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5. Determine the fraction of the radiation leaving the base of the cylindrical enclosure shown attached that escapes through a coaxial ring opening at its top surface. The radius and the length of the enclosure are r_1 = 10cm and L = 10cm, while the inner and outer radii of the ring are r_2 = 5 cm and r_3 = 8cm, respectively.
Assumption: The base surface is a diffuse emitter and reflector.

6. Consider the 5m x 5m x 5m cubical furnace, whose surfaces closely approximate black surfaces. The base (1), top (2) and side surfaces (3) of the furnace are maintained at uniform temperatures of 800 K, 1500 K and 500 K, respectively.

Determine

a) the net rate of radiation heat transfer between the base and the side surfaces,
b) the net rate of radiation heat transfer between the base and the top surface,
c) the net radiation heat transfer from the base surface.