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A cell model approach for thermal conductivity of nanofluids

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Abstract

This work presents a cell model for predicting the thermal conductivity of nanofluids. Effects due to the high specific surface area of the mono-dispersed nanoparticles and the micro-convective heat transfer enhancement associated with the Brownian motion of particles are addressed in detail. Novelty of the paper lies in its prediction of the non-linear dependence of thermal conductivity of nanofluids on particle volume fraction at low particle concentrations. The model is found to correctly predict the trends observed in experimental data over a wide range of particle sizes, temperatures and particle concentrations.

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Abbreviations

A m :

Heat transfer area per particle for conduction through liquid medium (m2)

A pc :

Volume averaged cross-sectional area for conduction through nanoparticle (m2)

A ps :

Surface area of nanoparticle (m2)

c :

Empirical constant

d p :

Average particle diameter (m)

dT/dx :

Temperature gradient (K/m)

h :

Convective heat transfer coefficient (W/m2 K)

k b :

Boltzmann constant (J/K)

k m :

Thermal conductivity of liquid medium (W/m K)

k p :

Thermal conductivity of particle (W/m K)

l :

Length scale of the unit cell (m)

Nu :

Nusselt number

n :

Number of nanoparticles per unit volume of nanofluid

Pe :

Peclet number

q m :

Heat flux in liquid medium by conduction (W/m2)

q nf :

Overall heat flux in nanofluid (W/m2)

R c :

Thermal resistance of micro-convection (K/W)

R eff :

Effective thermal resistance of the nanofluid system (K/W)

R m :

Thermal resistance of conduction in liquid medium (K/W)

R p :

Thermal resistance of a particle (K/W)

T :

Temperature (K)

u p :

Particle velocity due to Brownian motion (m/s)

eff:

Effective

m:

Liquid medium

nf:

Nanofluid

p:

Particle

α:

Thermal diffusivity (m2/s)

ɛ:

Particle volume fraction

η:

Dynamic viscosity (N s/m2)

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Acknowledgements

The authors acknowledge the support from Defence Research and Development Organisation (DRDO) and Department of Science and Technology (DST), Government of India, for the present research work.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, Tamilnadu, 600036, India

    Hrishikesh E. Patel, T. Sundararajan & Sarit Kumar Das

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  1. Hrishikesh E. Patel
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  2. T. Sundararajan
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  3. Sarit Kumar Das
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Correspondence to Sarit Kumar Das.

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Patel, H.E., Sundararajan, T. & Das, S.K. A cell model approach for thermal conductivity of nanofluids. J Nanopart Res 10, 87–97 (2008). https://doi.org/10.1007/s11051-007-9236-4

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  • DOI: https://doi.org/10.1007/s11051-007-9236-4

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