A small, opaque, diffuse object at Ts 400 K is suspended

Chapter , Problem 12.5

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QUESTION:

A small, opaque, diffuse object at Ts 400 K is suspended in a large furnace whose interior walls are at Tf 2000 K. The walls are diffuse and gray and have an emissivity of 0.20. The spectral, hemispherical emissivity for the surface of the small object is given below. (a) Determine the total emissivity and absorptivity of the surface. (b) Evaluate the reflected radiant flux and the net radiative flux to the surface. (c) What is the spectral emissive power at 2 m? (d) What is the wavelength 1/2 for which one-half of the total radiation emitted by the surface is in the spectral region 1/2? 12.5

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QUESTION:

A small, opaque, diffuse object at Ts 400 K is suspended in a large furnace whose interior walls are at Tf 2000 K. The walls are diffuse and gray and have an emissivity of 0.20. The spectral, hemispherical emissivity for the surface of the small object is given below. (a) Determine the total emissivity and absorptivity of the surface. (b) Evaluate the reflected radiant flux and the net radiative flux to the surface. (c) What is the spectral emissive power at 2 m? (d) What is the wavelength 1/2 for which one-half of the total radiation emitted by the surface is in the spectral region 1/2? 12.5

ANSWER:
% at 0.5 m 25.0% at 1.0 m 25.8% at 1.5 m 24.7% at 2.0 m 11.9% at 2.5 m

a) The total emissivity is: 0.125 + 0.25 + 0.258 + 0.247 + 0.119 = 0.94

The total absorptivity is: 1 - 0.94 = 0.06

b) The reflected radiant flux is given by the Stefan-Boltzmann law:

F = ?T4

Where ? is the emissivity, and T is the temperature. In this problem, ? is the emissivity of the walls at 0.2, and T is the temperature of the walls at 2000 K.

The reflected radiant flux i

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