Biomedical Engineering Reference
In-Depth Information
Or
T
o
5
T
s
2
ðT
s
2
T
i
Þe
2
hAs
ð
7
:
36
Þ
mc
p
Using the log mean temperature difference, the heat-transfer rate can also be calculated
from
Q
5
hA
s
ΔT
lm
ð
7
:
37
Þ
T
i
2
T
o
ln
T
s
2
T
o
T
s
2
T
i
h
i
ΔT
lm
5
where
ΔT
lm
is the log mean temperature difference.
Example
Determine the outflow temperature and the surface inlet and outlet temperatures, assuming
that there is fully developed blood flow through a 300-
m-long capillary (see Figure 7.6). The cap-
illary can be considered to provide the blood with a constant surface heat flux of
μ
1000 W/m
2
.
2
m, and its convection heat transfer coefficient is 2500 W/m
2
K.
Blood is flowing with a mass flow rate of 50 g/s at an inlet temperature of 25
C.
The diameter of the capillary is 15
μ
Solution
The specific heat at constant pressure for blood is 3.8 kJ/kgK.
First, determine the blood vessel heat transfer rate to obtain the outlet temperature:
1000
W
Q
5
q
s
A
s
5
q
s
πDL
52
10
5
W
m
2
ðπÞð
15
μ
m
Þð
300
μ
m
Þ
52
1
:
414
3
Q
mc
p
5
10
5
W
1
:
414
1
2
3
25
C
99992
C
T
o
5
T
i
1
24
:
50
s
kJ
kgK
3
:
8
FIGURE 7.6
Heat transfer through a
capillary.
h = 2500 W/m
2
K
q
s
=
1000 W/m
2
D = 15
µ
m
L = 300
µ
m
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