Thermal conductivity of nanofluids

0.6

0.62

0.64

0.66

0.68

0.7

0 0.002 0.004 0.006 0.008 0.01

N (M)

k (

Wm

-1K

-1)

0.6

0.62

0.64

0.66

0.68

0.7

2000 6000 10000 14000

<size>/N (nm/M)

k (

Wm

-1K

-1)

y = 2085x + 11.264

05

101520253035

0 0.003 0.006 0.009

N(M)

<s

ize

> (

nm

)

The abrupt and irregular behavior of thermal conductivity of nanofluids is very important and interesting domain of study in modern day nanophysics. Many experimental studies have been reported and theoretical (analytical and computational) models have been proposed. On the basis of the classical Maxwell model ( ), some scholars presented modified models, tried to fit the theories of microfluidics in the nano regime. But so far no exact match with the experimental data has been found. The models presented by Yu and Choi ( ), Xue ( ), Xie et al. ( ), Xuan et al. ( ), Wang et al. ( ), Kumar et al. ( ), Jang and Choi ( ), Prasher ( ) and Koo and Kleinstruer ( ) are some of the key attempts to describe the heat transfer phenomena in nanofluids though they are incapable of predicting the generalized behavior ( ). The soul of these studies reveals that the possible parameters controlling the thermal conductivity of nanofluids are i) the conductivity of nanoparticle material, ii) the conductivity of base fluids, iii) the volume fraction of nanomaterial, iv) geometry of nanoparticles, v) the characteristics of nanolayer of base liquid encompassing the surface of nanoparticles, vi) the Brownian motion of the suspended particles, vii) the dynamic viscosity of base material, vii) the temperature of base fluids, viii) thermal diffusion of nanoparticles in base fluids, ix) molecular interaction of base fluids and interaction with nanoparticles, x) the convection of heat due to the Brownian motion of suspended particles and xi) the agglomeration tendency of the nanoparticles. Recent work reported by Liqiu Wang and Jing Fan ( ) concise that the increment or decrement (as reported in some other works ( )) of thermal conductivity of base liquids due to the addition of nanoparticles can be attributed to dual-phase-lagging (DPL) heat conduction. The dialectics between the thermal waves and heat diffusion plays the key role to enhance or decrease the conductivity of base material due to the presence of highly conductive nanoparticles. The strong thermal waves and resonance are attributed to sharp increment.

In this work an attempt has been made to study the variation of conductivity of polyaniline-Ag nanofluids with the concentration of Ag nanoparticles and the average size of the particles at unit concentration. The concentration and average particle size variation is linear hence the average size per unit concentration is a valid approach to parameterize the data. The conductivity of polyaniline and Ag are 0.6095 Wm -1K-1 and 406 Wm-1K-1 respectively. This study explores that initially the conductivity of the nanofluid shows slow, then sharp increment and then saturate at the value of 0.6886 Wm-

1K-1 ( which is equivalent to 12.98 % increase ) as the concentration of Ag is varied from 0.001 M to 0.01 M. The average sizes of the nanoparticles are also enhanced from 14.37 nm to 32.40 nm. The variation of conductivity with the average particle size per unit concentration shows gradual decay of conductivity with the increment of particle size. It is proposed that initially the decisive factor governing the conductivity of the nanofluids is the concentration of the nanoparticles but after certain limit the other factors take the control to bend down the increment and to saturate it to 0.6886 Wm-1K-1. Another very important observation is that the increased conductivity of nanofluids is not in the range of the conductivity of silver naonparticles but very much around the polyaniline conductivity assuring that the main heat transfer phenomena is dominated by the mechanism of heat transfer in fluids. The idea of this proposal is that convection of heat is the soul mechanism of heat conduction in nanofluids where the concentration and

Brownian motion of the constituent particle plays very important role. The smaller the particle size the greater the random motion of the suspended particles encouraging the conductivity. As the Brownian motion of the Ag particles plays an important role, the viscosity of the base fluids must remain into considerations as well as the base temperature. The dependence of conductivity of nanofluids on the conductivity of silver nanoparticle is very poor and must be reduced to a fractional power form. The major difference between microfluidics and nanofluidics is that the volume fraction in the later case is of the order 1/1000 of the former. So, the classical dependence on the volume fraction must be corrected. It is obvious to suggest that to increase the thermal conductivity of the nanofluids the concentration and particle size product should be optimized.