivity of the interfacial layer. In the present work, the stationary model developed by Leong et al. (J Nanopart Res 8:245–254, 2006) is initially modified to include the thermal dispersion effect due to the Brownian motion of nanoparticles. This model is called the ‘*Leong et al.’s dynamic model*’. However, the Leong et al.’s dynamic model over-predicts the thermal conductivity of nanofluids in the case of the flowing fluid. This suggests that the enhancement in the thermal conductivity of the flowing nanofluids due to the increase in temperature does not come from the thermal dispersion effect. It is more likely that the enhancement in heat transfer of the flowing nanofluids comes from the temperature-dependent interfacial layer effect. Therefore, the Leong et al.’s stationary model is again modified to include the effect of temperature variation on the thermal conductivity of the interfacial layer for different sizes of nanoparticles. This *present model* is then evaluated and compared with the other thermal conductivity models for the turbulent convective heat transfer in nanofluids along a uniformly heated tube. The results show that the present model is more general than the other models in the sense that it can predict both the temperature and the volume fraction dependence of the thermal conductivity of nanofluids for both non-flowing and flowing fluids. Also, it is found to be more accurate than the other models due to the inclusion of the effect of the temperature-dependent interfacial layer. In conclusion, the present model can accurately predict the changes in thermal conductivity of nanofluids due to the changes in volume fraction and temperature for various nanoparticle sizes.

## Keywords

Nanofluids Thermal conductivity Interfacial layer Thermal dispersion Convective heat transfer Colloids## Nomenclature

*a*Particle radius

*c*Specific heat

*d*Diameter

*h*Interfacial layer thickness

*h*_{f}Averaged heat transfer coefficient of base fluid

*h*_{nf}Averaged heat transfer coefficient of nanofluid

*k*Thermal conductivity

*k*_{b}Boltzmann’s constant

*k*_{eff}Effective thermal conductivity

*k*_{static}Effective stagnant thermal conductivity of solid–liquid mixture

*k*_{V}Enhancement in the thermal conductivity due to the thermal dispersion

*p*Probability for a particle to travel along any direction

*u, v, w*Velocity components in

*X, Y, Z*Cartesian coordinates*C*Modified model constants

*T*Temperature

*T*_{∞}Temperature at the infinite distance

- \( \left| {\bar{V}} \right| \)
Averaged velocity

## Greek symbols

## Subscripts

- f
Base fluid

- lr
Interfacial layer

- nf
Nanofluid

- p
Particle

## Notes

### Acknowledgements

This research work is partly supported by the Thai National Grid Centre and the Sun Microsystems. The Financial supports from the Kasetsart University Research and Development Institute (KURDI) and the Thailand Research Fund (TRF) for the Senior Scholar Professor Pramote Dechaumphai and the Scholar Associate Professor Varangrat Juntasaro.

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