Certain wood stove designs rely exclusively on heat transfer by radiation and natural convection to the surroundings. Consider a stove that forms a cubical enclosure, Ls = 1 m on a side, in a large room. The exterior walls of the stove have an emissivity of ε = 0.8 and are at an operating temperature of Ts,s = 500 K.

The stove pipe, which may be assumed to be isothermal at an operating temperature of Ts,p = 400 K, has a diameter of Dp = 0.25 m and a height of Lp = 2m, extending from stove to ceiling. The stove is in a large room whose air and walls are at T∞ = Tsur = 300 K. Neglecting heat transfer from the small horizontal section of the pipe and radiation exchange between the pipe and stove, estimate the rate at which heat is transferred from the stove and pipe to the surroundings.

Quiescent air, T. Sur T.