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Effect of the multi-sized nanoparticle distribution on the thermal conductivity of nanofluids

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Abstract

Recent studies of nanofluids have shown that the nanoparticles when mixed in fluid medium such as water and ethylene glycol enhance the thermal conductivity of the colloids when compared to the fluid medium. However, numerous experimental studies conducted on the effective thermal conductivity of nanofluids, while using initial particle distribution consisting of range of diameters, have reported their results at volume-weighted average diameters. Here, we use computer simulations to investigate the effect of initial particle distribution or the effect of polydispersivity on the effective thermal conductivity of nanofluids. The study reveals that the simulations performed with multi-sized nanoparticles predict the effective thermal conductivity values of nanofluids closer to the experimental values than the corresponding volume weighted average diameters. Inhomogeneous coagulations in the multi-sized nanofluids were found to be a major factor for the deviation of effective thermal conductivity of the nanofluids in single- and multi-sized nanofluids. Our results suggest that initial distribution of particles has a significant role in predicting the effective thermal conductivity of nanofluids.

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Abbreviations

A :

Hamaker constant

C c :

Cunningham correction factor

C s :

Thermal slip coefficient

c p :

Specific heat of particle

d p :

Diameter of particle

F B :

Brownian force

F D :

Hydrodynamic drag force

F p :

Force exerted by particles on fluid

F T :

Thermophoretic force

F V :

Van der Waals force

G i :

Gaussian random distribution

h :

Distance between two particles

Kn :

Knudsen number

k B :

Boltzmann constant

k f :

Thermal conductivity of fluid

k nf :

Effective thermal conductivity of nanofluid

k r :

Thermal conductivity ratio of particle to fluid

k T :

Turbulent thermal conductivity

m p :

Mass of particle

Nu :

Nusselt number

N p :

Number of particles

Pr :

Prandtl number

p :

Pressure of fluid

q 2w :

Temperature coupling term

Re :

Reynolds number

T f :

Temperature of fluid

T p :

Temperature of particle

t :

Time

u :

Velocity of fluid

v :

Velocity of particle

x :

Position of particle

\( \overline{\nabla } T \) :

Mean temperature gradient

∇t :

Timestep

ρp :

Density of particle

ρf :

Density of fluid

τT :

Thermal response time of particle

τp :

Particle aerodynamic response time

ν:

Kinematic viscosity of fluid

μ:

Dynamic viscosity of fluid

δ:

London retardation wavelength

θ:

Fluctuation of temperature of fluid

Φ:

Volume fraction of particles

δ(x − x n):

Dirac delta function

λ:

Mean free path of the fluid molecule

i, j:

Tensor directions

,i :

Differentiation w.r.t x i

rms:

Root mean square

n :

nth particle

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Acknowledgement

This work was partially supported by grants from the National Science Foundation (ATM-0332910), National Oceanic and Atmospheric Administration (NA04OAR4310034), and National Aeronautics and Space Administration (NNG04GG46G).

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Authors and Affiliations

  1. Department of Aerospace and Mechanical Engineering, University of Arizona, 1130 N. Mountain Avenue, Tucson, AZ, 85721, USA

    Sasidhar Kondaraju

  2. Department of Atmospheric, Ocean and Earth Science, George Mason University, Fairfax, VA, USA

    E. K. Jin

  3. Department of Mechanical Engineering, Yonsei University, Seoul, Korea

    J. S. Lee

Authors
  1. Sasidhar Kondaraju
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  2. E. K. Jin
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  3. J. S. Lee
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Corresponding author

Correspondence to J. S. Lee.

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Kondaraju, S., Jin, E.K. & Lee, J.S. Effect of the multi-sized nanoparticle distribution on the thermal conductivity of nanofluids. Microfluid Nanofluid 10, 133–144 (2011). https://doi.org/10.1007/s10404-010-0653-9

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  • DOI: https://doi.org/10.1007/s10404-010-0653-9

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