Hot air flows from a furnace through a 0.15-m-diameter, thin-walled steel duct with a velocity of 3 m/s. The duct passes through the crawlspace of a house, and its uninsulated exterior surface is exposed to quiescent air and surroundings at 0°C.

(a) At a location in the duct for which the mean air temperature is 70°C, determine the heat loss per unit duct length and the duct wall temperature. The duct outer surface has an emissivity of 0.5.

(b) If the duct is wrapped with a 25-mm-thick layer of 85% magnesia insulation (k = 0.050 W/m ∙ K) having a surface emissivity of ε = 0.60, what are the duct wall temperature, the outer surface temperature, and the heat loss per unit length?