An annular fin of thickness t is used as a radiator to

Chapter , Problem 12.133

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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 GS. 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 ri , 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(ri ) Tb 400 K and the fin efficiency is 100%, what is the rate of heat dissipation for a fin of radius ro 0.5 m? Consider two cases, one for which the radiator is exposed to the sun with GS 1000 W/m2 and the other with no exposure (GS 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. 12.