Nanofluids including ceramic and other nanoparticles: synthesis and thermal properties - Ceramic Nanocomposites - page 360

11.9 Dynamic mechanisms of nanoparticles in base fluid (Murshed
et al., 2009).

coefficient was used. Also, both Brownian and potential forces were
considered on the complex nanoparticles (Fig. 11.9). This led to a very
complicated model for determining the thermal conductivity of nanofluids,
the details of which have been given elsewhere (Murshed et al., 2009).

11.4.3 Effect of clustering and aggregate formation of
nanoparticles

After the proposal of Keblinski et al. (2002) regarding the effect of clustering
being a mechanism for enhanced thermal heat conduction in nanofluids,
Wang et al. (2003) used a fractal model to predict the thermal conductivity
of nanofluids taking into account the effect of clustered nanoparticles in
suspension. The researchers made use of the effective medium theory and
the concept of fractal dimensions for nanoparticle clusters to predict the
effective thermal conductivity of nanofluids utilizing the model of
Bruggeman (1935) (equation 11.3). In the proposed model, the volume
concentration f was replaced by the fractal volume fraction f(r):

￿ ￿ ￿ ￿ ￿ ￿

D f1 3

r
a

f ð r Þ¼ ½ 11 : 11

to get the effective thermal conductivity of the cluster. The effective
medium/Maxwell-Garnett theory was modified to predict the thermal
conductivity of nanofluids as:

0 1

3 f R 0

k cl ð r Þ n ð r Þ

ð 1 f Þþ

k cl ð r Þþ 2k f dr

k eff
k f ¼

@ A

½ 11 : 12

3 f R 0

k f n ð r Þ

ð 1 f Þþ

k cl ð r Þþ 2k f dr