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11-101
11-123 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.
W/K22.53)KJ/kg 2047)(kg/s 026.0( === phhh cmC
The capacity ratio is
2516.0
W/K11.52
W/K3.225
max
min ====
c
h
C
C
C
C
c
11-103
11-125 Exhaust gases are used in a recuperative cross flow heat exchanger to heat air. For the given values of flow condition,
heat transfer coefficients and the fouling resistance, the air exit temperature and the area of heat exchanger is to be
determined.
Assumptions 1 Steady state conditions exist. 2 Heat exchanger is well insulated. 3 Fluid properties are constant.
Analysis (a) For the given flow conditions the energy balance between the two fluid streams gives,
U = 182.92 W/m2·K.
The heat capacity rate of the cold fluid (air) is
max
CW/K16035K)J/kg1069)(kg/s15(→=== pccc cmC
The heat capacity rate of the hot fluid (exhaust gas) is,
min
CW/K8017.5K)J/kg1069()kg/s5.7( →=== phhh cmC
Thus the capacity ratio is
5.0
16035
5.8017
max
min === C
C
c
The effectiveness of the heat exchanger is
383.0
)30500(
)320500(
)(
)(
,,min
,,
max
=
−
−
=
−
−
== C
C
TTC
TTC
Q
Q
o
o
incinh
outhinhh
Now the number of transfer units (NTU) for both fluids unmixed are obtained from Figure 11-27(e),
NTU = 0.6
11-104
Change in air exit temperature with change in the air mass flow rate.
11-105
11-126 Single pass cross flow heat exchanger uses water (mixed) to heat methanol (unmixed) initially at 10C. The heat
exchanger area corresponding to the effectiveness of 0.5 is to be determined. Further, the effect of mass flow rate of water on
)(
)(
5.0
,,min
,,
max incinh
incoutcc
TTC
TTC
Q
Q
−
−
==
kW 5005.0/250
max == kWQ
11-106
(b)
Variation of the total heat transfer rate with change in water mass flow rate
As shown in the figure above, a variation of ±30% in the water mass flow rate causes the heat transfer rate to vary by 85%.
11-107
Variation of overall heat transfer coefficient with change in water mass flow rate.
11-109
K/Wm )10652.110169.41034.4(
1
KW/m3.056
1
K)W/m250(2
)023.0/025.0ln()025.0(
m)0.023(K)W/m(2500
m0.025
1
2
)/ln(
1
2364
22
++=
+
+
=
++=
−−−
U
m
hk
DDD
Dh
D
Uo
ioo
ii
o
11-110
11-128 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
C100=C20C120
C40=C80C120
,,2
,,1
−=−=
−=−=
incouth
outcinh
TTT
TTT
120C
120C
Steam
20C
2.2 kg/s
11-111
11-129 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
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
11-112
11-130 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.
11-115
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
30.65
30.65
30.65
30.65
30.65
30.65
30.65
30.65
30.65
30.65
30.65
30.65
30.65
30.65
30.65
30.65
30.65
30.65
30.65
30.65
30.65
0.01261
0.01261
0.01261
0.01261
0.01261
0.01261
0.01261
0.01261
0.01261
0.01261
0.01261
0.01261
0.01261
0.01261
0.01261
0.01261
0.01261
0.01261
0.01261
0.01261
0.01261
1 1.2 1.4 1.6 1.8 2
30
30.25
30.5
30.75
31
0.012
0.0125
0.013
0.0135
0.014
D [cm]
Q [kW]
mcond [kg/s]
Qdot
mcond
11-117
11-134 Saturated steam flows over tubes in a shell and tube heat exchanger at specified conditions. Effectiveness of the heat
exchanger, length of the tube and the rate of steam condensation are to be determined.
Assumptions 1 Steady state conditions exist. 2 Fluid properties are constant. 3 Heat exchanger is well insulated.
Properties The properties of water are evaluated at an average temperature of (60 + 20)°C/2 = 40°C from Table A-9:
ρ = 992.1 kg/m3, μ = 0.653 × 10−3 kg/m·s, cp = 4179 J/kg·K, k = 0.631 W/m·K, and Pr = 4.32
𝑄̇max =𝐶𝑐(𝑇𝑐,out −𝑇𝑐,in)
𝐶min(𝑇ℎ,in −𝑇𝑐,in)=60−20
130−20 = 𝟎.𝟑𝟔𝟑𝟔𝟒
(b) Cmin is calculated as
𝐶min = 𝑚̇𝑐𝑐𝑝𝑐 = 4(0.25 kg/s)(4179 J/kg⋅K)=4179 W/K
For a phase change process, the number of transfer units (NTU) is calculated as
NTU = −ln(1−𝜀)= −ln(1 − 0.36364)= 0.45199
The convection heat transfer coefficient for water through the tubes is
ℎ𝑖=Nu 𝑘
𝐷=(194.42)(0.631 W/m⋅K)
0.0125 m =9814.3 W/m2⋅K
Thus the overall heat transfer coefficient is
𝑈 = (1
=981.78 W/m2⋅K
Therefore the length of heat exchanger tube is calculated as
𝐿 = NTU𝐶min
11-119
mass flow rate of cooling water has to be increased to account for this heat transfer reduction. Thus the new mass flow rate of
11-120
Selection of the Heat Exchangers
11-137C The first thing we need to do is determine the life expectancy of the system. Then we need to evaluate how much
11-138C 1) Calculate heat transfer rate, 2) select a suitable type of heat exchanger, 3) select a suitable type of cooling fluid,
and its temperature range, 4) calculate or select U, and 5) calculate the size (surface area) of heat exchanger
11-139 Oil is to be cooled by water in a heat exchanger. The heat transfer rating of the heat exchanger is to be determined and
a suitable type is to be proposed.
Assumptions 1 Steady operating conditions exist. 2 The heat exchanger is well-insulated so that heat loss to the surroundings
