Sciences Thermal III, Spring Semester 2011
Instructor:
Teaching assistants:
Prof. Wojciech Lipiski
Marc Dunham
Krithiga Ganesan
Vivek Ghosh
HOMEWORK 12
Due to May 5, 2011
Problem 1
The spectral distribution of the radiation emitted by a diuse surface may be approximated as
shown in Fig. 1.
Figure 1
Questions:
(a) Calculate the total hemispherical emissive power.
(b) Calculate the total intensity of the radiation emitted in the normal direction.
(c) Calculate the total intensity of the radiation emitted at an angle of 45 from the normal.
(d) Determine the fraction of the emissive power leaving the surface in the directions 30
60 .
Problem 2
A diuse and opaque surface at 1000 K has spectral emissivities of = 0 for 0 2 m, = 0.6
for 2 m 8 m, and = 0.8 for 8 m . A radiative ux of 1000 W m2 , which is
uniformly distributed between 1 and 6 m, is incident on the surface at an angle of 30 (Fig. 2).
Radiation leaving the surface is acquired by a detector. The aperture of the detector is 105 m2 , and
its distance from the surface is 1 m. Consider a surface element of area 104 m2 that is positioned
on-axis the with detector.
Question:
Calculate the total radiative power from the surface element that reaches the detector aperture.
Thermal Sciences III, Spring Semester 2011
Figure 2
Problem 3
An isothermal, diuse-gray, and innitely long equilateral-triangle bar of side a is enclosed by an
isothermal, diuse-gray, and innitely long square duct of side 2a. The temperatures and emissivities
of the bar and the duct are, respectively, T1 = 2900 K, 1 = 0.7, and T2 = 500 K, = 0.9. Assume
uniform radiative heat uxes on each surface.
Questions:
(a) Derive all view factors Fij , where i, j = 1, 2.
(b) Sketch the radiation network.
(c) Calculate the net radiative heat transfer rate per unit length of the enclosure from the bar to
the duct.
Problem 4
Consider enclosures shown in Fig. 3.
Figure 3
Questions:
Calculate the view factors F12 and F21 for:
(a) a sphere of diameter D inside a cubical box of side L = D (three-dimensional geometry),
(b) a diagonal partition with a long square duct (two-dimensional geometry),
(c) two concentric spheres of diameters D1 and D2 = 10D1 (three-dimensional geometry).