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11-64
11-81 A single-pass cross-flow heat exchanger with both fluids unmixed, the value of the overall heat transfer coefficient is
to be determined.
kg/s 755.2)min/s 60/1)(/minm 19.0)(kg/m 870(33 ===
V
h
m
Using energy balance on the hot fluid, we have
)(
out ,in ,
−= hhphhTTcmQ
11-66
11-92C The longer heat exchanger is more likely to have a higher effectiveness.
11-93C The NTU of a heat exchanger is defined as
minmin )( p
ss
cm
UA
C
UA
NTU
==
where U is the overall heat transfer
11-94C The value of effectiveness increases slowly with a large values of NTU (usually larger than 3). Therefore, doubling
the size of the heat exchanger will not save much energy in this case since the increase in the effectiveness will be very small.
11-67
11-96 Hot water coming from the engine of an automobile is cooled by air in the radiator. The outlet temperature of the air
and the rate of heat transfer are to be determined.
Assumptions 1 Steady operating conditions exist. 2 The heat exchanger is well-insulated so that heat loss to the surroundings
is negligible and thus heat transfer from the hot fluid is equal to the heat transfer to the cold fluid. 3 Changes in the kinetic
and potential energies of fluid streams are negligible. 4 Fluid properties are constant.
11-68
11-99 Glycerin is heated by ethylene glycol in a heat exchanger. Mass flow rates and inlet temperatures are given. The rate of
heat transfer and the outlet temperatures are to be determined.
Assumptions 1 Steady operating conditions exist. 2 The heat exchanger is well-insulated so that heat loss to the surroundings
is negligible and thus heat transfer from the hot fluid is equal to the heat transfer to the cold fluid. 3 Changes in the kinetic
C W/1250C)J/kg. kg/s)(2500 (0.5
===
pccc
cmC
Therefore,
C W/1200
min == h
CC
and
96.0
1250
1200
max
min === C
C
c
Ethylene
60C
0.5 kg/s
20C
0.5 kg/s
11-69
11-100 A thin-walled concentric tube counter-flow heat exchanger has specified mass flow rates and inlet temperatures, (a)
the heat transfer rate for the heat exchanger, (b) the outlet temperatures of the cold and hot fluids, and (c) the fouling factor
after a period of operation are to be determined.
5012.0
W/K20890
W/K04701
max
min ====
c
h
C
C
C
C
c
197.2
W/K10470
)m 23)(K W/m1000(
NTU
22
min
=
== C
UAs
7997.0
])5012.012.197(exp[)5012.0(1
])5012.01(197.2exp[1
])1NTU(exp[1
])1NTU(exp[1 =
−−−
−−−
=
−−−
−−−
=cc
c
)( in ,out , ccc TTCQ −=
→
C52.1=+
=+= C20
W/K20890
W1070.6 5
in ,out , c
c
cT
C
Q
T
)( out ,in , hhh TTCQ −=
→
C36.0=
−=−= W/K04701
W1070.6
C100
5
in ,out ,
h
hh C
Q
TT
(c) The overall heat transfer coefficient at clean conditions is Uclean = 1000 W/m2·K. After a period of operation, the overall
11-71
11-102 Prob. 11-101 is reconsidered. The effects of the mass flow rate of water and the tube length on the outlet
temperatures of water and air are to be investigated.
Analysis The problem is solved using EES, and the solution is given below.
D=0.012 [m]
"ANALYSIS"
"With EES, it is easier to solve this problem using LMTD method than NTU method. Below, we use LMTD
method. Both methods give the same results."
11-72
L
[m]
Tw,out
[C]
Tair,out
[C]
5
24.35
86.76
6
24.8
86.14
7
25.24
85.53
8
25.67
84.93
9
26.1
84.35
10
26.52
83.77
11
26.93
83.2
12
27.34
82.64
13
27.74
82.09
14
28.13
81.54
15
28.52
81.01
16
28.9
80.48
17
29.28
79.96
18
29.65
79.45
19
30.01
78.95
20
30.37
78.45
21
30.73
77.96
22
31.08
77.48
23
31.42
77
24
31.76
76.53
25
32.1
76.07
5 9 13 17 21 25
24
25
26
27
28
29
30
31
32
33
76
78
80
82
84
86
88
L [m]
Tw,out [C]
Tair,out [C]
Tw,out
Tair,out
11-74
Discussion The effectiveness for the counter-flow configuration is higher than the parallel-flow configuration. This led to
11-75
11-104 Cold water is heated by hot water in a heat exchanger. The net rate of heat transfer and the heat transfer surface area
of the heat exchanger are to be determined.
Assumptions 1 Steady operating conditions exist. 2 The heat exchanger is well-insulated so that heat loss to the surroundings
is negligible and thus heat transfer from the hot fluid is equal to the heat transfer to the cold fluid. 3 Changes in the kinetic
CW/ 570,12C)J/kg. kg/s)(4190 (3
===
phhh
cmC
Therefore,
C W/1045
min == c
CC
083.0
570,12
1045
max
min === C
C
c
Then the maximum heat transfer rate becomes
W825,88C)15-CC)(100 W/(1045)( ,,minmax ==−= incinhTTCQ
Hot water
100C
3 kg/s
15C
0.25 kg/s
45C
11-78
11-106 A double-pipe counter-flow heat exchanger is used to cool a hot fluid such that when it flows into a pipe system
it is below the temperature limit for polypropylene pipes, 99°C. The heat transfer surface area of the heat exchanger is to be
determined.
Assumptions 1 Steady state conditions. 2 The heat exchanger is well-insulated so that heat loss to the surroundings is
negligible and thus heat transfer from the hot fluid is equal to the heat transfer to the cold fluid. 3 Properties of fluids are
