Biomedical Engineering Reference
In-Depth Information
where
1
:
5
5p
2
p
2
5pcosh
1
p
p
2
L
11
¼
0
:
=ð
1
Þ
0
:
=ð
1
Þ
L
33
¼
1
2L
11
k
nc
k
f
b
11
¼
k
f
þ
L
11
ð
k
nc
k
f
Þ
p
¼
r
=
a
The thermal conductivity of the whole nanofluid system has been calculated
from the Maxwell-Garnet model as:
k
eff
k
f
¼
k
a
þ
2k
f
þ
2
f
a
ð
k
a
k
f
Þ
½
11
:
15
k
a
þ
2k
f
f
a
ð
k
a
k
f
Þ
Evans et al. (2008) used the theory of Prasher et al. (2006c) and compared
the effective thermal conductivity predicted from the fractal model using a
random walker Monte Carlo algorithm. It was predicted that thermal
conductivity enhancement due to aggregation was also strongly dependent
on the chemical dimension of the aggregates and the radius of gyration of
the aggregate. Wang et al. (2009c) proposed a statistical clustering model to
determine the macroscopic characteristics of clusters. It has been suggested
that the thermal conductivity of a nanofluid can be estimated from the
existing effective medium theory without considering the fractal model
reported earlier.
11.4.4 Other models
In several other models, molecular dynamic simulation has been utilized to
predict the thermal conductivity of nanofluids. For instance, Sarkar and
Selvam (2007) used the equilibrium molecular dynamic simulation method
utilizing the Green-Kubo formulation to predict the thermal conductivity of
copper and argon nanofluids as a function of particle concentration. In
another study, Sankar et al. (2008) predicted the thermal conductivity
enhancement of platinum-water nanofluids using equilibrium molecular
dynamic simulation as a function of nanoparticle concentration and showed
significant enhancement from a particle concentration of 1 to 7%.
11.5 Summary and future trends
The enhancement in thermal conductivity of nanofluids has been observed
to be dependent on a combination of factors such as concentration of
nanoparticles dispersed in the base fluid, operating temperature, size of the
nanoparticles, and type of surfactant used for preparation of the nanofluid.
