An annular fin of thickness t is used as a radiator to dissipate heat for a space power system. The fin is insulated on the bottom and may be exposed to solar irradiation G s . The fin is coated with a diffuse, spectrally selective material whose spectral reflectivity is specified Heat is conducted to the fin through a solid rod of radius r , and the exposed upper surface of the fin radiates to free space, which is essentially at absolute zero temperature. (a) If conduction through the rod maintains a fin base temperature of T ( r i ) = T b = 400 k and the fin efficiency is 100%, what is the rate of heat dissipation for a fin of radius r o = 0.5 m ? Consider two cases, one for which the radiator is exposed to the sun with G s = 1000 W/m 2 and the other with no exposure ( G s = 0 ) . (b) In practice, the fin efficiency will be less than 100% and its temperature will decrease with increasing radius. Beginning with an appropriate control volume, derive the differential equation that determines the steady-state, radial temperature distribution in the fin. Specify appropriate boundary conditions.
An annular fin of thickness t is used as a radiator to dissipate heat for a space power system. The fin is insulated on the bottom and may be exposed to solar irradiation G s . The fin is coated with a diffuse, spectrally selective material whose spectral reflectivity is specified Heat is conducted to the fin through a solid rod of radius r , and the exposed upper surface of the fin radiates to free space, which is essentially at absolute zero temperature. (a) If conduction through the rod maintains a fin base temperature of T ( r i ) = T b = 400 k and the fin efficiency is 100%, what is the rate of heat dissipation for a fin of radius r o = 0.5 m ? Consider two cases, one for which the radiator is exposed to the sun with G s = 1000 W/m 2 and the other with no exposure ( G s = 0 ) . (b) In practice, the fin efficiency will be less than 100% and its temperature will decrease with increasing radius. Beginning with an appropriate control volume, derive the differential equation that determines the steady-state, radial temperature distribution in the fin. Specify appropriate boundary conditions.
Solution Summary: The author explains the rate of heat dissipation for a fin if radiator is exposed to the sun with solar radiation.
An annular fin of thickness t is used as a radiator to dissipate heat for a space power system. The fin is insulated on the bottom and may be exposed to solar irradiation
G
s
. The fin is coated with a diffuse, spectrally selective material whose spectral reflectivity is specified
Heat is conducted to the fin through a solid rod of radius
r
, and the exposed upper surface of the fin radiates to free space, which is essentially at absolute zero temperature.
(a) If conduction through the rod maintains a fin base temperature of
T
(
r
i
)
=
T
b
=
400
k
and the fin efficiency is 100%, what is the rate of heat dissipation for a fin of radius
r
o
=
0.5
m
? Consider two cases, one for which the radiator is exposed to the sun with
G
s
=
1000
W/m
2
and the other with no exposure
(
G
s
=
0
)
.
(b) In practice, the fin efficiency will be less than 100% and its temperature will decrease with increasing radius. Beginning with an appropriate control volume, derive the differential equation that determines the steady-state, radial temperature distribution in the fin. Specify appropriate boundary conditions.
An engineered passive radiative cooler coating is placed under the Sun. Provided the following simplified spectral emissivity/absorptivity plot below, calculate the total diffuse emissivity and absorptivity if its uniform surface temperature is a Ts=20°C. Assume the Sun's irradiation onk Earth is Gsun=1380 W/m2 and its blackbody temperature is Tsun= 5800K. Ignore the radiation from the atmosphere (surroundings).
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