TABLE OF CONTENTS A furnace firebox is 20 ft (6.1 m) long, 10 ft (3.05 m) wide, and 5 ft (1.5 m) high. Because of a rich fuel-air mixture, all surfaces have become coated with lampblack, so that they all act as black-body surfaces with virtually complete absorption and emittance of radiant energy; emittance 
is 0.97. The furnace is overfired; i.e., its cold surface is the floor, composed of closely spaced tubes flowing water at 250 F (394 K). When the furnace is operating, its roof is at 1150 F (894 K), the sidewalls are at 920 F (766 K), and the end walls at around 800 F (700 K). A plant emergency suddenly shuts the furnace down. Determine the initial rate of heat transfer from each interior surface if the water in the tubes remains at 250 F. Assume that the tube surface is at the water temperature.
1. Analyze the situation to determine the type(s) of heat transfer involved. The temperatures are relatively high and the problem does not involve material flow; it is safe to treat it as a radiation problem. In view of the high emittance, consider the entire enclosure black in a radiation sense. Since all surfaces are black, they absorb all radiation incident upon them, with no reflection. Therefore, the radiant-interchange factors depend only on the geometric relationships among the surfaces. A radiant-interchange factor is the proportionality constant that indicates the fraction of radiant-energy-transfer potential between two surfaces,...
