Biomedical Engineering Reference
In-Depth Information
The effective thermal conductivity was modeled as:
2
k
eff
k
f
¼ð
f
k
p
3c
r
f
r
p
k
B
T
1
f
Þþ
k
f
þ
f
Pr
½
11
:
7
3
p
m
f
f
f
l
f
The empirical parameter c is a limiting factor for predicting the thermal
conductivity of nanofluids. This model was modified by Jang and Choi
(2007) considering nano-convection induced by Brownian motion.
Koo and Kleinstreuer (2004) predicted the thermal conductivity of CuO
nanofluids modifying the equation of Maxwell (1904) and using the
Brownian motion effect. The thermal conductivity was predicted as:
k
p
k
f
k
eff
¼
k
f
þ
3
f
k
f
2k
f
þ
k
p
f
ð
k
p
k
f
Þ
1
=
2
k
B
T
2
r
p
r
p
10
4
br
f
C
pf
f
þ
5
6
½ð
134
:
63
þ
1722
:
3
f
Þ
þð
0
:
4705
6
:
04
f
Þ
T
½
11
:
8
where
β
is related to the Brownian motion of
the nanoparticle and
empirically determined as:
Þ
0
:
8229
b
¼
0
:
0137
ð
100
f
f
<
0
:
01
Þ
0
:
7272
b
¼
0
:
0011
ð
100
f
f
>
0
:
01
½
11
:
9
On the other hand, Evans et al. (2006) used kinetic theory to demonstrate
that the hydrodynamic effects associated with Brownian motion of the
particles have only a minor effect on the thermal conductivity of nanofluids.
This was supported by molecular dynamic simulation studies considering
suitable parameters required for the simulation. Prasher et al. (2006b)
argued that Keblinski et al. (2002) and Evans et al. (2006) had not
considered the energy transport due to convection caused by the Brownian
motion of the particles. Accordingly, they analyzed the problem considering
convection and the effective thermal conductivity was expressed on the lines
of the Maxwell-Garnet model as:
½
k
eff
k
f
¼
Re
:
Pr
4
k
p
ð
1
þ
2
a
Þþ
2k
m
þ
2
f
½
k
p
ð
1
a
Þ
k
m
Þ
1
þ
½
11
:
10
½
k
p
ð
1
þ
2
a
Þþ
2k
m
f
½
k
p
ð
1
a
Þ
k
m
Þ
where
=2R
b
k
m
/d is the nanoparticle Biot number, d is the particle
diameter, and R
b
is the interfacial thermal resistance.
Murshed et al. (2009) predicted the thermal conductivity of nanofluids
considering static and dynamic effects. In considering the dynamic effect on
the thermal conductivity of nanofluids, a modified effective diffusion
α
