Abstract
Maxwell’s classical model for predicting effective thermal conductivity of colloidal solution predicts the thermal conductivity of nanofluids quite satisfactorily. However, Maxwell’s model does not consider the effect of interfacial layer, Brownian motion of nano-particle and nanoparticle aggregation. In this paper, the effect of interfacial layer on thermal conductivity is considered. A simple expression has been derived to determine thermal conductivity of nanofluid considering interfacial layer formed on the nano particles. The thermal conductivity of the interfacial layer has been precisely determined and results are found to be closer to the experimental values, hence, further improving the results of classical Maxwell model.
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Abbreviations
- n:
-
Particle shape factor
- Mw :
-
Molecular weight of liquid
- NA :
-
Avogadro’s constant
- ρ:
-
Density of the liquid
- rp :
-
Radius of nanoparticle
- t:
-
Thickness of the interfacial nano-layer
- υ :
-
Particle volume concentration
- kp :
-
Thermal conductivity of particle
- km :
-
Thermal conductivity of liquid medium
- Q:
-
Heat flow rate through interfacial layer
- r:
-
Radial distance from the centre of the particle
- A:
-
Surface area at a distance ‘r’ from the centre of nanoparticle
- T:
-
Temperature at a distance ‘r’ from the centre of nanoparticle
- kl :
-
Thermal conductivity of interfacial nano-layer
- kc :
-
Thermal conductivity of particle and interfacial nano-layer composite
- keff :
-
Effective thermal conductivity of nanofluid
- EG:
-
Ethylene glycol
References
Choi US (1995) Enhancing thermal conductivity of fluids with nanoparticles. ASME FED 231:99–103
Xuan Y, Li Q (2003) Investigation on convective heat transfer and flow features of nanofluids. J Heat Trans ASME 125:151–155
Choi SUS, Zhang ZG, Yu W, Lockwood FE, Grulke EA (2001) Anomalous thermal conductivity enhancement in nanotube suspensions. Appl Phys Lett 79(14):2252–2254
Eastman JA, Choi SUS, Li S, Yu W, Thompson LJ (2001) Anomalously increased effective thermal conductivity of ethylene glycol-based nanofluids containing copper nanoparticles. Appl Phys Lett 78:718–720
Patal HE, Das SK, Sundarajan T (2003) Thermal conductivities of naked and monolayer protected metal nanoparticle based nanofluid: manifestation of anomalous enhancement and chemical effects. Appl Phys Lett 83:2931–2933
Maxwell JC (1904) A treatise on electricity and magnetism, 2nd edn. Oxford University Press, Cambridge
Hamilton RL, Crosser OK (1962) Thermal conductivity of heterogeneous two component systems. Ind Eng Chem Fundam 1(3):187–191
Wang BX, Zhou LP, Peng XF (2003) A fractal model for predicting the effective thermal conductivity of liquid with suspension of nanoparticles. Int J Heat Mass Transf 46:2665–2672
Tillman P, Hill JM (2007) Determination of nanolayer thickness for a nanofluid. Int Commun Heat Mass Transf 34:399–407
Evans W, Prasher R, Fish J, Meakin P, Phelan P, Keblinski P (2008) Effect of aggregation and interfacial thermal resistance on thermal conductivity of nanocomposites and colloidal nanofluids. Int J Heat Mass Transf 51:1431–1438
Karthikeyan NR, Philip J, Raj B (2008) Effect of clustering on the thermal conductivity of nanofluids. Mater Chem Phys 109:50–55
Buongiorno J et al (2009) A benchmark study on the thermal conductivity of nanofluids. J Appl Phys 106:094312
Koo J, Kleinstreuer C (2004) A new thermal conductivity model for nanofluids. J Nanoparticle Res 6:577–588
Jang SP, Choi SUS (2004) Role of Brownian motion in the enhanced thermal conductivity of nanofluids. Appl Phys Lett 84:4316–4318
Henderson JR, van Swol F (1984) On the interface between fluid and the planner wall: theory and simulations of a hard sphere fluid at a hard wall. Mol Phys 51:1991–1010
Yu C-J, Richter AG, Datta A, Durbin MK, Dutta P (2000) Molecular layering in a liquid on a solid substrate: an X-Ray reflectivity study. Phys B 283:27–31
Yu W, Choi SUS (2003) The role of interfacial layer in the enhanced thermal conductivity of nanofluids: a renovated Hamilton Crosser Model. J Nanoparticle Res 6:355–361
Jeffrey DJ (1973) Conduction through a random suspension of spheres. Proc R Soc Lond Ser A 335:355–367
Davis RH (1986) The effective thermal conductivity of a composite material with spherical inclusions. Int J Thermophys 7(3):609
Lu S, Lin H (1996) Effective conductivity of composites containing aligned spheroidal inclusions of finite conductivity. J Appl Phys 79:6761
Xue Q, Xue WM (2005) A model of thermal conductivity of nanofluids with interfacial shells. Mat Chem Phys 90:298–301
Bruggeman DAG (1935) Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. Ann Phys Lpz 24:636
Xie H, Wang J, Xi T, Liu Y (2002) Thermal conductivity enhancement of suspensions containing nano-sized alumina particles. J Appl Phys 91:4568–4572
Kwak K, Kim C (2005) Viscosity and thermal conductivity of copper oxide nanofluid dispersed in ethylene glycol. Korea-Aust Rheol J 17(2):35–40
Lee S, Choi SU-S, Li S, Eastman JA (1999) Measuring thermal conductivity of fluids containing oxide nanoparticles. Trans ASME J Heat Transf 121:280–289
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Rizvi, I.H., Jain, A., Ghosh, S.K. et al. Mathematical modelling of thermal conductivity for nanofluid considering interfacial nano-layer. Heat Mass Transfer 49, 595–600 (2013). https://doi.org/10.1007/s00231-013-1117-z
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DOI: https://doi.org/10.1007/s00231-013-1117-z