# Thermal Conductivity and Rheology of Graphene Oxide Nanofluids and a Modified Predication Model

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Section

#### 2.1. Experimental Materials

#### 2.2. Nanofluid Preparation

#### 2.3. Stability Characterization

#### 2.4. Characterization and Measurements

## 3. Results and Discussion

#### 3.1. Stability of Graphene Oxide Nanofluids

#### 3.2. Rheological Properties of GO Nanofluids

#### 3.3. Thermal Conductivity of Graphene Oxide Nanofluids

#### 3.3.1. Effect of Temperature

#### 3.3.2. Effect of Particle Concentration

#### 3.3.3. Existing Models for the Effective Thermal Conductivity of Nanofluid

#### 3.3.4. Our Proposed Model

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Gonçalves, I.; Souza, R.; Coutinho, G.; Miranda, J.; Moita, A.; Pereira, J.; Moreira, A.; Lima, R. Thermal Conductivity of Nanofluids: A Review on Prediction Models, Controversies and Challenges. Appl. Sci.
**2021**, 11, 2525. [Google Scholar] [CrossRef] - Yu, S.-P.; Lue, Y.-F.; Teng, T.-P.; Hsieh, H.-K.; Huang, C.-C. Enhanced Heat Transfer Performance of the Tube Heat Exchangers Using Carbon-Based Nanofluids. Appl. Sci.
**2021**, 11, 8139. [Google Scholar] [CrossRef] - Jin, J.Y.; Hatami, M.; Jing, D.W. Experimental investigation and prediction of the thermal conductivity of water-based oxide nanofluids with low volume fractions. J. Therm. Anal. Calorim.
**2019**, 135, 257–269. [Google Scholar] [CrossRef] - Kleinstreuer, C.; Yu, F. Experimental and theoretical studies of nanofluid thermal conductivity enhancement: A review. Nanoscale Res. Lett.
**2011**, 6, 229. [Google Scholar] [CrossRef] [Green Version] - Mehrali, M.; Latibari, S.T.; Mehrali, M.; Mahlia, T.M.I.; Metselaar, H.S.C. Preparation and properties of highly conductive palmitic acid/graphene oxide composites as thermal energy storage materials. Energy
**2013**, 58, 628–634. [Google Scholar] [CrossRef] - Baby, T.T.; Ramaprabhu, S. Enhanced convective heat transfer using graphene dispersed nanofluids. Nanoscale Res. Lett.
**2011**, 6, 289–299. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Chen, L.; Xie, H. Surfactant-free nanofluids containing double- and single-walled carbon nanotubes functionalized by a wet-mechanochemical reaction. Thermochim. Acta
**2010**, 497, 67–71. [Google Scholar] [CrossRef] - Wakif, A.; Zaydan, M.; Alshomrani, A.S.; Muhammad, T.; Sehaqui, R. New insights into the dynamics of alumina-(60% ethylene glycol + 40% water) over an isothermal stretching sheet using a renovated Buongiorno’s approach: A numerical GDQLLM analysis. Int. Commun. Heat Mass Transf.
**2022**, 133, 105937. [Google Scholar] [CrossRef] - Nayak, M.K.; Wakif, A.; Animasaun, I.L.; Alaoui, M.S.H. Numerical Differential Quadrature Examination of Steady Mixed Convection Nanofluid Flows Over an Isothermal Thin Needle Conveying Metallic and Metallic Oxide Nanomaterials: A Comparative Investigation. Arab. J. Sci. Eng.
**2020**, 45, 5331–5346. [Google Scholar] [CrossRef] - Zaydan, M.; Wakif, A.; Alshomrani, I.L.; Khan, U.; Baleanu, D.; Sehaqui, R. Significances of blowing and suction processes on the occurrence of thermo-magneto-convection phenomenon in a narrow nanofluidic medium: A revised Buongiorno’s nanofluid model. Case Stud. Therm. Eng.
**2022**, 22, 100726. [Google Scholar] [CrossRef] - Rasool, G.; Wakif, A. Numerical spectral examination of EMHD mixed convective flow of second-grade nanofluid towards a vertical Riga plate using an advanced version of the revised Buongiorno’s nanofluid model. J. Therm. Anal. Calorim.
**2021**, 143, 2379–2393. [Google Scholar] [CrossRef] - Xia, W.F.; Alshomrani, A.S.; Wakif, A.; Shah, N.A.; Yook, S.-J. Gear-generalized differential quadrature analysis of oscillatory convective Taylor-Couette flows of second-grade fluids subject to Lorentz and Darcy-Forchheimer quadratic drag forces. Int. Commun. Heat Mass Transf.
**2021**, 126, 105395. [Google Scholar] [CrossRef] - Wakif, A.; Animasaun, I.L.; Khan, U.; Shah, N.A.; Thumma, T. Dynamics of radiative-reactive Walters-b fluid due to mixed convection conveying gyrotactic microorganisms, tiny particles experience haphazard motion, thermo-migration, and Lorentz force. Phys. Scr.
**2021**, 96, 125239. [Google Scholar] [CrossRef] - Alghamdi, M.; Wakif, A.; Thumm, T.; Khan, U.; Baleanu, D.; Rasool, G. Significance of variability in magnetic field strength and heat source on the radiative-convective motion of sodium alginate-based nanofluid within a Darcy-Brinkman porous structure bounded vertically by an irregular slender surface. Case Stud. Therm. Eng.
**2021**, 28, 101428. [Google Scholar] [CrossRef] - Ghozatloo, A.; Shariaty-Niasar, M.; Rashidi, A.M. Preparation of nanofluids from functionalized Graphene by new alkaline method and study on the thermal conductivity and stability. Int. Commun. Heat Mass Transf.
**2013**, 42, 89–94. [Google Scholar] [CrossRef] - Jing, D.W.; Hu, Y.; Liu, M.C.; Wei, J.J.; Guo, L.J. Preparation of highly dispersed nanofluid and CFD study of its utilization in a concentrating PV/T system. Sol. Energy
**2015**, 112, 30–40. [Google Scholar] [CrossRef] - Sun, L.; Zhao, Q.Y.; Zhang, Y.M.; Gao, W.; Jing, D.W. Insights into the rheological behavior of ethanol-based metal oxide nanofluids. J. Mol. Liq.
**2021**, 323, 115006. [Google Scholar] [CrossRef] - Chopkar, M.; Sudarshan, S.; Das, P.; Manna, I. Effect of Particle Size on Thermal Conductivity of Nanofluid. Met. Mater. Trans.
**2008**, 39, 1535–1542. [Google Scholar] [CrossRef] - Lu, S.-Y.; Lin, H.-C. Effective conductivity of composites containing aligned spheroidal inclusions of finite conductivity. J. Appl. Phys.
**1996**, 79, 6761. [Google Scholar] [CrossRef] - Taherialekouhi, R.; Rasouli, S.; Khosravi, A. An experimental study on stability and thermal conductivity of water-graphene oxide/aluminum oxide nanoparticles as a cooling hybrid nanofluid. Int. J. Heat Mass Transf.
**2019**, 145, 118751. [Google Scholar] [CrossRef]

**Figure 2.**(

**a**) UV–Vis absorption spectra of GO nanofluids with different concentrations and (

**b**) relationship between mass concentration and maximum absorption.

**Figure 3.**(

**a**) Zeta potential of 0.002% GO nanofluid and (

**b**) particle size distribution intensity curve of 0.002% GO nanofluid.

**Figure 4.**Relationship between viscosity and shear rate of nanofluids (

**a**–

**e**) GO–water 0.002%, 0.004% 0.006%, 0.008% and 0.010% and (

**f**) relationship between temperature and dynamic viscosity.

**Figure 5.**Thermal conductivity of GO–water nanofluid versus temperature. (

**a**): absolute, (

**b**): relative to water.

**Figure 7.**Comparison of experimental data for GO/DI-water-based nanofluids with results from models. (

**a**–

**f**) under temperature of 25, 30, 35, 40, 45 and 50 °C, respectively.

**Figure 9.**Deviation between the output value of the correlation and the experimentally measured value.

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**MDPI and ACS Style**

Mei, X.; Sha, X.; Jing, D.; Ma, L.
Thermal Conductivity and Rheology of Graphene Oxide Nanofluids and a Modified Predication Model. *Appl. Sci.* **2022**, *12*, 3567.
https://doi.org/10.3390/app12073567

**AMA Style**

Mei X, Sha X, Jing D, Ma L.
Thermal Conductivity and Rheology of Graphene Oxide Nanofluids and a Modified Predication Model. *Applied Sciences*. 2022; 12(7):3567.
https://doi.org/10.3390/app12073567

**Chicago/Turabian Style**

Mei, Xinyu, Xin Sha, Dengwei Jing, and Lijing Ma.
2022. "Thermal Conductivity and Rheology of Graphene Oxide Nanofluids and a Modified Predication Model" *Applied Sciences* 12, no. 7: 3567.
https://doi.org/10.3390/app12073567