Brownian dynamic simulation for the prediction of effective thermal conductivity of nanofluid

  • Shashi Jain
  • Hrishikesh E. Patel
  • Sarit Kumar Das
Research Paper


Nanofluid is a colloidal solution of nanosized solid particles in liquids. Nanofluids show anomalously high thermal conductivity in comparison to the base fluid, a fact that has drawn the interest of lots of research groups. Thermal conductivity of nanofluids depends on factors such as the nature of base fluid and nanoparticle, particle concentration, temperature of the fluid and size of the particles. Also, the nanofluids show significant change in properties such as viscosity and specific heat in comparison to the base fluid. Hence, a theoretical model becomes important in order to optimize the nanofluid dispersion (with respect to particle size, volume fraction, temperature, etc.) for its performance. As molecular dynamic simulation is computationally expensive, here the technique of Brownian dynamic simulation coupled with the Green Kubo model has been used in order to compute the thermal conductivity of nanofluids. The simulations were performed for different concentration ranging from 0.5 to 3 vol%, particle size ranging from 15 to 150 nm and temperature ranging from 290 to 320 K. The results were compared with the available experimental data, and they were found to be in close agreement. The model also brings to light important physical aspect like the role of Brownian motion in the thermal conductivity enhancement of nanofluids.


Nanofluids Suspensions Thermal conduction Brownian dynamic simulation Effective conductivity Nanoparticles Modeling 


  1. Allen MP, Tildesley DJ (1987) Computer simulation of liquids. Oxford science, Oxford, pp 23–32MATHGoogle Scholar
  2. Bhattacharya P et al (2004) Brownian dynamics simulation to determine the effective thermal conductivity of nanofluids. J Appl Phys 95(11):6492–6494. doi:10.1063/1.1736319 CrossRefADSGoogle Scholar
  3. Das SK, Putra N, Thiesen P, Roetzel W (2003) Temperature dependence of thermal conductivity enhancement for nanofluids. Trans ASME, J Heat Transf 125:567–574. doi:10.1115/1.1571080 CrossRefGoogle Scholar
  4. Deutch JM, Oppenheim I (1971) Molecular theory of Brownian motion for several particles. J Chem Phys 54:3547. doi:10.1063/1.1675379 CrossRefADSGoogle Scholar
  5. Ermak DL, McCammon JA (1978) Brownian dynamics with hydrodynamic interactions. J Chem Phys 69:1352–1360. doi:10.1063/1.436761 CrossRefADSGoogle Scholar
  6. Evans W, Fish J, Keblinski P (2006) Role of Brownian motion hydrodynamics on nanofluid thermal conductivity. Appl Phys Lett 88:093116. doi:10.1063/1.2179118 CrossRefADSGoogle Scholar
  7. Hamilton RL, Crosser OK (1962) Thermal conductivity of heterogeneous two component systems. I EC Fundam 1(3):187–191. doi:10.1021/i160003a005 CrossRefGoogle Scholar
  8. Kumar DH et al (2004) Model for heat conduction in nanofluids. Phys Rev Lett 93(14):144301. doi:10.1103/PhysRevLett.93.144301 PubMedCrossRefADSGoogle Scholar
  9. Lee YH, Biswas R, Soukoulis CM, Wang CZ, Chan CT, Ho KM (1991) Molecular dynamics simulation of the thermal conductivity of amorphous silicon. Phys Rev B 43:6573. doi:10.1103/PhysRevB.43.6573 CrossRefADSGoogle Scholar
  10. Li J, Porter L, Yip S (1998) Atomistic modeling of finite-temperature properties of crystalline beta-SiC. II. Thermal conductivity and effects of point defects. J Nucl Mater 255:139–152. doi:10.1016/S0022-3115(98)00034-8 CrossRefADSGoogle Scholar
  11. Masuda H et al (1993) Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles (dispersions of γ-Al2o3, SiO2, and TiO2 ultra-fine particles). Netsu Bussei Jpn 4:227–233Google Scholar
  12. McQuarrie DA (1976) Statistical mechanics. Harper & Row, New York, pp 512–522Google Scholar
  13. Pak BC, Cho YI (1998) Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Exp Heat Transf 11(2):151. doi:10.1080/08916159808946559 CrossRefADSGoogle Scholar
  14. Patel HE (2007) Experimental and theoretical investigation on thermal conductivity enhancement of nanofluids. Doctoral thesis, Indian Institute of Technology, MadrasGoogle Scholar
  15. Prasher R, Bhattacharya P, Pehlan P (2006) Brownian-motion-based convective-conductive model for the effective thermal conductivity of nanofluids. Trans ASME, J Heat Transf 128:588–595. doi:10.1115/1.2188509 CrossRefGoogle Scholar
  16. Rotne J, Prager S (1969) Variational treatment of hydrodynamic interaction in polymers. J Chem Phys 50:4831–4837. doi:10.1063/1.1670977 CrossRefADSGoogle Scholar
  17. Sarkar RS, Selvam P (2007) Molecular dynamics simulation of effective thermal conductivity and study of enhanced thermal transport mechanism in nanofluids. J Appl Phys 102:074302. doi:10.1063/1.2785009 CrossRefADSGoogle Scholar
  18. Wang X et al (1999) Thermal conductivity of nanoparticle-fluid mixture. J Thermophys Heat Transf 13(4):474–480CrossRefGoogle Scholar
  19. Xie H, Wang J, Xi T, Liu Y, Ai F, Wu Q (2002) Thermal conductivity enhancement of suspensions containing nanosized alumina particles. J Appl Phys 91:4568–4572. doi:10.1063/1.1454184 CrossRefADSGoogle Scholar
  20. Xuan Y, Yao Z (2005) Lattice Boltzmann model for nanofluids. Heat Mass Transf 41(3):199. doi:10.1007/s00231-004-0539-z ADSGoogle Scholar
  21. Xue QZ (2003) Model for effective thermal conductivity of nanofluids. Phys Lett A 307:313–317. doi:10.1016/S0375-9601(02)01728-0 CrossRefADSGoogle Scholar
  22. Yamakawa H (1971) Modern theory of polymer solutions. Harper and Row, New YorkGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Shashi Jain
    • 1
  • Hrishikesh E. Patel
    • 1
  • Sarit Kumar Das
    • 1
    • 2
  1. 1.Department of Mechanical EngineeringIndian Institute of Technology MadrasChennaiIndia
  2. 2.Department of Mechanical EngineeringMassachusetts Institute of Technology (MIT)CambridgeUSA

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