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13-61
13-71 Liquid NH3 flows in an insulated tube that is protected by a concentric shield. The surrounding temperature is to
be determined so that the NH3 is maintained in the liquid state.
Assumptions 1 Steady operating conditions exist. 2 The surfaces are opaque, diffuse, and gray. 3 The ambient temperature is
equal to the temperature of the surrounding surfaces, T∞ = Tsurr.
Properties The emissivity of both surfaces is given to be ε = ε1 = ε2 = 0.33.
The natural convection heat transfer rate from the outer surface is
)( 22conv TThAQ−=
Performing the energy balance on the outer surface, we have
radconv12 QQQ +=
)( 4
4
4
1
4
21 TTATThA
TTA −+−=
−
13-62
13-72 Hot fluid flowing inside a long tube and the tube is enclosed in a concentric cylindrical thin cover. The emissivity
of the inside tube is to be determined so that the outer surface temperature is kept below 45°C to prevent thermal burn
hazards.
Assumptions 1 Steady operating conditions exist. 2 The surfaces are opaque, diffuse, and gray. 3 The ambient temperature is
equal to the temperature of the surrounding surfaces, T∞ = Tsurr.
)( 4
surr
4
222rad TTAQ −=
The natural convection heat transfer rate from the outer surface is
)( 22conv
−= TThAQ
Performing the energy balance on the outer surface, we have
convrad12 QQQ +=
)(
4
4
4
2
4
11
−TThATTA
TTA
0.573=
−
−
−+−
−
=
−
−
−+−
−
=
−
−
−+−
−
=
−
−
−
−
−
1
1
2444428
444428
1
2
1
2
2
22
4
surr
4
222
4
2
4
11
1
2
1
2
2
22
4
surr
4
222
4
2
4
11
1
m 05.0
m 025.0
6.0
6.01
K)293318)(m 05.0()K W/m8(K)293318)(K W/m1067.5)(m 05.0)(6.0(
K)318423)(K W/m1067.5)(m 025.0(
1
)()(
)(
1
)()(
)(
D
D
TThDTTD
TTD
D
D
TThATTA
TTA
13-65
13-75 Liquid nitrogen is stored in a spherical tank this is enclosed by a concentric spherical surface at 273 K. The rate of
vaporization for the liquid nitrogen is to be determined.
Assumptions 1 Steady operating conditions exist. 2 The
surfaces are opaque, diffuse, and gray. 3 Heat transfer by
radiation only.
13-69
1
21
Q
[W]
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
227.9
340.9
453.3
565
676
786.4
896.2
1005
1114
1222
1329
1436
1542
1648
1753
1857
1961
2
21
Q
[W]
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
189.6
202.6
209.7
214.3
217.5
219.8
221.5
222.9
224.1
225
225.8
226.4
227
227.5
227.9
228.3
228.7
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
200
400
600
800
1000
1200
1400
1600
1800
2000
1
Q21 [W]
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
185
190
195
200
205
210
215
220
225
230
2
Q21 [W]
13-70
13-81 Cold fluid stored in a spherical tank enclosed in a concentric outer cover. The gap of the vacuumed enclosure is to
be determined so that the outer surface temperature is not below the dew point.
Assumptions 1 Steady operating conditions exist. 2 The surfaces are opaque, diffuse, and gray. 3 Radiation heat transfer
between the outer surface and the surrounding is negligible.
Properties The emissivity of both surfaces is given to be ε = ε1 = ε2 = 0.6.
m 38.3
)m 3)(6.01(
K)286283)(KW/m3(
K)283278)(K W/m1067.5)(6.0()m 3(
)1(
)(
)(
5.0
2
2
4444282
5.0
2
1
2
4
2
4
1
2
1
2
=
−−
−
−
=
−−
−
−
=
−
D
TTh
TTD
D
m 0.19=
−
=
−
=m
2
338.3
2
12
gap
DD
L
13-74
13-85 A circular grill is considered. The bottom of the grill is covered with hot coal bricks, while the wire mesh on top of the
grill is covered with steaks. The initial rate of radiation heat transfer from coal bricks to the steaks is to be determined for two
cases.
13-75
13-86E Top and side surfaces of a cubical furnace are black, and are maintained at uniform temperatures. Net radiation heat
transfer rate to the base from the top and side surfaces are to be determined.
Assumptions 1 Steady operating conditions exist 2 The surfaces are opaque, diffuse, and gray. 3 Convection heat transfer is
not considered.
Properties The emissivities are given to be
= 0.4 for the bottom surface and 1 for other surfaces.
24428
4
33
22
Btu/h.ft 866,56)R 2400)(R.Btu/h.ft 101714.0(
===
−
TE
b
b
The view factor from the base to the top surface of the cube is
2.0
12 =F
. From the
T3 = 2400 R
3 = 1
13-76
13-87E Prob. 13-86E is reconsidered. The effect of base surface emissivity on the net rates of radiation heat transfer
between the base and the side surfaces, between the base and top surfaces, and to the base surface is to be investigated.
Analysis The problem is solved using EES, and the solution is given below.
"GIVEN"
a=10 [ft]
A_1=a^2
A_2=A_1
A_3=4*a^2
F_12=0.2 "view factor from the base to the top of a cube"
F_11+F_12+F_13=1 "summation rule"
Q_dot_1=Q_dot_21+Q_dot_31
1
31
Q
[Btu/h]
12
Q
[Btu/h]
1
Q
[Btu/h]
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
1.106E+06
1.295E+06
1.483E+06
1.671E+06
1.859E+06
2.047E+06
2.235E+06
2.423E+06
2.612E+06
2.800E+06
636061
589024
541986
494948
447911
400873
353835
306798
259760
212722
470376
705565
940753
1.176E+06
1.411E+06
1.646E+06
1.882E+06
2.117E+06
2.352E+06
2.587E+06
13-78
Radiation Shields and the Radiation Effect
13-88C Radiation heat transfer between two surfaces can be reduced greatly by inserting a thin, high reflectivity(low
emissivity) sheet of material between the two surfaces. Such highly reflective thin plates or shells are known as radiation
13-89C The influence of radiation on heat transfer or temperature of a surface is called the radiation effect. The radiation
13-90C A person who feels fine in a room at a specified temperature may feel chilly in another room at the same temperature
as a result of radiation effect if the walls of second room are at a considerably lower temperature. For example most people
13-80
13-92 Prob. 13-91 is reconsidered. The net rate of radiation heat transfer between the two plates as a function of the
emissivity of the aluminum sheet is to be plotted.
Analysis The problem is solved using EES, and the solution is given below.
"GIVEN"
