# Thermal Conductivity and Rheology of Graphene Oxide Nanofluids and a Modified Prediction Model
## 4 Conclusions  
In this study, the viscosity and thermal conductivity of graphene oxide nanofluids were measured. The range of temperature is 25-50 \({}^{\circ}\)C and the mass concentrations are 0.002%, 0.004%, 0.006%, 0.008% and 0.010%, respectively. Agglomeration and sedimentation of the prepared nanofluids after standing for 20 days were not observed, showing the good stability of the prepared graphene oxide-water nanofluid. Our results show that with an increase in temperature, the dynamic viscosity of nanofluids decreases, but the thermal conductivity increases. We demonstrate that graphene oxide nanofluids can improve the heat transfer performance, especially at high temperature. The reason for thermal conductivity increasing can be attributed to the increased Brownian motion of nanoparticles and the enhanced molecular kinetic energy with the increase in temperature. The enhanced nanoparticle collision finally results in improved thermal conductivity. The highest thermal conductivity increase is obtained when the nanofluid concentration is 0.01% and the temperature is 50 \({}^{\circ}\)C. Finally, and most importantly, considering the inaccuracy of the existing experimental correlations to the predicted values of thermal conductivity, we propose our own mathematical model of correlation and carry out a series of tests to verify its accuracy. The experimental correlations with temperature and concentration as independent variables show good agreement and accuracy with the experimental data. It is worth noting that our correlation is in fact a semi-empirical one, which is based on our experimental data over five kinds of graphene oxide nanofluids, with a mass fraction of 0.002% to 0.01%, which have been studied in the temperature range of 25-50 \({}^{\circ}\)C. Therefore, the model is strictly reliable in terms of volume fraction and temperature working within this range. Fortunately, with this range combined with the reported data for higher temperatures, we can ensure that our model can be a useful tool for most of the application cases.  
Conceptualization, L.M.; methodology, X.M.; software, X.S.; validation, X.M. and X.S.; formal analysis, D.J.; writing--original draft preparation, X.M.; writing--review and editing, L.M.; supervision and funding acquisition, L.M. All authors have read and agreed to the published version of the manuscript.  
Figure 9: Deviation between the output value of the correlation and the experimentally measured value.  
**Funding:** This research was funded by the National Key Research and Development Program of China (2018 YFB1502000), the Royal Society Newton Advanced Fellowship grant (NAF\R1\191163) and The Youth Innovation Team of Shaanxi Universities.  
**Acknowledgments:** The authors gratefully acknowledge the financial support of the National Key Research and Development Program of China (2018 YFB1502000), the Royal Society Newton Advanced Fellowship grant (NAF\R1\191163) and The Youth Innovation Team of Shaanxi Universities.  
**Conflicts of Interest:** The authors declare no conflict of interest that could have appeared to influence the work reported in this paper.