A furnace is constructed in three sections, which include insulated circular (2) and cylindrical (3) sections, as well as an intermediate cylindrical section (1) with imbedded electrical resistance heaters. The overall length and diameter are 200 mm and 100 mm, respectively, and the cylindrical sections are of equal length. The surroundings are at 0 K.

(a) If all the surfaces are black, determine the electrical power, q I' required to maintain the heated section at 1000 K.

(b) What are the temperatures of the insulated sections, T₂ and T₃?

(c) For D = 100 mm, generate a plot of q_l, T₂, and T₃ as functions of the length-to-diameter ratio, with 1 L/D 5.

A2