978-0073398198 Chapter 12 Part 3

subject Type Homework Help
subject Pages 14
subject Words 1775
subject Authors Afshin Ghajar, Yunus Cengel

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page-pf1
12-41
page-pf2
12-42
12-71 A radiometer is used to monitor the surface temperature of a stainless steel sheet. The surface temperature of the
sheet is to be determined from the irradiation measured by the radiometer and whether it complies with the ASME Code for
Process Piping.
Assumptions 1 The sheet surface is gray and diffuse. 2 Irradiation on the surface of the sheet from the surroundings is
negligible. 3 Both target surface and radiometer can be approximated as differential surfaces since both are very small
page-pf3
12-43
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12-44
12-77E A spherical ball emits radiation at a certain rate. The average emissivity of the ball is to be determined at the given
temperature.
R) 950)(RBtu/h.ft 10)(0.1714ft (0.5454
TA
12-78 A radiation sensor (A2) is placed normal to the direction of viewing from another surface (A1). An optical filter with
specified spectral transmissivity is placed in front of the sensor. The irradiation that is measured by the sensor is to be
Km 2000)K 1000)(m 2(
1==
T
Hence, the transmissivity of the optical filter is
4666.0)066728.01(5.0)066728.0(0)1()( 11 21 =+=+=
ff
2
22
2
2,
12
cos
L
A
L
An
=
and
4
1
1
1
)( T
TE
Ib==
Since the radiation sensor is placed normal to the direction of viewing from A1, we have θ1 = θ2 = 0°, hence
21
4
1
AAT
Ball
T=950 R
D = 5 in
page-pf5
12-45
page-pf6
12-46
12-80 The variation of transmissivity of the glass window of a furnace at a specified temperature with wavelength is given.
The fraction and the rate of radiation coming from the furnace and transmitted through the window are to be determined.
through the window is
0.2825=
+=
)1()( 21
ffT
Then the rate of radiation coming from the furnace and transmitted
12-81 The variation of emissivity of a surface at a specified temperature with wavelength is given. The average emissivity of
the surface and its emissive power are to be determined.
Analysis The average emissivity of the surface can be determined from
)1(+)(+
++
)()(
)(
)(
2121
2211
2
2
1
1
321
-3-2-01
4
3
4
2
4
0
1
ffff
fff
T
dTE
T
dTE
T
dTE
T
bb
b
=
=
++=
where
f f
 
1 2
and
are blackbody radiation functions corresponding to
TT 21 and
, determined from
273232.0mK 3000=K) m)(1000 3(
1
1
==
λ
fT
0.7
0.4
0.3
page-pf7
12-47
12-82 The spectral emissivity for an ASTM A240 410S stainless steel plate is given. The highest rate of radiation
emission that the plate can achieve without exceeding the maximum use temperature specified by the ASME code is to be
determined.
Assumptions 1 The plate is diffuse. 2 Uniform surface temperature.
Analysis The average emissivity of the plate surface can be determined from
𝜆1
𝜆2
page-pf8
12-48
page-pf9
12-49
12-84 The variation of emissivity of a tungsten filament with wavelength is given. The average emissivity, absorptivity, and
reflectivity of the filament are to be determined for two temperatures.
Analysis (a) T = 1500 K
013754.0mK 1500=K) m)(1500 1( 1
1== λ
fT
The average emissivity of this surface is
0.155=
+=
+=
)013754.01)(15.0()013754.0)(5.0(
)1()( 11 21
ffT
From Kirchhoff’s law,
and
0.845====+ 155.0111
(b) T = 2500 K
0.207==
(at 2500 K)
and
0.793====+ 207.0111
, m
1
0.5
0.15
page-pfa
12-50
page-pfb
12-51
page-pfc
12-52
12-88 The variation of reflectivity of a surface with wavelength is given. The average reflectivity, emissivity, and
absorptivity of the surface are to be determined for two source temperatures.
Analysis The average reflectivity of this surface for solar
0.362=
+=
+=
+=
)978746.01)(95.0()978746.0)(35.0(
)1(
)()()(
11
11
21
201
ff
TfTfT
Noting that this is an opaque surface,
0=
At T = 5800 K:
0.638====+ 362.0111
s
, m
3
0.95
0.35
page-pfd
12-53
page-pfe
12-54
12-90 The variation of transmissivity of a glass is given. The average transmissivity of the pane at two temperatures and the
amount of solar radiation transmitted through the pane are to be determined.
Analysis For T=5800 K:
mK 1740=K) m)(5800 3.0(
11
=
T
page-pff
12-55
12-92 An opaque horizontal plate that is well insulated on the edges and the lower surface experiences irradiation, the total
emissivity and absorptivity of the plate are to be determined.
page-pf10
12-56
12-94 An opaque horizontal plate that is well insulated on the edges and the lower surface is uniformly irradiated from above,
(a) the irradiation on the plate, (b) the total reflectivity of the plate, (c) the emissive power of the plate, and (d) the total
emissivity of the plate are to be determined.
Assumptions 1 The plate has a uniform temperature. 2 The plate is well insulated on the edges and the lower surface.
0.60== 040.01
(c) The emissive power of the plate is
GEGEJ
+=+= ref
GJE
=
2
page-pf11
12-57
page-pf12
12-58
12-96 A horizontal non-opaque plate is experiencing uniform irradiation on the both upper and lower surfaces. The
irradiation and emissivity of the plate are to be determined.
Assumptions 1 Steady operating condition exists. 2 The plate has a uniform temperature. 3 The convection heat transfer
coefficient is uniform.
Properties The absorptivity of the plate is given to be 0.527.
0.525=
=
4428
2
4
)K 390()K W/m1067.5(
W/m]7000)527.01(4000[
s
T
Discussion Since α ε ≈ 0.53, the plate can be considered as a gray surface.
page-pf13
12-59
page-pf14
12-60
Atmospheric and Solar Radiation
12-98C The reason for different seasons is the tilt of the earth which causes the solar radiation to travel through a longer path
12-99C Because of different wavelengths of solar radiation and radiation originating from surrounding bodies, the surfaces
12-100C There is heat loss from both sides of the bridge (top and bottom surfaces of the bridge) which reduces temperature
12-101C The amount of solar radiation incident on earth will decrease by a factor of
5762
4
4
sun
T

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