Heat and Mass Transfer

, Volume 53, Issue 6, pp 1873–1892 | Cite as

Effect of time dependent nanoclusters morphology on the thermal conductivity and heat transport mechanism of TiO2 based nanofluid



The effect of time dependent nanoclusters morphology on heat conduction mechanism of a nanofluid has been presented over here. The time dependent growth of nanoclusters of TiO2 nanoparticles (size 25–30 nm, volume fraction of 0.05%) along with surfactant (SDBS) in water (DI), has been investigated. A detailed report on the size distribution of nanoparticles while in suspension for an actual volume fraction of the nanoparticles at a particular instant of time is presented. The different pH values (2.92–11.62) along with surfactant (SDBS, 1:1 by wt.) have been used to investigate the suspension stabilities of different smaples of the nanofluid. The suspension stabilities have been evaluated by measuring the zeta potential and stability ratios of TiO2–H2O nanofluid. A quantitative analysis on the role of nanoparticles presented in the form of dead-ends and backbone chains, has been carried out. The effect of liquid layering of the water present inside the characteristic dimension of a nanocluster is taken into account to determine the effective thermal conductivity of a nanofluid. The so, obtained experimental and theoretical results of thermal conductivities have been correlated and found to be predicted well with a new developed model and with an accuracy level of +2.82 to −1.5%. Whereas, the predictions from other fundamental models and empirical correlations are found to be vary with an error from +3 to +8.1% on one side and from −4.87 to −12.62% on other side, in the volume fraction from 0.01 to 0.12%, when analysed.

List of symbols


Average hydrodynamic size (diameter) of the particle (nm)


Hamaker’s constant (J)

B (x)

Parameter represents the hydration interaction among the nanoparticles and the basefluid


Aggregate density of the nanoparticles per unit cluster


Chemical dimension of a cluster


Fractal dimension of a cluster


Electrostatic repulsion (J)


Vander Waals attraction (J)


Total interaction energy (J)


Concentration of ions in aqueous medium


Thermal conductivity of nanofluid (W/mK)


Experimental thermal conductivity (W/mK)


Thermal conductivity of bulk base fluid (W/mK)


Thermal conductivity of nanopowder (W/mK)


Thermal conductivity of the fluid present inside the nanocluster (W/mK)


Thermal conductivity enhancement of the fluid present inside the nanocluster (W/mK)


Thermal conductivity enhancement inside the nanocluster due to deadend nanoparticles (W/mK)


Cluster thermal conductivity due to presence of nanoparticles as dead-ends and backbone chains (W/mK)


Boltzmann constant (1.3807 × 10−23 J/K)


Average number of nanoparticles per cluster


Number of nanoparticles belongs to backbone chains


Aspect ratio


pH level of the nanofluid


Resistance due to thermal boundary layer (m2 K/W)


Cluster characteristic dimension (nm)


Average radius of the nanoparticle (nm)


Surfactant amount (mg)


Aggregation time constant (s)


Temperature (°C)


Volume of a cluster


Volume of the nanoparticles per cluster


Stability ratio


Weight (mg)


Particle surface to surface distance (nm)



De-ionized water


Dynamic light scattering


Diffusion limited colloidal aggregation


Model Maxwell Garnet Model


Specific surface area


X-rays diffraction


Sodium dodecyl benzene sulphonate




Transmission electronic microscope

Greek symbols


A constant (13.58 × 1020 s/m3)


Thermal diffusivity (m2/s)


Density of nanofluid (kg/m3)


Density of base fluid (kg/m3)


Density of TiO2 nanoparticles(kg/m3)


Viscosity of basefluid (Pas)


Volume fraction of the primary nanoparticles in the basefluid (%)


Volume fraction of the nanoparticles in an aggregate


Volume fraction of backbone particles in the aggregate


Volume fraction of the particles belonging to deadends


Volume fraction of fluid elements present in the aggregate


Total Volume fraction of the aggregates present in the base fluid (%)


Relative dielectric constant of the liquid


Dielectric constant of free space


Zeta potential (mV)


Debye parameter


Pi (3.14159)


  1. 1.
    Lee S, Choi SUS, Li S, Eastman JA (1999) Measuring thermal conductivity of fluids containing nanoparticles. J Heat Transf 121(2):280–289CrossRefGoogle Scholar
  2. 2.
    Xie HQ, Wang JC, Xi TG, Liu Y, Ai F, Wu QR (2002) Thermal conductivity enhancement of suspensions containing nanosized alumia particles. Appl Phys 91(7):4568–4572CrossRefGoogle Scholar
  3. 3.
    Masuda H, Ebata A, Teramae K, Hishinuma N (1993) Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles. Netsu Bussei 7(4):227–233CrossRefGoogle Scholar
  4. 4.
    Das SK, Putra N, Thiesen P, Roetzel W (2003) Temperature dependence of thermal conductivity enhancement for nanofluids. J Heat Transf 125:567–574CrossRefGoogle Scholar
  5. 5.
    Esfe MH, Saedodin S, Mahian O, Saedodin S (2014) Thermal conductivity of Al2O3/water nanofluids: measurement, correlation, sensitivity analysis and comparisons with literature reports. J Therm Anal Calorim 117:675–681CrossRefGoogle Scholar
  6. 6.
    Jiang W, Ding G, Peng H, Haitao H (2010) Modelling of nanoparticles’ aggregation and sedimentation in nanofluid. Curr Appl Phys 10(3):934–941CrossRefGoogle Scholar
  7. 7.
    Prasher R, Phelen PE, Bhattacharya P (2006) Effect of aggregation kinetics on the thermal conductivity of nanoscale colloidal solutions (nanofluid). Nanoletter 6:1529–1534CrossRefGoogle Scholar
  8. 8.
    Timofeeva EV, Gavrilov AN, McCloskey JM, Tolmachev YV, Sprunt S, Lopatina LM, Selinger JV (2007) Thermal conductivity and particle agglomeration in alumina nanofluids: experiment and theory. J Phys Rev E 76:061703-1–061703-16CrossRefGoogle Scholar
  9. 9.
    Lin CY, Wang JC, Chen TC (2011) Analysis of suspension and heat transfer characteristics of Al2O3 nanofluids prepared through ultrasonic vibration. J Appl Energy 88:4527–4533CrossRefGoogle Scholar
  10. 10.
    Chanderasekar M, Suresh S (2009) A review on the mechanisms of heat transport in nanofluids. Heat Transf Eng 30(14):1136–1150CrossRefGoogle Scholar
  11. 11.
    Wang X, Xu X, Choi SUS (1999) Thermal conductivity of nanoparticle-fluid mixture. J Thermophys Heat Transf 13(4):474–480CrossRefGoogle Scholar
  12. 12.
    Yu W, Choi SUS (2003) The role of interfacial layers in the enhanced thermal conductivity of nanofluids: a renovated Maxwell model. J Nanoparticle Res 5:167–171CrossRefGoogle Scholar
  13. 13.
    Gao JW, Zheng RT, Ohtani H, Zhu DS, Chen G (2009) Experimental investigation of heat conduction mechanisms in nanofluids: clue on clustering. Nanoletter 9:4128–4132CrossRefGoogle Scholar
  14. 14.
    Ozerinc S, Kakac S, Guvenc AY (2010) Enhanced thermal conductivity of nanofluids: a state-of-the-art review. Microfluid Nanofluid 8:145–170CrossRefGoogle Scholar
  15. 15.
    Mishra A, Kundan L, Mallick SS (2014) Modeling thermal conductivity for alumina-water nanofluids. Part Sci Technol 32(3):319–326CrossRefGoogle Scholar
  16. 16.
    Karthikeyan NR, Philip J, Raj B (2008) Effect of clustering on the thermal conductivity of nanofluids. Mater Chem Phys 109:50–55CrossRefGoogle Scholar
  17. 17.
    Shih WH, Shih WY, Kim SI, Liu J, Aksay A (1990) Scaling behavior of the elastic properties of colloidal gels. Phys Rev A 42:4772–4779CrossRefGoogle Scholar
  18. 18.
    Evans W, Prasher R, Fish J, Meakin P, Phelan PE, Keblinski P (2008) Effect of aggregation and interfacial thermal resistance on thermal conductivity of nanocomposites and colloidal nanofluids. Int J Heat Mass Transf 51:1431–1438CrossRefMATHGoogle Scholar
  19. 19.
    Xuan Y, Li Q, Hu W (2003) Aggregation structure and thermal conductivity of nanofluids. AIChE J 49:1038–1043CrossRefGoogle Scholar
  20. 20.
    Philip J, Shima PD, Raj B (2008) Evidence for enhanced thermal conduction through percolating structures in nanofluids. Nanotechnology 19:305706CrossRefGoogle Scholar
  21. 21.
    Pang C, Lee JW, Kang YT (2016) Enhanced thermal conductivity of nanofluids by nanoconvection and percolation network. Heat Mass Transf 52:511–520CrossRefGoogle Scholar
  22. 22.
    Longo G, Zilio AC (2011) experimental measurement of thermophysical properties of oxide–water nano- fluids down to ice-point. Exp Thermal Fluid Sci 35:1313–1324CrossRefGoogle Scholar
  23. 23.
    Longo G, Zilio AC, Ceseracciu E, Reggiani M (2012) Application of artificial neural network (ANN) for the prediction of thermal conductivity of oxide–water nanofluids. Nano Energy 1:290–296CrossRefGoogle Scholar
  24. 24.
    Hays A, Marsh CP, Alvarado J, Franks R (2006) The effect of nanoparticle agglomeration on enhanced nanofluidic thermal conductivity. In: Proceedings of international refrigeration and air conditioning conference, Purdue University, vol R132, pp 1–7Google Scholar
  25. 25.
    Alipour R, Ghoranneviss M, Mirzaee M, Jafari A (2014) The direct effect of interfacial nanolayers on thermal conductivity of nanofluids. Heat Mass Transf 50:1727–1735CrossRefGoogle Scholar
  26. 26.
    Mallick SS, Mishra A, Kundan L (2013) An investigation into modelling thermal conductivity for alumina-water nanofluids. Powder Technol 233:234–244CrossRefGoogle Scholar
  27. 27.
    Maxwell JC (1873) A treatise on electricity and magnetism, 2nd edn. Clarendon Press, OxfordMATHGoogle Scholar
  28. 28.
    Hamilton RL, Crosser OK (1962) Thermal conductivity of heterogeneous two-component systems. I EC Fundam 1:182–191CrossRefGoogle Scholar
  29. 29.
    Hui PM, Zhang XA, Markworth J, Stroud D (1999) Thermal conductivity of graded composites: numerical simulations and an effective medium approximation. J Mater Sci 34:5497–5503CrossRefGoogle Scholar
  30. 30.
    Rizvi IH, Jain A, Ghosh SK, Mukherjee PS (2013) Mathematical modelling of thermal conductivity for nanofluid considering interfacial nano-layer. Heat Mass Transf 49:595–600CrossRefGoogle Scholar
  31. 31.
    Kumar DH, Patel HE, Rajeev Kumar VR, Sundararajan T, Pradeep T, Das SK (2004) Model for heat conduction in nanofluids. Phys Rev Lett 93:144301CrossRefGoogle Scholar
  32. 32.
    Prasher R, Bhattacharya P, Phelan PE (2005) Thermal conductivity of nanoscale colloidal solutions (nanofluids). Phys Rev Lett 94(2):025901CrossRefGoogle Scholar
  33. 33.
    Jang SP, Choi SUS (2004) Role of Brownian motion in the enhanced thermal conductivity of nanofluids. Appl Phys Lett 84:4316–4318CrossRefGoogle Scholar
  34. 34.
    Bhattacharya P, Saha SK, Yadav A, Phelan PE, Prasher RS (2004) Brownian dynamics simulation to determine the effective thermal conductivity of nanofluids. J Appl Phys 95:6492–6494CrossRefGoogle Scholar
  35. 35.
    Koo J, Kleinstreuer C (2004) A new thermal conductivity models for nanofluids. J Nanopart Res 6:577–588CrossRefGoogle Scholar
  36. 36.
    Mukherjee S, Mishra PCh, Prashar SKS, Chaudhuri P (2016) Role of temperature on thermal conductivity of nanofluids: a brief literature review. Heat Mass Transf. doi:10.1007/s00231-016-1753-1 Google Scholar
  37. 37.
    Zhu D, Li X, Wang N, Wang X, Gao J, Li H (2009) Dispersion behavior and thermal conductivity characteristics of Al2O3–H2O nanofluids. Curr Appl Phys 9:131–139CrossRefGoogle Scholar
  38. 38.
    Das SK, Choi SUS, Yu W, Pardeep T (2008) Nanofluids science and technology. Wiley, New YorkGoogle Scholar
  39. 39.
    Xie HQ, Lee H, Youn W, Choi M (2003) Nanofluids containing multiwalled carbon nanotubes and their enhanced thermal conductivities. J Appl Phys 94:4967–4971CrossRefGoogle Scholar
  40. 40.
    Lee D, Kim JW, Kim BG (2006) A new parameter to control heat transport in nanofluids: surface charge state of the particles in suspension. J Phys Chem B 110:4323–4328CrossRefGoogle Scholar
  41. 41.
    Xie HQ, Wang JC, Xi TG, Liu Y, Ai F, Wu QR (2007) Thermal conductivity enhancement of suspensions containing nanosized alumia particles. Appl Phys 91(7):4568–4572CrossRefGoogle Scholar
  42. 42.
    Putra N, Roetzel W, Das SK (2003) Natural convection of nano-fluids. Heat Mass Transf 39:775–784CrossRefMATHGoogle Scholar
  43. 43.
    Jang SP, Choi SUS (2004) Role of Brownian motion in the enhanced thermal conductivity of nanofluids. Appl Phys Lett 84(21):4316–4318CrossRefGoogle Scholar
  44. 44.
    Wen DS, Ding YL (2004) Experimental investigation into convective heat transfer of nanofluids at the entrance region under laminar flow conditions. Int J Heat Mass Transf 47(24):5181–5188CrossRefGoogle Scholar
  45. 45.
    Zhang X, Gu H, Fujii M (2006) Effective thermal conductivity and thermal diffusivity of nanofluids containing spherical and cylindrical nanoparticles. J Appl Phys 100(4):044325CrossRefGoogle Scholar
  46. 46.
    Russel WB, Saville DA, Schowalter WR (1989) Colloidal dispersions. Cambridge University Press, New YorkCrossRefMATHGoogle Scholar
  47. 47.
    Hunter RJ (2001) Foundations of colloid science. Clarendon Press, OxfordGoogle Scholar
  48. 48.
    Hidalgo-Alvarez R, Martin A, Fernandez A, Bastos D, Martinez F (1996) Electrokinetic properties, colloidal stability and aggregation kinetics of polymer colloids. Adv Colloid Interface Sci 67:1–118CrossRefGoogle Scholar
  49. 49.
    Hemker DJ, Frank CW (1990) Dynamic light scattering studies of fractal aggregation of poly (methacrylic acid) and poly (ethylene glycol). Macromolecules 23:4404–4410CrossRefGoogle Scholar
  50. 50.
    Lin MY, Lindsay HM, Weitz DA, Ball RC, Klein R, Meakin P (1989) Universality in colloid aggregation. Nature 339:360–362CrossRefGoogle Scholar
  51. 51.
    De Rooij R, Potanin AA, Van den Ende D, Mellema J (1993) Steady shear viscosity of weakly aggregating polystyrene latex dispersions. J Chem Phys 99:1993–9213CrossRefGoogle Scholar
  52. 52.
    Lin MY, Lindsay HM, Weitz DA, Ball RC, Klein R, Meakin P (1990) Universal diffusion-limited colloid aggregation. J Phys Condens Matter 2:3093–3113CrossRefGoogle Scholar
  53. 53.
    Wang BX, Zhou LP, Peng XF (2013) A fractal model for predicting the effective thermal conductivity of liquid with suspension of nanoparticles. Int J Heat Mass Transf 46(14):2665–2672CrossRefMATHGoogle Scholar
  54. 54.
    Waite TD, Cleaver JK, Beattie JK (2001) Aggregation kinetics and fractal structure of γ-alumina assemblages. J Colloid Interface Sci 241:333–339CrossRefGoogle Scholar
  55. 55.
    Bruggeman DAG (1935) Berechnung verschiedener physikalischer konstanten von heterogenen substanzen, i. dielektrizitatskonstanten und leitfahigkeiten der mischkorper aus isotropen substanzen. Annal Phys Leipz 24:636–679CrossRefGoogle Scholar
  56. 56.
    Holthoff H, Egelhaaf SU, Borkovec M, Schurtenberger P, Sticher H (1996) Coagulation rate measurements of colloidal particles by simultaneous static and dynamic light scattering. Langmuir 12:5541–5549CrossRefGoogle Scholar
  57. 57.
    Carpineti M, Giglio M (1993) Aggregation phenomena. Adv Colloid Interface Sci 46:73–90CrossRefGoogle Scholar
  58. 58.
    Potanin AA, De Rooij R, Van den Ende D, Mellema J (1995) Microrheological modeling of weakly aggregated dispersions. J Chem Phys 102:5845CrossRefGoogle Scholar
  59. 59.
    Kallay N, Zalac S (2001) Introduction of the surface complexation model into the theory of colloid stability. Croat Chem Acta 74(3):479–497Google Scholar
  60. 60.
    Bergstrom L (1997) Hamaker constants of inorganic materials. Adv Colloid Interface Sci 70:125–169CrossRefGoogle Scholar
  61. 61.
    Hiemenz PC (1997) Principles of colloid and surface chemistry. Marcel Dekker, New YorkCrossRefGoogle Scholar
  62. 62.
    Honig EP, Roebersen GJ, Wiersema PH (1971) Effect of hydrodynamic interaction on the coagulation rate of hydrophobic colloids. J Colloid Interface Sci 36(1):97–109CrossRefGoogle Scholar
  63. 63.
    Nan CW, Birringer R, Clarke DR, Gleiter H (1997) Effective thermal conductivity of particulate composites with interfacial thermal resistance. J Appl Phys 81:6692–6699CrossRefGoogle Scholar
  64. 64.
    Ge ZB, Cahill DG, Braun PV (2006) Thermal conductance of hydrophilic and hydrophobic interfaces. Phys Rev Lett 96:186101–186104CrossRefGoogle Scholar
  65. 65.
    Schmidt AJ, Alper JD, Chiesa M, Chen G, Das SK, Hamad-Schifferli K (2008) Probing the gold nanorod-ligand-solvent interface by plasmonic absorption and thermal decay. J Phys Chem C 112:13320–13323CrossRefGoogle Scholar
  66. 66.
    Bailar JC (1973) Comprehensive inorganic chemistry. Pergamon, OxfordGoogle Scholar
  67. 67.
    Patnaik P (2002) Handbook of inorganic chemicals. McGraw-Hill, New YorkGoogle Scholar
  68. 68.
    Li X, Li F, Zhu DS, Wang XJ (2007) evaluation on dispersion behavior of the aqueous copper nano- suspensions. J Colloid Interface Sci 310(2):456–463CrossRefGoogle Scholar
  69. 69.
    Jeffrey D (1973) Conduction through a random suspension of spheres. R Soc Lond Ser A 335(1602):355–367CrossRefGoogle Scholar
  70. 70.
    Pak BC, Choi YI (1998) Hydraulic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Exp Heat Transf 11:151–170CrossRefGoogle Scholar
  71. 71.
    Li C, Peterson GP (2006) Experimental investigation of temperature and volume fraction variations on the effective thermal conductivity of nanoparticles suspensions (nanofluids). J Appl Phys 99(8):084314CrossRefGoogle Scholar
  72. 72.
    Teng TP, Hung YH, Teng TC, Moa HE, Hsu HG (2010) The effect of alumina/water nanofluid particle size on thermal conductivity. J Appl Therm Eng 30:2213–2218CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Lal Kundan
    • 1
  • Soumya Suddha Mallick
    • 1
  • Bonamali Pal
    • 2
  1. 1.Mechanical Engineering DepartmentThapar UniversityPatialaIndia
  2. 2.Department of Chemistry and BiochemistryThapar UniversityPatialaIndia

Personalised recommendations