Respostas_Livro FT
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Respostas_Livro FT


DisciplinaFenômenos de Transporte I13.310 materiais113.312 seguidores
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is one-dimensional since there is thermal symmetry about the centerline and no significant 
variation in the axial direction. 3 Thermal properties are constant. 
Properties The thermal conductivity of cast iron is given to be k = 52 W/m\u22c5°C. 
Analysis Using water properties at room temperature, the mass flow rate of 
water and rate of heat transfer from the water are determined to be 
 
[ ]
 W13,296=C)6770)(CJ/kg. kg/s)(4180 06.1(
kg/s 06.1m4/(0.03)m/s) )(1.5kg/m 1000( 223
°\u2212°=\u394=
====
TcmQ
VAm
p
cc
&&
&& \u3c0\u3c1\u3c1V
 
The thermal resistances for convection in the pipe and 
the pipe itself are 
 
C/W 001768.0
m)]15((0.03)C)[. W/m400(
11
C/W 000031.0
)m 15(C) W/m.52(2
)5.1/75.1ln(
2
)/ln(
22iconv,
12
pipe
°=°==
°=°=
=
\u3c0
\u3c0
\u3c0
ii Ah
R
kL
rr
R
 
Rconv ,i Rpipe Rcombined ,o 
T\u221e1 T\u221e2
Using arithmetic mean temperature (70+67)/2 = 68.5°C for water, the heat transfer can be expressed as 
 
o
aveaveave
Ah
RR
TT
RRR
TT
R
TT
Q
combined
pipeiconv,
2,1,
ocombined,pipeiconv,
2,1,
total
2,1,
1++
\u2212=++
\u2212=\u2212= \u221e\u221e\u221e\u221e\u221e\u221e& 
Substituting, 
2
combined )]m(0.035)(15[
1+C/W) 001768.0(+C/W) 000031.0(
C)155.68( W296,13
\u3c0h°°
°\u2212= 
Solving for the combined heat transfer coefficient gives 
 C. W/m272.5 2 °=combinedh
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. 
 3-106
3-163 An 10-m long section of a steam pipe exposed to the ambient is to be insulated to reduce the heat 
loss through that section of the pipe by 90 percent. The amount of heat loss from the steam in 10 h and the 
amount of saved per year by insulating the steam pipe. 
Tair =8°C 
Ts =82°C 
 
 Steam pipe 
 
 
Assumptions 1 Heat transfer through the pipe is steady and one-dimensional. 2 Thermal conductivities are 
constant. 3 The furnace operates continuously. 4 The given heat transfer coefficients accounts for the 
radiation effects. 5 The temperatures of the pipe surface and the surroundings are representative of annual 
average during operating hours. 6 The plant operates 110 days a year. 
Analysis The rate of heat transfer for the uninsulated case is 
2
o m 77.3m) 10(m) 12.0( === \u3c0\u3c0 LDA o 
 W9764C)882)(m 77.3)(C. W/m35()( 22 =°\u2212°=\u2212= airso TThAQ& 
The amount of heat loss during a 10-hour period is 
 day)(per )s 3600kJ/s)(10 764.9( kJ 103.515 5×=×=\u394= tQQ &
The steam generator has an efficiency of 85%, and steam heating is used for 110 days a year. Then the 
amount of natural gas consumed per year and its cost are 
 therms/yr2.431days/yr) 110(
kJ 105,500
 therm1
0.85
kJ 10515.3used Fuel
5
=\u239f\u239f\u23a0
\u239e\u239c\u239c\u239d
\u239b×=
 
$517.4/yr=erm))($1.20/th therms/yr2.431(
fuel) ofcost fuel)(Unit ofAmount (fuel ofCost 
=
=
Then the money saved by reducing the heat loss by 90% by insulation becomes 
 $466=$517.4/yr0.9fuel) of(Cost 0.9=savedMoney ×=× 
 
 
 
3-164 A multilayer circuit board dissipating 27 W of heat consists of 4 layers of copper and 3 layers of 
epoxy glass sandwiched together. The circuit board is attached to a heat sink from both ends maintained at 
35°C. The magnitude and location of the maximum temperature that occurs in the board is to be 
determined. 
Assumptions 1 Steady operating conditions exist. 2 Heat transfer can be approximated as being one-
dimensional. 3 Thermal conductivities are constant. 4 Heat is generated uniformly in the epoxy layers of 
the board. 5 Heat transfer from the top and bottom surfaces of the board is negligible. 6 The thermal 
contact resistances at the copper-epoxy interfaces are negligible. 
Properties The thermal conductivities are given to be k = 386 W/m\u22c5°C for copper layers and k = 0.26 
W/m\u22c5°C for epoxy glass boards. 
Analysis The effective conductivity of the multilayer circuit board is first determined to be 
 
C W/m.48.58
m)0015.0(3)0002.0(4[
CW/)00117.03088.0()()(
C W/00117.0)]m 0015.0)(C W/m.26.0[(3)(
C W/3088.0)]m 0002.0)(C W/m.386[(4)(
epoxycopper
epoxycopper
epoxy
copper
°=+
°+=+
+=
°=°=
°=°=
tt
ktkt
k
kt
kt
eff
 
Copper 
Epoxy 
The maximum temperature will occur at the midplane of the board that is the 
farthest to the heat sink. Its value is 
 
C56.8°=°+°=+==
\u2212=
=+=
)m 000954.0)(C W/m.48.58(
)m 2/18.0)( W2/27(
C35
)(
m 000954.0)]0015.0(3)0002.0(4[18.0
2
eff
21max
21
eff
2
Ak
LQTTT
TT
L
Ak
Q
A
&
& 
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. 
 3-107
3-165 The plumbing system of a house involves some section of a plastic pipe exposed to the ambient air. 
The pipe is initially filled with stationary water at 0°C. It is to be determined if the water in the pipe will 
completely freeze during a cold night. 
Assumptions 1 Heat transfer is transient, but can be treated as steady since the water temperature remains 
constant during freezing. 2 Heat transfer is one-dimensional since there is thermal symmetry about the 
centerline and no variation in the axial direction. 3 Thermal properties of water are constant. 4 The water in 
the pipe is stationary, and its initial temperature is 0°C. 5 The convection resistance inside the pipe is 
negligible so that the inner surface temperature of the pipe is 0°C. 
Properties The thermal conductivity of the pipe is given to be k = 0.16 W/m\u22c5°C. The density and latent heat 
of fusion of water at 0°C are \u3c1 = 1000 kg/m3 and hif = 333.7 kJ/kg (Table A-9). 
Analysis We assume the inner surface of the pipe to be at 0°C at all times. The thermal resistances involved 
and the rate of heat transfer are 
Water pipe 
Tair = -5°C
Soil 
 
C/W 0258.16631.03627.0
C/W 6631.0
m)] 5.0)(m 024.0(C)[. W/m40(
11
C/W 3627.0
)m 5.0(C) W/m.16.0(2
)1/2.1ln(
2
)/ln(
oconv,pipetotal
2oconv,
12
pipe
°=+=+=
°=°==
°=°==
RRR
Ah
R
kL
rr
R
o \u3c0
\u3c0\u3c0
 
 W874.4
C/W 1.0258
C)]5(0[
total
21 =°
°\u2212\u2212=\u2212= \u221e
R
TT
Q s& 
The total amount of heat lost by the water during a 14-h period that night is 
 kJ 7.245)s 3600J/s)(14 874.4( =×=\u394= tQQ &
The amount of heat required to freeze the water in the pipe completely is 
 
 
kg 157.0)m 5.0()m 01.0()kg/m 1000( 232 ==== \u3c0\u3c1\u3c0\u3c1 Lrm V
kJ 4.52kJ/kg) 7.333kg)( 157.0( === fgmhQ 
The water in the pipe will freeze completely that night since the amount heat loss is greater than the 
amount it takes to freeze the water completely . )4.527.245( >
 
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. 
 3-108
3-166 The plumbing system of a house involves some section of a plastic pipe exposed to the ambient air. 
The pipe is initially filled with stationary water at 0°C. It is to be determined if the water in the pipe will 
completely freeze during a cold night. 
Assumptions 1 Heat transfer is transient, but can be treated as steady since the water temperature remains 
constant during freezing. 2 Heat transfer is one-dimensional since there is thermal symmetry about the 
centerline and no variation in the axial direction. 3 Thermal properties of water are constant. 4 The water in 
the pipe is stationary, and its initial temperature is 0°C. 5 The convection resistance inside the pipe is 
negligible so that the inner surface temperature of the pipe is 0°C. 
Properties The thermal conductivity of the pipe is given to be k = 0.16 W/m\u22c5°C. The density and latent heat 
of fusion of water at 0°C are \u3c1 = 1000 kg/m3 and hif = 333.7 kJ/kg (Table A-9). 
Analysis We assume the inner surface of the pipe to be at 0°C at all times. The thermal resistances involved 
and the rate of heat transfer are 
 
C/W 0153.36526.23627.0
C/W 6526.2
m)] 5.0)(m 024.0(C)[. W/m10(
11
C/W 3627.0
)m 5.0(C) W/m.16.0(2
)1/2.1ln(