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11-142
,
=
TFUAQCFlms
11-145
11-165 A single-pass cross-flow heat exchanger uses hot air (mixed) to heat water (unmixed), and the required surface area
of the heat exchanger is to be determined.
Assumptions 1 Steady operating condition exists. 2 The heat exchanger is well-insulated so that heat loss to the surroundings
0.92
4.2
3080
100220
26.0
30220
3080
12
21
11
12
=
−
−
=
−
−
=
=
−
−
=
−
−
=
F
tt
TT
R
tT
tt
P
(Fig. 11-19d)
W10275.6K )3080)(KJ/kg 4183)(kg/s 3()( 5
in ,out , =−=−= ccpccTTcmQ
The log mean temperature difference for the counter-flow arrangement is
)30100()80220(
21
−−−
−
TT
11-147
11-168 A water-to-water counter-flow heat exchanger is considered. The outlet temperature of the cold water, the
effectiveness of the heat exchanger, the mass flow rate of the cold water, and the heat transfer rate 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
cc
min
and
27.6
18.4
max
min ===
c
c
m
m
C
C
The rate of heat transfer can be expressed as
)20)(18.4()( outc,inc,outc, −=−= TmTTCQ cc
)75)(27.6()15(90)27.6()( outc,outc,outh,h,in TmTmTTCQ cch −=+−=−=
c,out c,out
c,out c,out c,out
4.18 ( 20) 6.27 (75 )
4.18( 20) 6.27(75 )
cc
Q m T m T
T T T
= - = -
- = - ¾ ¾® = °
53.0 C
90C
11-148
11-169 Water is heated by geothermal water in a double-pipe counter-flow heat exchanger. The mass flow rate of the
geothermal water and the outlet temperatures of both fluids 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
CkW/ 5.016=C)kJ/kg. kg/s)(4.18 (1.2
==
pccc
cmC
CkW/ 016.5
min == c
CC
hh mmC
C
1802.1
25.4
016.5
max
min ===
The NTU of this heat exchanger is
392.2
CkW/ 016.5
)m C)(25.kW/m 480.0( 22
min
=
== C
UA
NTU s
Using the effectiveness relation, we find the capacity ratio
494.0
)1(392.2exp1
)1(392.2exp1
823.0
)1(NTUexp1
)1(NTUexp1 =⎯→⎯
−−−
−−−
=⎯→⎯
−−−
−−−
=c
cc
c
cc
c
Geothermal
water
75C
17C
1.2 kg/s
11-150
11-171 A water-to-water heat exchanger is proposed to preheat the incoming cold water by the drained hot water in a plant to
save energy. The heat transfer rating of the heat exchanger and the amount of money this heat exchanger will save are to be
determined.
Assumptions 1 Steady operating conditions exist. 2 The heat exchanger is well-insulated so that heat loss to the surroundings
kW 6.25
=
Noting that the heat exchanger will recover 72% of it, the actual
heat transfer rate becomes
kW 18.43=kJ/s) 6.25)(72.0(
max == QQ
= 1.38x108 kJ/year
Then amount of fuel and money saved will be
ar therms/ye1677
kJ 500,105
therm1
78.0
kJ/year 1038.1
efficiency Furnace
savedEnergy
saved Fuel
8
=
==
Money saved = (fuel saved)(the price of fuel)
= (1677 therms/year)($1.00/therm)
= $1677/year
Hot water
60C
8 kg/s
11-152
11-173 Air is to be heated by hot oil in a cross-flow heat exchanger with both fluids unmixed. The effectiveness of the heat
exchanger, the mass flow rate of the cold fluid, and the rate of heat transfer 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
