Fundamentals of Heat and Mass Transfer
Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470501979
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
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Chapter 12, Problem 12.133P

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

Chapter 12, Problem 12.133P, An annular fin of thickness t is used as a radiator to dissipate heat for a space power system. The

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.

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Chapter 12 Solutions

Fundamentals of Heat and Mass Transfer

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