22–82
minpccc CW/K 7954.2K)J/kgkg/s)(196405.4(cmC
Thus the capacity ratio is
333.0
4.23855
2.7954
max
min C
C
c
The effectiveness of heat exchanger is
6.0
)10110(
)1070(
)(
)(
,,min
,,
max
C
C
TTC
TTC
Q
Q
o
o
incinh
incoutcc
The number of transfer units (NTU) of heat exchanger is calculated from Table 22-5 with Cmax mixed and Cmin unmixed as
106.1
333.0
)333.06.01ln(
1ln
)1ln(
1ln
c
c
NTU
From the definition of NTU, we find the surface area of the heat exchanger as,
2
2
min m 38.18
KW/m478.4
W/K)2.7954()106.1(
U
CNTU
As
Also the surface area of heat exchanger is expressed as
TLos NNLDA
22–83
22-104 Water is heated by steam condensing in a condenser. The required length of the tube is 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
C103=C17C120
C40=C80C120
,,2
,,1
incouth
outcinh
TTT
TTT
120C
120C
Steam
Water
17C
1.8 kg/s
22–84
22-105 Ethanol is vaporized by hot oil in a double-pipe parallel-flow heat exchanger. The outlet temperature and the mass
flow rate of oil are to be determined using the LMTD and NTU methods.
Assumptions 1 Steady operating conditions exist. 2 The heat exchanger is well-insulated so that heat loss to the surroundings
22–85
22-106 Saturated water vapor condenses in a 1-shell and 2-tube heat exchanger, (a) the heat transfer effectiveness, (b) the
outlet temperature of the cold water, and (c) the heat transfer rate for the heat exchanger are to be determined.
Assumptions 1 Steady operating condition exists. 2 The heat exchanger is well-insulated so that heat loss to the surroundings
is negligible. 3 Fluid properties are constant. 4 Changes in the kinetic and potential energies of fluid streams are negligible.
22–88
D
[cm]
Q
[kW]
cond
m
[kg/s]
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
1.9
1.95
2
31.35
31.35
31.35
31.35
31.35
31.35
31.35
31.35
31.35
31.35
31.35
31.35
31.35
31.35
31.35
31.35
31.35
31.35
31.35
31.35
31.35
0.0129
0.0129
0.0129
0.0129
0.0129
0.0129
0.0129
0.0129
0.0129
0.0129
0.0129
0.0129
0.0129
0.0129
0.0129
0.0129
0.0129
0.0129
0.0129
0.0129
0.0129
1 1.2 1.4 1.6 1.8 2
31
31.25
31.5
31.75
32
0.0125
0.013
0.0135
D [cm]
Q [kW]
mcond [kg/s]
Qdot
mcond
22–89
22-109E The hot water exiting the condenser is to be cooled by passing it through a heat exchanger immersed in large lake.
Using
NTU
method, exit temperature of the water from immersed heat exchanger is to be determined.
Assumptions 1 Steady state conditions exist. 2 Fluid properties remain constant. 3 Lake water is an infinite medium.
Analysis Since the problem statement requires use of
NTU
method we first calculate the heat capacity rates of cold and
The heat transfer rate is,
Btu/s 55.159)45100(F)Btu/s06.3()948.0(
)( ,,minmax
FQ
TTCQQ incinh
Thus from energy balance we can find the exit temperature of the water from immersed heat exchanger as,
F 47.9 o
outh
outhouthinhh
T
TTTCQ
,
,,, F)100(F)Btu/s06.3()(
Discussion In case of the heat exchangers immersed in ponds or lakes, the immersion depth plays a key role in maintaining
the fluid exit temperature. For shallow depths, the lake water temperature is subject to change with change in environmental
conditions and hence influences the fluid exit temperature.
22–91
Review Problems
22-111 The inlet and outlet temperatures of the cold and hot fluids in a double-pipe heat exchanger are given. It is to be
22-112 It is to be shown that when T1 = T2 for a heat exchanger, the Tlm relation reduces to Tlm = T1 = T2.
Analysis When T1 = T2, we obtain
0
21
TT
22–94
22-115 Hot water is cooled by cold water in a 1-shell pass and 2-tube passes heat exchanger. The mass flow rates of both
fluid streams 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
88.0
0.1
6036
317
45.0
607
6031
12
21
11
12
F
tt
TT
R
tT
tt
P
(Fig. 22-19)
Water
60C
1 shell pass
2 tube passes
31C
22–96
22-117 Water is used to cool a process stream in a shell and tube heat exchanger. The tube length is to be determined for one
tube pass and four tube pass cases.
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.
C2.114C8.45C160
,,1 outcinhTTT
C90C10C100
,,2 incouthTTT
C6.101
90
2.114
ln
902.114
ln
2
1
21
T
T
TT
Tlm
The Reynolds number is
968,11
skg/m 0.002
)kg/m m)(950 m/s)(0.025 (1.008
Re
m/s 008.1
4/m) (0.025)kg/m (100)(950
kg/s) (47
4/
3
232
VD
DN
m
A
m
V
tube
which is greater than 10,000. Therefore, we have turbulent flow. We assume fully developed flow and evaluate the Nusselt
9.92)14()968,11(023.0PrRe023.0
14
C W/m0.50
C)J/kg s)(3500kg/m 002.0(
Pr
3.08.03.08.0
k
hD
Nu
k
cp
stream
160C
22–97
6.281)14()872,47(023.0PrRe023.0 3.08.03.08.0 k
hD
Nu
C. W/m5632)6.281(
m 025.0
C W/m.50.0 2
Nu
D
k
hi
C W/m2339
4000
1
5632
1
1
11
12
oi hh
U