Biomedical Engineering Reference
In-Depth Information
11.8 Schematic cross-section of nanofluid structure consisting of
nanoparticles, bulk liquid, and nanolayers at the solid/liquid interface
(Yu and Choi, 2003).
Modified Hamilton and Crosser:
3
k
eff
k
f
¼
k
pe
þ
2k
f
2
f
ð
k
pe
k
f
Þð
1
þ
b
Þ
½
11
:
1
3
k
pe
þ
2k
f
f
ð
k
pe
k
f
Þð
þ
b
Þ
1
where
3
k
pe
¼
½
2
ð
1
g
Þþð
1
þ
b
Þ
ð
1
þ
2
g
Þ
g
k
p
3
ð
1
g
Þþð
1
þ
b
Þ
ð
1
þ
2
g
Þ
b
¼
h
=
r and
g
¼
k
layer
=
k
p
for layer thickness of h and particle radius r.
Modified Maxwell:
n
f
eff
A
k
eff
k
f
¼
1
þ
½
11
:
2
1
f
eff
A
where
3
X
j
¼
a
;
b
;
c
1
k
pj
k
f
A
¼
k
pj
þð
n
1
Þ
k
f
Xue and Xu (2005) derived an expression for the effective thermal
conductivity of nanofluids taking into consideration the thermal conductiv-
ity of the solid and liquid, their relative volume fraction, particle size, and
interfacial properties. They calculated the thermal conductivity of the
complex particle-liquid structure and adopted the model of Bruggeman
