A long, uninsulated steam line with a diameter of \(100 \mathrm{~mm}\) and a surface emissivity of 0.8 transports steam at \(150^{\circ} \mathrm{C}\) and is exposed to atmospheric air and large surroundings at an equivalent temperature of \(20^{\circ} \mathrm{C}\).

(a) Calculate the rate of heat loss per unit length for a calm day.

(b) Calculate the rate of heat loss on a breezy day when the wind speed is \(8 \mathrm{~m} / \mathrm{s}\).

(c) For the conditions of part (a), calculate the rate of heat loss with a 20-mm-thick layer of insulation ( \(k=\) \(0.08 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\). Would the heat loss change significantly with an appreciable wind speed?