11–81
The capacity ratio of the 1st heat exchangers is
48.0
5.3670
8.1761
max
min
1=== C
C
c
11–82
11–84
11-110 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.
W/K8.5802)KJ/kg 4178)(h/s 3600/1)(kg/h 5000( === pccc cmC
499.0
W/K633,11
W/K8.5802
max
min ====
h
c
C
C
C
C
c
11–85
11-111 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
kW 59.36C)18–CC)(160 W/(418)( ,,minmax ==−= incinhTTCQ
The heat transfer surface area is
2
0.2 kg/s
11–87
11-113 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
11–89
11-115 A shell-and-tube heat exchanger is used to heat water for a commercial warewashing equipment by geothermal
brine. The number of passes for the tubes inside the shell is to be determined so that the heated water is within the
temperature range required by the ANIS/NSF 3 standard.
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
𝐶ℎ=𝐶𝑐(𝑇𝑐,out −𝑇𝑐,in)
(𝑇ℎ,in −𝑇ℎ,out)=(2100 W/K)(86−48)°C
(98−90)°C=9975 W/K
The capacity ratio is
𝑐 = 𝐶𝑚𝑖𝑛
NTU=− 1
√1+(0.21053)2ln[2 0.76
⁄−1−0.21053−√1+(0.21053)2
2 0.76
⁄−1−0.21053+√1+(0.21053)2]=1.7728
The heat transfer surface area is
𝐴𝑠=NTU𝐶min
11–90
Thus,
11–92
566.0
)70600(
)300600(
)(
)(
,,min
,,
max
=
−
−
=
−
−
==
incinh
outhinhh
TTC
TTC
Q
Q
The NTU of the heat exchanger is calculated using expressions given in Table 11–5.
952.0
301.3
233.1
ln
034.1
1
266.01266.01566.0/2
266.01266.01566.0/2
ln
266.01
1
11/2
11/2
ln
1
1
2
2
2
2
2
2
=
−=
++−−
+−−−
+
−=
++−−
+−−−
+
−=
NTU
cc
cc
c
NTU
From definition of NTU we get,
2
ft 454.95=
=
=→=
F)ftBtu/h27.9
F)Btu/h(13333.33(0.952)
2
min
min U
CNTU
A
C
UA
NTU s
s
Discussion The surface area of the heat exchanger calculated using LMTD and NTU methods is within 0.1% of each other.
11–93
11-117 A shell-and-tube (two-shell passes) heat exchanger is used to heat water for a commercial warewashing
equipment by geothermal brine. The number of tube passes inside each shell is to be determined so that the heated water is
within the temperature range required by the ANIS/NSF 3 standard.
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
𝐶ℎ=𝐶𝑐(𝑇𝑐,out −𝑇𝑐,in)
(𝑇ℎ,in −𝑇ℎ,out)=(2100 W/K)(86−20)
(98−90)=17325 W/K
The capacity ratio is
𝑐=𝐶𝑐
0.84615−1 ]1 2
0.84615−1 ]1 2
The effectiveness–NTU relation for 1-shell pass is
⁄−1−𝑐−√1+𝑐2
11–94
The NTU for the 2-shell passes becomes
NTU=𝑛NTU1=(2)(1.0255)=2.051
The total heat transfer surface area for 2-shell passes is
11–96
NTU1=− 1
√1+(0.30666)2ln[2 0.52129
⁄−1−0.30666−√1+(0.30666)2
2 0.52129
⁄−1−0.30666+√1+(0.30666)2]=0.84083
11–97
11–119 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.
Analysis The heat capacity rates of the hot and cold fluids are
C W/4190C)J/kg. kg/s)(4190 (1
===
phhh
cmC
70C
11–98
11-120 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
11–99
11-121 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
CkW/ 09.9
min == c
CC
544.0
72.16
09.9
max
min === C
C
C
= 0.65 is determined from Fig. 11-27 to be
NTU = 1.5
Then the surface area of this heat exchanger becomes
2
)CkW/ 09.9)(5.1(
NTU
min
C
UA
s
Hot air
100C
9 kg/s
