Chapter 9, Problem 9.71P

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 $\left(k=0.050\text{W/m}\cdot \text{K}\right)$ having a surface emissivity of $\epsilon =0.60$ , what are the duct wall temperature, the outer surface temperature, and the heat loss per unit length?