Abstract
A model for predicting the effective thermal conductivity of nanofluids is proposed. It has been documented that the interfacial layer at the solid (particle)/liquid interface and particle size is one of the major mechanisms for enhancing the thermal conductivity of nanofluids. Comparing with other classical models, the proposed model takes into account some additional effects including volume fraction, thickness, thermal conductivity of the interfacial layer and particle size. The proposed model is found to be better than the existing models since the predicted effective thermal conductivity of different types of nanofluids are closer to the experimental results.
Similar content being viewed by others
Abbreviations
- T :
-
temperature
- k :
-
thermal conductivity
- r :
-
radial position in spherical coordinates
- h :
-
interfacial layer thickness
- q :
-
heat flux
- V :
-
volume
- a :
-
particle radius
- γ:
-
ratio of interfacial layer thickness and particle radius (h/a)
- θ:
-
angular position in spherical coordinates
- ϕ:
-
volume fraction
- eff:
-
effective
- p:
-
particle
- lr:
-
interfacial layer
- f:
-
base fluid
- pe:
-
equivalent particle
References
Choi S.U.S., 1995. Enhancing thermal conductivity of fluids with nanoparticles. In: Siginer, D.A. and Wang, H.P. eds. Developments and Application of Non-Newtonian Flows, ASME, New York, FED-Vol. 231/MD- Vol. 66, pp. 99–103
Choi S.U.S., Xu X., Keblinski P., Yu W., (2002). Nanofluids can take the heat, DOE BES 20th Symposium on Energy Engineering Sciences. Argonne, USA
Ding Y., Wen D., Williams R.W., (2004). Nanofluids for heat transfer intensification - Where are we and where should we go? Proceedings of 6th International Symposium on Heat Transfer, Beijing, pp. 66–76
Das S.K., Putra N., Thiesen P., Roetzel W., (2003). Temperature dependence of thermal conductivity enhancement for nanofluids. J. Heat Transfer 125: 567–574
Eastman J.A., S.U.S. Choi, S. Li & L.J. Thompson, 1997. Enhanced thermal conductivity through the development of nanofluids. Proceedings of the Symposium on Nanophase and Nanocomposite Materials II, Boston, Vol. 457, pp. 3–11
Eastman J.A., Choi S.U.S., Li S., Yu W., Thompson L.J., (2001). Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles. Appl. Phys. Lett. 78(6): 718–720
Eastman J.A., Phillpot S.R., Choi S.U.S., Keblinski P., (2004). Thermal transport in nanofluids. Annu. Rev. Mater. Res. 34: 219–246
Hamilton R.L., Crosser O.K., (1962). Thermal conductivity of heterogeneous two component systems. I & EC Fundamentals 1: 187–191
Hui P.M., Zhang X., Markworth A.J., Stroud D., (1999). Thermal conductivity of graded composites: Numerical simulations and an effective medium approximation. J. Mater. Sci. 34: 5497–5503
Jang S.P., Choi S.U.S., (2004). Role of Brownian motion in the enhanced thermal conductivity of nanofluids. Appl. Phys. Lett. 84: 4316–4318
Keblinski P., Phillpot S.R., Choi S.U.S., Eastman J.A., (2002). Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids). Int. J. Heat Mass Transfer 45: 855–863
Kumar D.H., Patel H.E., Kumar V.R.R., Sundararajan T., Pradeep T., Das S.K., (2004). Model for heat conduction in nanofluids. Phys. Rev. Lett. 93(14): 4301–4304
Lee S., Choi S.U.S., Li S., Eastman J.A., (1999). Measuring thermal conductivity of fluids containing oxide nanoparticles. J. Heat Transfer 121: 280–289
Masuda H., Ebata A., Teramae K., Hishinuma N., (1993). Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles (Dispersion of Gama-Al2O3, SiO2, and TiO2 ultra-fine particles). Netsu Bussei (Japan) 4(4): 227–233
Maxwell J.C., (1891). A treatise on electricity and magnetism 3rd edition. Clarendon Press, Oxford U.K
Murshed S.M.S., Leong K. C., Yang C., (2005). Enhanced thermal conductivity of TiO2-water based nanofluids. Int. J. Therm. Sci. 44(4): 367–373
Tinga W.R., Voss W.A.G., Blossey D.F., (1973). Generalized approach to multiphase dielectric mixture theory. J. Appl. Phys. 44(9): 3897–3902
Wang Y., T.S. Fisher, J.L. Davidson & L. Jiang, 2002. Thermal conductivity of nanoparticle suspensions. Proceedings of 8th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, Missouri, AIAA 2002–3345, pp. 1–6
Wang B.-X., Zhou L.-P., Peng X.-P., (2003). A fractal model for predicting the effective thermal conductivity of liquid with suspension of nanoparticles. Int. J. Heat Mass Transfer 46: 2665–2672
Xie H., Wang J., Xi T., Liu Y., Ai F., (2002). Thermal conductivity enhancement of suspensions containing nanosized alumina particles. J. Appl. Phys. 91: 4568- 4572
Xuan Y., Li Q., Hu W., (2003). Aggregation structure and thermal conductivity of nanofluids. AIChE Journal 49: 1038–1043
Xue Q.-Z., (2003). Model for effective thermal conductivity of nanofluids. Phys. Lett. A 307: 313–317
Xue L., Keblinski P., Phillpot S.R., Choi S.U.S., Eastman J.A., (2004). Effect of liquid layering at the liquid-solid interface on thermal transport. Int. J. Heat Mass Transfer 47: 4277–4284
Yu W., Choi S.U.S., (2003). The role of interfacial layers in the enhanced thermal conductivity of nanofluids: a renovated Maxwell model. J. Nanoparticle Res. 5: 167–171
Yu C.-J., A.G. Richter, A. Datta, M.K. Durbin & P. Dutta, 2000. Molecular layering in a liquid on a solid substrate: An X-ray reflectivity study. Physica B 283, 27–31
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Leong, K., Yang, C. & Murshed, S. A model for the thermal conductivity of nanofluids – the effect of interfacial layer. J Nanopart Res 8, 245–254 (2006). https://doi.org/10.1007/s11051-005-9018-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11051-005-9018-9