17–41
Btu/h 817.3
F/Btuh 098.13
F)3080(
F/Btuh 098.136400.00667.1618.80667.17068.1
F/Btuh 618.8
389.9
1
62.355
1
57.308
1
288
111111
21
61
5432
total
omiditotal
mid
mid
R
TT
Q
RRRRRR
R
RRRRR
Then steady rate of heat transfer through entire wall becomes
Btu/h 2932 2
ft 3906.0
ft) 10(ft) 30(
Btu/h) 817.3(
total
Q
17–43
17–64 In an experiment, the convection heat transfer coefficients of (a) air and (b) water flowing over the metal foil are to be
determined.
Assumptions 1 Steady operating conditions exist. 2 Heat transfer is one-dimensional. 3 Thermal properties are constant. 4
Thermal resistance of the thin metal foil is negligible.
Properties Thermal conductivity of the slab is given to be k = 0.023 W/m ∙ K and the emissivity of the metal foil is 0.02.
cond
rad
conv
R
R
R
or
1
elec
rad
1surr
cond
21
conv
11
TT
Aq
R
TT
R
TT
R
1surr
21 1
TT
TT
K W/m215.0
K )293423(K )293423)(K W/m1067.5)(02.0(
))((
2
222428
surr
2
surr
2
rad
TTTTh ss
K W/m37.3 2
(b) For water flowing over the metal foil, the radiation heat transfer coefficient is
))((
222428
surr
2
surr
2
rad
TTTTh ss
PROPRIETARY MATERIAL. © 2017 McGraw-Hill Education. 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.
17–65C When the diameter of cylinder is very small compared to its length, it can be treated as an infinitely long cylinder.
17–66C No. In steady-operation the temperature of a solid cylinder or sphere does not change in radial direction (unless there
is heat generation).
17–45
17–68 A steam pipe covered with 17-cm thick glass wool insulation is subjected to convection on its surfaces. The rate of
heat transfer per unit length and the temperature drops across the pipe and the insulation are 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 center line and no variation in the axial direction. 3 Thermal
conductivities are constant. 4 The thermal contact resistance at the interface is negligible.
C/W 354.31845.0089.300101.008.0
C/W 1845.0
)m 361.0(C) W/m15(
11
C/W 089.3
)m 1(C) W/m038.0(2
)75.2/75.5ln(
2
)/ln(
C/W 00101.0
)m 1(C) W/m15(2
)5.2/75.2ln(
2
)/ln(
C/W 08.0
)m 157.0(C) W/m80(
11
21
22
2
23
2
1
12
1
22
oitotal
oo
o
insulation
pipe
ii
i
RRRRR
Ah
R
Lk
rr
RR
Lk
rr
RR
Ah
R
17–47
17-70 A 50-m long section of a steam pipe passes through an open space at 15C. The rate of heat loss from the steam pipe,
the annual cost of this heat loss, and the thickness of fiberglass insulation needed to save 90 percent of the heat lost are to be
determined.
Assumptions 1 Heat transfer is steady since there is no indication of any change with time. 2 Heat transfer is one-
17–48
17-71 Steam flows in a steel pipe, which is insulated by gypsum plaster. The rate of heat transfer from the steam and the
temperature on the outside surface of the insulation are 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
conductivities are constant. 4 The thermal contact resistance at the interface is negligible.
17–52
Do
[in]
Ltube
[ft]
0.5
0.525
0.55
0.575
0.6
0.625
0.65
0.675
0.7
0.725
0.75
0.775
0.8
0.825
0.85
0.875
0.9
0.925
0.95
0.975
1
1154
1153
1152
1151
1151
1150
1149
1149
1148
1148
1148
1147
1147
1147
1146
1146
1146
1146
1145
1145
1145
0.5 0.6 0.7 0.8 0.9 1
1145.0
1147.5
1150.0
1152.5
1155.0
Do [in]
Ltube [ft]
17–53
17–75 An electric wire is tightly wrapped with a 1-mm thick plastic cover. The interface temperature and the effect of
doubling the thickness of the plastic cover on the interface temperature are to be determined.
W104)A 13)(V 8( IWQ eV
C/W 3844.00686.03158.0
C/W 0686.0
)m 10(C) W/m.15.0(2
)1.1/1.2ln(
2
)/ln(
C/W 3158.0
m)] m)(10 (0.0042C)[. W/m24(
11
plasticconvtotal
12
plastic
2
conv
RRR
kL
rr
R
Ah
R
oo
T2
T1
17–57
17–79 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. The rate of heat loss from the hot water and the average velocity of the water in the pipe as it passes through the
basement are to be determined.
Assumptions 1 Heat transfer is steady since there is no indication of any change with time. 2 Heat transfer is one-
2
m 168.2m) 15(m) 046.0(
LDA
oo
C/W 00003.0
)m 15(C) W/m.52(2
)2/3.2ln(
2
)/ln(
C/W 00442.0
)m 885.1(C). W/m120(
11
1
12
22
Lk
rr
R
Ah
R
pipe
ii
i
T1
T2
17-59
17-81 Liquid H2 flows in a pipe, which is insulated. The insulation thickness on the pipe that is necessary to keep the
liquid H2 temperature below −300°C 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 conductivities are
constant. 4 The thermal contact resistance at the interface is negligible.
Lk
pipe
pipe 2
Lk
DD
R
ins
23
ins 2
)/ln(
(insulation layer resistance)
LDhAh
R
ooo
o
3
11
(ambient air convection resistance)
The total thermal resistance and the rate of heat transfer are
oi RRRRR inspipetotal
and
o
oio
R
TT
R
TT
Q3
total
and the insulation thickness is
2
23 DD
t
Solving for the insulation thickness yields
cm 5.1 m 051.0t
Solved by EES Software. Copy-and-paste the following lines on a blank EES screen to verify the solutions.
“GIVEN”
h_i=200 [W/m^2-K] “liq. H2 convection heat transfer coefficient”
h_o=50 [W/m^2-K] “ambient air convection heat transfer coefficient”
