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12-74
12-130 A radiation sensor is measuring radiation rate emitted by another surface (A1). The distance at which the sensor is
measuring two-thirds of the radiation rate corresponding to the position of A1 directly under the sensor is to be determined.
Assumptions 1 The surface A1 emits diffusely as a blackbody. 2 Both surface A1 and sensor can be approximated as
2/322
2
2
2
12 )(
LH
rr
r
r
+
−
Note that
2/122 )( LHr +=
12-75
12-76
12-132 The variation of absorptivity of a surface with wavelength is given. The average absorptivity of the surface is to be
Analysis (a) T = 1000 K. The average absorptivity of the surface can be determined from
++)(
2211
-3-2-01
fffT
=
12-133 The variation of absorptivity of a surface with wavelength is given. The surface receives solar radiation at a specified
rate. The solar absorptivity of the surface and the rate of absorption of solar radiation are to be determined.
Analysis For solar radiation, T = 5800 K. The solar
0.5456=
The rate of absorption of solar radiation is determined from
2
absorbed IE
, m
0.3
1.2
0.70
0.15
0
, m
0.3
1.2
0.15
0
12-77
12-78
12-135 The spectral transmissivity of a glass cover used in a solar collector is given. Solar radiation is incident on the
Analysis (a) For solar radiation, T = 5800 K. The average transmissivity of the surface can be determined from
)1(+)(+)( 2121 321
ffffT −−=
2
W/m808.5=== ) W/m950(851.0 2
plate abs. IE
(b) For radiation emitted by the absorber plate, we take T = 300 K, and calculate the transmissivity as follows:
0.0mK 90=K) m)(300 3.0(
1
1
=⎯→⎯=
λ
fT
roomsolarwater IQ
0.9
12-79
12-136 In a configuration involving a small opaque surface A1 and a radiation sensor, the rate at which radiation emitted from
A1 that is intercepted by the sensor is to be determined.
Assumptions 1 Surface A1 is an opaque, diffuse emitter and reflector. 2 Both A1 and A2 can be approximated as differential
surfaces since both are very small compared to the square of the distance between them.
12-80
12-81
12-138 A horizontal opaque flat plate is well insulated on the edges and the lower surface is experiencing irradiation and heat
loss by convection. The absorptivity, reflectivity, and emissivity of the plate are to be determined.
Assumptions 1 Steady operating condition exists. 2 The plate has a uniform temperature. 3 The plate is well insulated on the
edges and the lower surface.
Analysis The irradiation on the plate is
2
W5000 ==G
0.80=== 2
2
abs
W/m1000
W/m800
G
G
0.20=−= 80.01
Finally, the emissivity of the plate is
2
W/m700
E
E
12-82
12-83
12-142 A surface absorbs 10% of radiation at wavelengths less than 3 m and 50% of radiation at wavelengths greater than 3
m. The average absorptivity of this surface for radiation emitted by a source at 3000 K is
Abs2=0.5
F1=0.890029 "The radiation fraction corresponding to lamda-T = 9000, from Table 12-2"
Abs =F1*Abs1+(1-F1)*Abs2
12-143 A surface at 300oC has an emissivity of 0.7 in the wavelength range of 0-4.4 m and 0.3 over the rest of the
wavelength range. At a temperature of 300oC, 19 percent of the blackbody emissive power is in wavelength range up to 4.4
e1=0.7
12-84
12-144 Consider a 4-cm-diameter and 6-cm-long cylindrical rod at 1200 K. If the emissivity of the rod surface is 0.75, the
total amount of radiation emitted by all surfaces of the rod in 20 min is
L=0.06 [m]
T=1200 [K]
epsilon=0.75
time=20*60 [s]
12-145 Solar radiation is incident on a semi-transparent body at a rate of 500 W/m2. If 150 W/m2 of this incident radiation is
reflected back and 225 W/m2 is transmitted across the body, the absorptivity of the body is
(a) 0 (b) 0.25 (c) 0.30 (d) 0.45 (e) 1
Answer (b) 0.25
12-85
12-146 Solar radiation is incident on an opaque surface at a rate of 400 W/m2. The emissivity of the surface is 0.65 and the
absorptivity to solar radiation is 0.85. The convection coefficient between the surface and the environment at 25ºC is 6
W/m2ºC. If the surface is exposed to atmosphere with an effective sky temperature of 250 K, the equilibrium temperature of
the surface is
(a) 281 K (b) 298 K (c) 303 K (d) 317 K (e) 339 K
12-86
