Biomedical Engineering Reference
In-Depth Information
The surface inlet and outlet temperatures can be found by
1000
m
2
2500
m
2
K
5
T
s;i
5
T
i
1
q
s
1
2
25
C
6
C
24
:
h
5
1000
m
2
2500
m
2
K
5
T
s;o
5
T
o
1
q
s
1
2
99992
C
59992
C
:
:
h
5
24
24
Example
Determine the outflow temperature, the log mean temperature difference and the heat trans-
fer rate, assuming that there is fully developed blood flow through a 300-
m-long capillary (see
Figure 7.7). The capillary can be considered to provide the blood with a constant surface temper-
ature of 24
C. The diameter of the capillary is 15
μ
m, and its convection heat transfer coefficient
is 2250 W/m
2
K. Blood is flowing with a mass flow rate of 50 g/s at an inlet temperature of 25
C.
μ
Solution
To calculate the outflow temperature, we use
2250
W
m
2
K
πð
15
μ
m
Þ
300
μ
m
ð
Þ
kgK
2
50
s
3
:
8
kJ
pLh
mc
p
T
o
5
T
s
2
ðT
s
2
T
i
Þe
2
24
C
24
C
25
C
99998
C
2
ð
Þe
24
:
5
2
5
The log mean temperature difference is
Þ
C
T
i
2
T
o
ln
5
ð
25
24
:
99998
2
52
9999
C
ΔT
lm
5
0
:
ln
24
2
24
:
99998
24
T
s
2
T
o
T
s
2
T
i
25
2
The heat transfer rate will be
2250
W
Q
5
hA
s
ΔT
lm
5
9999
C
m
2
K
ðπÞð
μ
Þð
μ
Þð
2
:
Þ
52
:
15
m
300
m
0
0
000032 W
FIGURE 7.7
Heat transfer through a
capillary.
h = 2250 W/m
2
K
T
s
= 24°C
D = 15
µ
m
L = 300
µ
m
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