Respostas_Livro FT
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Respostas_Livro FT


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to kt. Substituting, the fraction of heat conducted along the 
copper layer and the effective thermal conductivity of the plate are determined to be 
FBtu/h. 56125.0)00375.05575.0()()()(
FBtu/h. 00375.0ft) F)(0.15/12Btu/h.ft. 15.0(2)(
FBtu/h. 5575.0ft) F)(0.03/12Btu/h.ft. 223()(
epoxycoppertotal
epoxy
copper
°=+=+=
°=°=
°=°=
ktktkt
kt
kt
 
and 
F.Btu/h.ft 20.4 2 °=+
°=
+
+=
ft )]12/15.0(2)12/03.0[(
FBtu/h. 56125.0
t
)()(
epoxycopper
epoxycopper
t
ktkt
keff
 
99.3%==== 993.0
56125.0
5575.0
)(
)(
total
copper
copper kt
kt
f 
 
PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and 
educators for course preparation. If you are a student using this Manual, you are using it without permission. 
 3-102
Review Problems 
 
 
3-159E Steam is produced in copper tubes by heat transferred from another fluid condensing outside the 
tubes at a high temperature. The rate of heat transfer per foot length of the tube when a 0.01 in thick layer 
of limestone is formed on the inner surface of the tube is to be determined. 
Assumptions 1 Heat transfer is steady since there is no indication of any change with time. 2 Heat transfer 
is one-dimensional since there is thermal symmetry about the centerline and no variation in the axial 
direction. 3 Thermal properties are constant. 4 Heat transfer coefficients are constant and uniform over the 
surfaces. 
Properties The thermal conductivities are given to be k = 223 
Btu/h\u22c5ft\u22c5°F for copper tubes and k = 1.7 Btu/h\u22c5ft\u22c5°F for 
limestone. T\u221e2
Rtotal, new HX 
T\u221e1
Analysis The total thermal resistance of the new heat exchanger is 
 F/Btuh. 005.0
Btu/h 102
F)250350(
4
new
21
newtotal,
newtotal,
21
new °=×
°\u2212=\u2212=\u23af\u2192\u23af\u2212= \u221e\u221e\u221e\u221e
Q
TT
R
R
TT
Q &
& 
After 0.01 in thick layer of limestone forms, the new 
value of thermal resistance and heat transfer rate are 
determined to be 
F/Btuh 00689.000189.0005.0
F/Btuh 00189.0
)ft 1(F)Btu/h.ft. 7.1(2
)49.0/5.0ln(
2
)/ln(
ilimestone,newtotal,w/limetotal,
1
ilimestone,
°=+=+=
°=°==
RRR
kL
rr
R i \u3c0\u3c0 
Rlimestone 
T\u221e2
Rtotal, new HX 
T\u221e1
 27%) of decline (a 
F/Btuh 0.00689
F)250350(
w/limetotal,
21
w/lime Btu/h 101.45
4×=°
°\u2212=\u2212= \u221e\u221e
R
TT
Q& 
Discussion Note that the limestone layer will change the inner surface area of the pipe and thus the internal 
convection resistance slightly, but this effect should be negligible. 
 
PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and 
educators for course preparation. If you are a student using this Manual, you are using it without permission. 
 3-103
3-160E Steam is produced in copper tubes by heat transferred from another fluid condensing outside the 
tubes at a high temperature. The rate of heat transfer per foot length of the tube when a 0.01 in thick layer 
of limestone is formed on the inner and outer surfaces of the tube is to be determined. 
Assumptions 1 Heat transfer is steady since there is no indication of any change with time. 2 Heat transfer 
is one-dimensional since there is thermal symmetry about the centerline and no variation in the axial 
direction. 3 Thermal properties are constant. 4 Heat transfer coefficients are constant and uniform over the 
surfaces. 
Properties The thermal conductivities are given to be k = 223 
Btu/h\u22c5ft\u22c5°F for copper tubes and k = 1.7 Btu/h\u22c5ft\u22c5°F for limestone. 
T\u221e2
Rtotal, new HX 
T\u221e1
Analysis The total thermal resistance of the new heat exchanger is 
 F/Btuh. 005.0
Btu/h 102
F)250350(
4
new
21
newtotal,
newtotal,
21
new °=×
°\u2212=\u2212=\u23af\u2192\u23af\u2212= \u221e\u221e\u221e\u221e
Q
TT
R
R
TT
Q &
& 
After 0.01 in thick layer of limestone forms, the new value of thermal resistance and heat transfer rate are 
determined to be 
 Rlimestone, o 
T\u221e2
Rtotal, new HX 
T\u221e1
Rlimestone, i 
 
 
F/Btuh. 00832.000143.000189.0005.0
F/Btuh. 00143.0
)ft 1(F)Btu/h.ft. 7.1(2
)65.0/66.0ln(
2
)/ln(
F/Btuh. 00189.0
)ft 1(F)Btu/h.ft. 7.1(2
)49.0/5.0ln(
2
)/ln(
olimestone,ilimestone,newtotal,w/limetotal,
2
ilimestone,
1
ilimestone,
°=++=++=
°=°==
°=°==
RRRR
kL
rr
R
kL
rr
R
o
i
\u3c0\u3c0
\u3c0\u3c0
 
40%) of decline (a 
F/Btuh 0.00832
F)250350(
w/limetotal,
21
w/lime Btu/h 101.20
4×=°
°\u2212=\u2212= \u221e\u221e
R
TT
Q& 
Discussion Note that the limestone layer will change the inner surface area of the pipe and thus the internal 
convection resistance slightly, but this effect should be negligible. 
 
PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and 
educators for course preparation. If you are a student using this Manual, you are using it without permission. 
 3-104
3-161 A cylindrical tank filled with liquid propane at 1 atm is exposed to convection and radiation. The 
time it will take for the propane to evaporate completely as a result of the heat gain from the surroundings 
for the cases of no insulation and 5-cm thick glass wool insulation are to be determined. 
Assumptions 1 Heat transfer is steady. 2 Heat transfer is one-dimensional. 3 The combined heat transfer 
coefficient is constant and uniform over the entire surface. 4 The temperature of the thin-shelled spherical 
tank is said to be nearly equal to the temperature of the propane inside, and thus thermal resistance of the 
tank and the internal convection resistance are negligible. 
Properties The heat of vaporization and density of liquid propane at 1 atm are given to be 425 kJ/kg and 
581 kg/m3, respectively. The thermal conductivity of glass wool insulation is given to be k = 0.038 
W/m\u22c5°C. 
Analysis (a) If the tank is not insulated, the heat transfer rate is determined to be 
 222tank m 88.244/m) (1.22+m) 6(m) 2.1()4/(2 ==+= \u3c0\u3c0\u3c0\u3c0\u3c0 DDLA
 W787,44C)]42(30)[m 88.24)(C. W/m25()( 2221tank =°\u2212\u2212°=\u2212= \u221e\u221e TThAQ&
The volume of the tank and the mass of the propane are 
Propane 
tank, -42°C kg 6.3942)m 786.6)(kg/m 581(
m 786.6)m 6()m 6.0(
33
322
===
===
V
V
\u3c1
\u3c0\u3c0
m
Lr
The rate of vaporization of propane is 
 kg/s 1054.0
kJ/kg 425
kJ/s 787.44 ===\u2192=
fg
fg h
QmhmQ
&
&&& Rins, ends 
Rsins, sides 
Rconv, o 
Ts T\u221eThen the time period for the propane tank to empty becomes 
 hours 10.4====\u394 s 413,37
kg/s 0.1054
kg 6.3942
m
mt & 
(b) We now repeat calculations for the case of insulated tank with 5-cm thick insulation. 
 
 
222
o m 16.274/m) (1.32+m) 6(m) 3.1()4/(2 ==+= \u3c0\u3c0\u3c0\u3c0\u3c0 DDLA
C/W 1444.2
]4/)m 25.1(C)[ W/m.038.0(
m 05.022
C/W 05587.0
)m 6(C) W/m.038.0(2
)60/65ln(
2
)/ln(
C/W 001473.0
)m 16.27(C). W/m25(
11
2ends,insulation
12
side,insulation
22oconv,
°=°
×==
°=°==
°=°==
\u3c0
\u3c0\u3c0
avg
oo
kA
LR
kL
rr
R
Ah
R
 
Noting that the insulation on the side surface and the end surfaces are in parallel, the equivalent resistance 
for the insulation is determined to be 
 C/W 05445.0
C/W 1444.2
1
C/W 05587.0
111 1
1
ends,insulationside,insulation
insulation °=\u239f\u23a0
\u239e\u239c\u239d
\u239b
°+°=\u239f\u239f\u23a0
\u239e
\u239c\u239c\u239d
\u239b +=
\u2212\u2212
RR
R 
Then the total thermal resistance and the heat transfer rate become 
 C/W 05592.005445.0001473.0insulationoconv,total °=+=+= RRR 
 W1288
C/W 0.05592
C)]42(30[
total
=°
°\u2212\u2212=\u2212= \u221e
R
TT
Q s& 
Then the time period for the propane tank to empty becomes 
 
days 15.1==×===\u394
===\u2192=
hours 4.361s 10301.1
kg/s 0.003031
kg 6.3942
kg/s 003031.0
kJ/kg 425
kJ/s 288.1
6
m
mt
h
QmhmQ
fg
fg
&
&
&&&
 
PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and 
educators for course preparation. If you are a student using this Manual, you are using it without permission. 
 3-105
3-162 Hot water is flowing through a 15-m section of a cast iron pipe. The pipe is exposed to cold air and 
surfaces in the basement, and it experiences a 3°C-temperature drop. The combined convection and 
radiation heat transfer coefficient at the outer surface of the pipe is to be determined. 
Assumptions 1 Heat transfer is steady since there is no indication of any significant change with time. 2 
Heat transfer