Modeling of Effective Thermal Conductivity and Viscosity of Carbon Structured Nanofluid

Document Type : Original Research Paper


1 Mechanical Engineering Department, University of Shahrood, Shahrood, I.R. Iran

2 Nanotechnology Reasearch Institute, University of Sistan and Baluchestan, Zahedan, I.R. Iran

3 Nanotechnology Research Center, Research Institute of Petroleum Industry, I.R. Iran

4 Chemical Engineering Department, University of Tehran, Tehran, I.R. Iran


This paper was aimed to address the modeling of effective thermal conductivity and viscosity of carbon structured nanofluids. Response surface methodology, D_optimal design (DOD) was employed to assess the main and interactive effects of temperature (T) and weight percentage (wt %) to model effective thermal conductivity and viscosity of multi wall and single wall carbon nanotube, CVD and RGO Graphene and nanoporous Graphene sheet. The second-order polynomial regression model was proposed for effective thermal conductivity and viscosity as a function of relevant investigated parameters. Effective thermal conductivity and viscosity of nanofluids measured using an accurate transient short hot wire system and a viscometer, respectively. nanofluids was prepared using two-step method and showed a desirable stability. In general, Graphene nanosheets have more effective thermal conductivity and viscosity compared to carbon nanotube because of variation in shape and likely size.


[1] J. C. Maxwell, Electricity and magnetism. Claredon, Oxford (1873).
[2] J. C. Maxwell, A Treatise on Electricity and Magnetism, vol. II. Clarendon, Oxford (1904).
[3] S. U. S. Choi, J. A. Eastman, Enhancing thermal conductivity of fluids with nanoparticles (1995).
[4] W.Yu, S. U. Choi, The role of interfacial layers in the enhanced thermal conductivity of nanofluids: a renovated Maxwell model. Journal of Nanoparticle Research 5 (2003) 167–171.
[5] S. K. Das, N. Putra, P. Thiesen, W. Roetzel, Temperature dependence of thermal conductivity enhancement for nanofluids. Journal of Heat Transfer 125 (2003) 567–574.
[6] D. Wen, Y.Ding, Effective thermal conductivity of aqueous suspensions of carbon nanotubes (carbon nanotube nanofluids), Journal of Thermophysics and Heat Transfer 18 (2004) 481–485.
[7] D. Wen, Y.Ding, Experimental investigation into convective heat transfer of nanofluids at the entrance region under laminar flow conditions. International journal of heat and mass transfer 47 (2004) 5181–5188.
[8] C. H. Li, G. P. Peterson, Experimental investigation of temperature and volume fraction variations on the effective thermal conductivity of nanoparticle suspensions (nanofluids). Journal of Applied Physics 99 (2006) 84314.
[9] S. M. Murshed, , K. C. Leong, C. Yang, Investigations of thermal conductivity and viscosity of nanofluids. International Journal of Thermal Sciences 47 (2008) 560–568.
[10] W. Duangthongsuk, S. Wongwises, Measurement of temperature-dependent thermal conductivity and viscosity of TiO< sub> 2-water nanofluids. Experimental Thermal and Fluid Science 33 (2009) 706–714.
[11] T. X. Phuoc, M.  Massoudi, R.-H. Chen, Viscosity and thermal conductivity of nanofluids containing multi-walled carbon nanotubes stabilized by chitosan. International Journal of Thermal Sciences 50 (2011) 12–18.
[12] M. Corcione, Empirical correlating equations for predicting the effective thermal conductivity and dynamic viscosity of nanofluids. Energy Conversion and Management 52 (2011) 789–793.
[13] R. L. Hamilton, O. K. Crosser, Thermal conductivity of heterogeneous two-component systems. Industrial & Engineering chemistry fundamentals 1(1962) 187–191.
[14] D. H. Kumar, H. E. Patel, V. R. Kumar, T. Sundararajan, T. Pradeep, S. K. Das, Model for heat conduction in nanofluids. Physical Review Letters 93 (2004) 144301.
[15] K. C. Leong, C. Yang, S. M. Murshed, A model for the thermal conductivity of nanofluids–the effect of interfacial layer. Journal of Nanoparticle Research 8 (2006) 245–254.
[16] G. H. Ko, K. Heo, K. Lee, , D. S. Kim, , C. Kim, , Y. Sohn, M. Choi, An experimental study on the pressure drop of nanofluids containing carbon nanotubes in a horizontal tube. International journal of heat and mass transfer 50 (2007) 4749–4753.
[17]  L. Girifalco, M. Hodak, R. S. Lee, Carbon nanotubes, buckyballs, ropes, and a universal graphitic potential. Physical Review B 62 ( 2000) 13104.
[18] T. Lin,V. Bajpai, T. Ji, L .Dai, Chemistry of carbon nanotubes. Australian journal of chemistry 56 (2003) 635–651.
[19] C. Park, Z. Ounaies, K. A. Watson, R. E. Crooks,  J. Smith Jr, S. E. Lowther, , J. W. Connell, , E. J. Siochi, J. S. Harrison, St. Clair, Terry L  Dispersion of single wall carbon nanotubes by in situ polymerization under sonication. Chemical physics letters 364 (2002) 303–308.
[20] D. C. Montgomery, Design and analysis of experiments, John Wiley & Sons (2008).
[21]  R. H. Meyers, D.C. Montgomery, Response surface methodology: Wiley New York NY (2002).
[22] M. A. Bezerra, R. E. Santelli, , E. P. Oliveira, L. S. Villar, L. A. Escaleira, Response surface methodology (RSM) as a tool for optimization in analytical chemistry. Talanta 76(2008) 965–977.
[23] H. C. Brinkman, The viscosity of concentrated suspensions and solutions. The Journal of Chemical Physics 20 (2004) 571.