22–21
22-40 Water is heated in a double-pipe parallel-flow heat exchanger by geothermal water. The required length of tube is to be
determined.
Assumptions 1 Steady operating conditions exist. 2 The heat
60C
22–22
22-41 Prob. 22-40 is reconsidered. The effects of temperature and mass flow rate of geothermal water on the length of
the tube are to be investigated.
Analysis The problem is solved using EES, and the solution is given below.
U=0.55 [kW/m^2-C]
“ANALYSIS”
Q_dot=m_dot_w*c_p_w*(T_w_out-T_w_in)
22–23
geo
m
[kg/s]
L
[m]
0.1
46.31
0.125
35.52
0.15
31.57
0.175
29.44
0.2
28.1
0.225
27.16
0.25
26.48
0.275
25.96
0.3
25.54
0.325
25.21
0.35
24.93
0.375
24.69
0.4
24.49
0.425
24.32
0.45
24.17
0.475
24.04
0.5
23.92
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
20
25
30
35
40
45
50
mgeo [kg/s]
L [m]
22–25
22–43 The heat transfer rate of a heat exchanger containing 400 tubes with specified inner and outer diameters and length is
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. 5
Thermal resistance of the tubes is negligible.
22–28
22–46 The hot and cold fluid streams at specified temperature and mass flow rate enter a parallel heat exchanger. For the
known values of convection heat transfer coefficients and fouling factors, the overall heat transfer coefficient, the exit
temperature of the hot fluid and the surface area of the heat exchanger are to be determined.
Assumptions 1 Thermal resistance due to pipe thickness is negligible. 2 Thermal properties of the hot and cold fluids are
constant. 3 Heat exchanger is well insulated.
Analysis (a) The overall heat transfer coefficient is calculated based on the given heat transfer coefficients and fouling factors
at the tube inlet and outlet surface. Since the tube is of negligible thickness, the inner and outer surface areas of the tube may
K W/m800
K W/m300
2
2
o
ih
hU
K W/m200.67 2U
22–29
22–47 Ethylene glycol is heated in a tube while steam condenses on the outside tube surface. The tube length is to be
determined.
0.01545 kg/ms, Pr = 148.5. The thermal conductivity of copper is given to be 386 W/mK.
Analysis The rate of heat transfer is
22–31
22–49 Oil is cooled by water in a thin-walled double-pipe counter-flow heat exchanger. The overall heat transfer coefficient
of the heat exchanger 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
and potential energies of fluid streams are negligible. 4 There is no fouling. 5 Fluid properties are constant. 6 The thermal
resistance of the inner tube is negligible since the tube is thin-walled and highly conductive.
2.20 kJ/kg.C, respectively.
Analysis The rate of heat transfer from the water to the oil is
kW 484=
)]([ oil
outinpTTcmQ
The outlet temperature of the water is determined from
C19.99
C)kJ/kg. kg/s)(4.18 5.1(
kW 484
+C22
)]([ water
p
inoutinoutpcm
Q
TTTTcmQ
The logarithmic mean temperature difference is
C50.81=C19.99C150
,,1
outcinh
TTT
Cold water
22C
1.5 kg/s
Hot oil
150C
2 kg/s
40C
22–33
Tw,in
[C]
U
[kW/m2C]
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
20.7
21.15
21.61
22.09
22.6
23.13
23.69
24.28
24.9
25.55
26.24
26.97
27.75
28.58
29.46
30.4
31.4
32.49
33.65
34.92
36.29
5 9 13 17 21 25
20
22
24
26
28
30
32
34
36
38
Tw,in [C]
U [kW/m2-C]
22–34
22-51 Cold water is heated by hot water in a double-pipe counter-flow heat exchanger. The rate of heat transfer and the heat
transfer surface area of the heat exchanger are to be determined.
Analysis The rate of heat transfer in this heat exchanger is
kW 156.8=
)]([ watercold
inoutpTTcmQ
The outlet temperature of the hot water is determined from
C53.87
C)kJ/kg. kg/s)(4.19 3(
kW 8.156
C100)]([ hot water
p
inoutoutinpcm
Q
TTTTcmQ
The temperature differences at the two ends of the heat exchanger are
C72.53=C15C53.87
C55=C45C100
,,2
,,1
incouth
outcinh
TTT
TTT
and
C36.63
)53.72/55ln(
53.7255
)/ln( 21
21
TT
TT
Tlm
Then the surface area of this heat exchanger becomes
2
kW 8.156
Q
Hot water
3 kg/s
1.25 kg/s
45C
22–36
22–53E Prob. 22-52E is reconsidered. The effect of the condensing steam temperature on the rate of heat transfer, the
rate of condensation of steam, and the mass flow rate of cold water is to be investigated.
Analysis The problem is solved using EES, and the solution is given below.
“GIVEN”
N_pass=8
104
106
108
110
112
2430
2562
2694
2826
2958
2.329
2.456
2.583
2.709
2.836
186.9
197.1
207.2
217.4
227.5
22–37
80 85 90 95 100 105 110 115 120
500
1000
1500
2000
2500
3000
3500
0.5
1
1.5
2
2.5
3
3.5
Tsteam [F]
Q [Btu/s]
msteam [lbm/s]
80 85 90 95 100 105 110 115 120
50
100
150
200
250
300
Tsteam [F]
mw [lbm/s]
22–38
22–54 Water is evaporated by hot exhaust gases in an evaporator. The rate of heat transfer, the exit temperature of the exhaust
gases, and the rate of evaporation of water 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 There is no fouling. 5 Fluid properties are constant.
Analysis The temperature differences between the water and the
C)200(
outh,inc,outh,2
TTTT
and
)200(350
outh,
21
T
TT
200C
550C
Th,out
22–39
22–55 Prob. 22–54 is reconsidered. The effect of the exhaust gas inlet temperature on the rate of heat transfer, the exit
temperature of exhaust gases, and the rate of evaporation of water is to be investigated.
Analysis The problem is solved using EES, and the solution is given below.
U=1.780 [kW/m^2-C]
“ANALYSIS”
DELTAT_1=T_exhaust_in-T_w
22–40
300 350 400 450 500 550 600
20
30
40
50
60
70
80
90
100
110
202
204
206
208
210
212
214
Texhaust,in [C]
Q [kW]
Texhaust,out [C]
heat
temperature
300 350 400 450 500 550 600
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
0.055
Texhaust,in [C]
mw [kg/s]