A small furnace consists of a cylindrical, black-walled enclosure, 20 cm long and with a diameter of 10 cm. The bottom surface is electrically heated to 1500K, while the cylindrical sidewall is insulated. The top plate is exposed to the environment, such that its temperature is 500K. In class, this problem was discussed by treating the sidewall as one single zone.

(a) Estimate the heating requirements for the bottom wall, and the temperature of the cylindrical sidewall by treating the sidewall as two equal rings of 10 cm height each.

( b) Compare the solution with the one for the sidewall treated as one single zone.

(c) Make qualitative statements about sidewall temperatures and heating requirements if the sidewall would be separated in more segments.

(d) If the sidewall were treated as a single segment but were gray with an emissivity of ε ₂= 0.7 while bottom and top surface remain black, how would that change the solution discussed in class for a completely black cavity?

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