22–61
22–88 Prob. 22–87 is reconsidered. The effects of the inlet temperature of hot water and the heat transfer coefficient on
the rate of heat transfer and the surface area are to be investigated.
Analysis The problem is solved using EES, and the solution is given below.
U=0.95 [kW/m^2-C]
“ANALYSIS”
“With EES, it is easier to solve this problem using LMTD method than NTU method. Below, we use LMTD
22–62
Q
[kW]
A
[m2]
31.35
0.6163
31.35
0.5778
31.35
0.5438
31.35
0.5136
31.35
0.4865
31.35
0.4622
31.35
0.4402
31.35
0.4202
31.35
0.4019
31.35
0.3852
31.35
0.3698
0.7 0.8 0.9 1 1.1 1.2 1.3
31
31.25
31.5
31.75
32
0.35
0.4
0.45
0.5
0.55
0.6
0.65
U [kW/m2-C]
Q [kW]
A [m2]
heat
area
effectiveness and (b) the actual heat transfer rate in 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.
Analysis (a) The heat capacity rates are given as
5.1
FBtu/hr 000,20
)ft 100)(FftBtu/hr 300(
NTU
22
min
C
UAs
Using the equation listed in Table 22-4, the heat transfer effectiveness is
1
2
2
2
]1NTUexp[1
]1NTUexp[1
112
c
c
cc
22–65
22–91 Cold water is being heated in a 1-shell and 2-tube heat exchanger, the outlet temperatures of the cold water and hot
water 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.
Analysis The heat capacity rates are
The capacity ratio is
499.0
W/K633,11
W/K8.5802
max
min
h
c
C
C
C
C
c
22–66
22–92 Hot oil is to be cooled by water in a heat exchanger. The mass flow rates and the inlet temperatures are given. The rate
of heat transfer and the outlet temperatures are to be determined.
C W/418C)J/kg. kg/s)(4180 (0.1
C W/440C)J/kg. kg/s)(2200 (0.2
pccc
phhh
cmC
cmC
95.0
440
418
max
min C
C
c
The heat transfer surface area is
2
be
C77.7
C104.6
CkW/ 44.0
kW 2.36
C160)(
C/kW 418.0
kW 2.36
+C18)(
,,,,
,,,,
h
inhouthouthinhh
c
incoutcincoutcc
C
Q
TTTTCQ
C
Q
TTTTCQ
0.2 kg/s
22–68
22–94 Ethyl alcohol is heated by water in a shell-and-tube heat exchanger. The heat transfer surface area of the heat
exchanger is to be determined using both 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
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 The overall heat transfer coefficient is constant and uniform.
/35)25ln(
)/ln( 21
93.0
78.0
2570
6095
64.0
2595
2570
11
12
11
12
F
tt
TT
R
tT
tt
P
25C
2.1 kg/s
2-shell pass
8 tube passes
60C
22–69
22–95E In a one shell pass and eight tube pass heat exchanger, water is to be heated using hot air at 600F. For the given
value of convection heat transfer coefficient on the outer surface of the tubes and the fouling resistances, the heat exchanger
= 0.999 Btu/1bm·F 1 Btu/1bm·F
Analysis The heat gained by water from hot air is,
Btu/h 104F70)–)(150Btu/lbm (1lbm/h)000,50()( 6
,, FTTcmQ incoutcpcc
From energy balance we have, heat lost by air = heat gained by water.
lbm/h 53,333.33
F300)–F)(600Btu/lbm(0.25
Btu/h104
)(
)(
)()(
6
,,
,,
,,,,
outhinhph
incoutcpcc
h
incoutcpccouthinhphh
TTc
TTcm
m
TTcmTTcm
Now the logarithmic temperature difference for a counter flow heat exchanger is calculated as
 
21
21
,/ln TT
TT
TCFlm
F 450150600 o
,,1 outcinhTTT
and
F23070300 o
,,2 incouthTTT
 
F 78.327
230/450ln
230450 o
,
CFlm
T
In order to determine correction factor we first need to find the temperature ratios P and R as follows:
566.0
60070
600300
11
12
tT
tt
P
and
266.0
600300
15070
12
21
tt
TT
R
From Figure 22-19 (a), the correction factor is
CFlmsTFUAQ,
The overall heat transfer coefficient is to be calculated from the given value of convection heat transfer coefficient on the
266.0
000,50
33.13333
max
min C
C
c
22–70
The effectiveness of the heat exchanger is,
566.0
)70600(
)300600(
)(
)(
,,min
,,
max
incinh
outhinhh
TTC
TTC
Q
Q
22–71
22–96 Air is heated by a hot water stream in a cross-flow heat exchanger. The maximum heat transfer rate and the outlet
temperatures of the cold and hot fluid streams are to be determined.
4.19 and 1.005 kJ/kg.C.
C W/3015C)J/kg. kg/s)(1005 (3
pccc
cmC
Therefore
which is the smaller of the two heat capacity rates. Then the maximum heat transfer rate becomes
3 kg/s
1 kg/s
70C
22–72
22–97 A cross-flow heat exchanger with both fluids unmixed has a specified overall heat transfer coefficient, and the exit
temperature of the cold fluid is to be determined.
Assumptions 1 Steady operating condition exists. 2 The heat exchanger is well-insulated so that heat loss to the surroundings
5.0
W/K000,80
W/K000,40
max
min
c
h
C
C
C
C
c
22–73
22–98 Water is heated by hot air in a heat exchanger. The mass flow rates and the inlet temperatures are given. The heat
transfer surface area of the heat exchanger on the water side 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
544.0
72.16
09.9
max
min C
C
C
Then the surface area of this heat exchanger becomes
2
)CkW/ 09.9)(5.1(
NTU
min
C
UA
s
22–74
22–99 Water is heated by a hot water stream in a heat exchanger. The maximum outlet temperature of the cold water and the
effectiveness 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
and potential energies of fluid streams are negligible. 4 Fluid properties are constant.
22–75
22-100 Oil in an engine is being cooled by air in a cross-flow heat exchanger, where both fluids are unmixed; (a) the heat
transfer effectiveness and (b) the outlet temperature of the oil are to be determined.
The capacity ratio is
2516.0
W/K11.52
W/K3.225
max
min
c
h
C
C
C
C
c
22–77
Change in air exit temperature with change in the air mass flow rate.
22–79
Variation of the total heat transfer rate with change in water mass flow rate
Variation of the methanol exit temperature witch change in water mass flow rate.
22–80
Variation of overall heat transfer coefficient with change in water mass flow rate.
Variation of the heat exchanger effectiveness with change in water mass flow rate