Problem Set 7 (2.006, Spring 08)
Problem 1
a) The E-NTU single stream heat exchanger expression is used to calculate the temperature of the blood
leaving the foot (T
f,out
).
()
63
3
min
*
min
max
min
25 10
1000
/
4000 /
1.667
/
60
1.5
/
/0
,
0
.
9
0
1.667
/
hb
p
foot
m
C
C
Vc
kg m
J kgK
W K
s
UA
WK
CC C
N
T
U
CW
K
ρ
−
⎛⎞
×
==
=
=
⎜⎟
⎝⎠
=
=
=
&
Use
1e
x
p
NTU
ε
=−
−
,
configuration #1 from Table 12.1 of the course note. Then
h
C
=
,,
min
fi
n
fo
u
t
TT
C
−
,
,
,
42
1 exp
0.90
42 ( 7)
12.9
o
f out
o
o
n
i
c
e
o
f out
CT
C
C
TC
−
−
−
−−
−
∴
=
The heat lost to the ice per foot is
1.667
/
42
12.9
48.5
oo
hf
i
n f
o
u
t
QCT T
C
C
W
=
−=
&
b) In this case we have two heat exchangers.
The first heat exchanger is the single stream heat exchanger that
models the heat transfer from the duck’s foot to the ice.
The second heat exchanger is a counter flow heat
exchanger that models heat transfer between the arteries.
To find a value for T
c,out
we first guess a value for the blood temperature leaving the duck’s foot (T
f,out
in the
figure). We then use that temperature and the E-NTU expression for a counter flow concentric tube heat
exchanger to calculate the blood temperature entering the duck’s foot, T
f,in
.
Next, the calculation done in part
(a) is repeated to calculate T
f,out
.
This temperature is then compared to the guessed temperature.
The desired
result is obtained when the guessed temperature equals the calculated temperature exiting the duck’s foot.
Once T
f,out
is converged, then calculate T
c,out
.
T
f,in
=T
h,out
T
f,out
=T
c,in
T
c,out
T
h,in=
42
o
C
T
f, in
T
f, out