Experimental investigation and prediction of the thermal conductivity of water-based oxide nanofluids with low volume fractions

  • Jingyu Jin
  • Mohammad Hatami
  • Dengwei JingEmail author


Although there are already many models for prediction of the thermal conductivity of nanoparticle suspension, most of them only consider the cases for high nanoparticle volume fractions (often > 0.1%). Considering the cost of particle itself, pumping and transportation, dispersion stability, etc., low particle concentrations are obviously more preferred. The present study firstly experimentally investigated the thermal conductivity of some oxide colloid suspensions with low particle concentrations. It was found that the famous multi-sphere Brownian model (MSBM) showed a large deviation for thermal conductivity prediction when the particle concentrations are below 0.1%. By introducing an adjustable exponential constant, n, into the volume fraction item of MSBM, the predicted thermal conductivity can be in good agreement with experimental data for the particle volume fractions ranging from 0.001 to 10%. The dependency of n on the particle volume fraction and its possible physical significance were discussed in detail. It turns out that, when the volume fraction is larger than 1%, the modified model can be reduced to the original MSBM. The value of n approximately equals to 0.7 when the volume fractions of nanofluids are lower than 0.005%. Between these two volume fractions, n is found to follow a nearly linear relation with the logarithm of volume fraction. The validity of the modified MSBM model for practical supplication was further justified based on numerical method. The simulation results showed that our model has excellent agreement with Maxwell–Garnetts model in low volume fraction ranges due to the weak interaction between various nanoparticles in the system. Our study should be of value for numerical simulation and engineering design of nanofluids in the future.


Nanoparticle suspension Thermal conductivity Multi-sphere Brownian model Low volume fractions 

List of symbols

Roman letters


Empirical constant


Specific heat of the base fluid (J kg−1 K−1)


Diameter of the nanoparticle (m)


Thermal conductivity (W m−1 K−1)


Boltzmann constant = 1.3807 × 10−23 (J K−1)


Empirical constant


Multi-sphere Brownian model


Empirical constant


Nusselt number


Prandtl number


Thermal boundary resistance (m2 K W−1)


Reynolds number


Kelvin temperature (K)

Greek symbols


Biot number


Particle volume fraction


Dynamic viscosity (kg m−1 s−1)


Kinematic viscosity (m2 s−1)


Density (kg m−3)












The authors gratefully acknowledge the financial supports of the National Natural Science Foundation of China (No. 51776165). This work was also supported by the China Fundamental Research Funds for the Central Universities.


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Multiphase Flow in Power Engineering and International Research Center for Renewable EnergyXi’an Jiaotong UniversityXi’anChina

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