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Mathematical modelling of thermal conductivity for nanofluid considering interfacial nano-layer

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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

  1. Choi US (1995) Enhancing thermal conductivity of fluids with nanoparticles. ASME FED 231:99–103

    Google Scholar 

  2. Xuan Y, Li Q (2003) Investigation on convective heat transfer and flow features of nanofluids. J Heat Trans ASME 125:151–155

    Article  Google Scholar 

  3. 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

    Article  Google Scholar 

  4. 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

    Article  Google Scholar 

  5. 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

    Article  Google Scholar 

  6. Maxwell JC (1904) A treatise on electricity and magnetism, 2nd edn. Oxford University Press, Cambridge

    Google Scholar 

  7. Hamilton RL, Crosser OK (1962) Thermal conductivity of heterogeneous two component systems. Ind Eng Chem Fundam 1(3):187–191

    Article  Google Scholar 

  8. 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

    Article  MATH  Google Scholar 

  9. Tillman P, Hill JM (2007) Determination of nanolayer thickness for a nanofluid. Int Commun Heat Mass Transf 34:399–407

    Article  Google Scholar 

  10. 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

    Article  MATH  Google Scholar 

  11. Karthikeyan NR, Philip J, Raj B (2008) Effect of clustering on the thermal conductivity of nanofluids. Mater Chem Phys 109:50–55

    Article  Google Scholar 

  12. Buongiorno J et al (2009) A benchmark study on the thermal conductivity of nanofluids. J Appl Phys 106:094312

    Article  Google Scholar 

  13. Koo J, Kleinstreuer C (2004) A new thermal conductivity model for nanofluids. J Nanoparticle Res 6:577–588

    Article  Google Scholar 

  14. Jang SP, Choi SUS (2004) Role of Brownian motion in the enhanced thermal conductivity of nanofluids. Appl Phys Lett 84:4316–4318

    Article  Google Scholar 

  15. 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

    Article  Google Scholar 

  16. 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

    Article  Google Scholar 

  17. 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

    Article  Google Scholar 

  18. Jeffrey DJ (1973) Conduction through a random suspension of spheres. Proc R Soc Lond Ser A 335:355–367

    Article  Google Scholar 

  19. Davis RH (1986) The effective thermal conductivity of a composite material with spherical inclusions. Int J Thermophys 7(3):609

    Article  Google Scholar 

  20. Lu S, Lin H (1996) Effective conductivity of composites containing aligned spheroidal inclusions of finite conductivity. J Appl Phys 79:6761

    Article  Google Scholar 

  21. Xue Q, Xue WM (2005) A model of thermal conductivity of nanofluids with interfacial shells. Mat Chem Phys 90:298–301

    Article  Google Scholar 

  22. Bruggeman DAG (1935) Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. Ann Phys Lpz 24:636

    Article  Google Scholar 

  23. 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

    Article  Google Scholar 

  24. 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

    MathSciNet  Google Scholar 

  25. 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

    Article  Google Scholar 

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Correspondence to Subrata Kr. Ghosh.

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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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