Dry, compressed air at \(T_{m, i}=55^{\circ} \mathrm{C}, p=15 \mathrm{~atm}\), with a mass flow rate of \(\dot{m}=0.05 \mathrm{~kg} / \mathrm{s}\), enters a \(50-\mathrm{mm}-\) diameter, \(2.5-\mathrm{m}\)-long tube whose surface temperature is \(T_{s}=25^{\circ} \mathrm{C}\).

(a) Determine the mean temperature of the air at the tube outlet, the rate of heat transfer from the air to the tube wall, and the power required to flow the air through the tube.

(b) In an effort to reduce the capital cost of the installation it is proposed to use a smaller, 40 -mm-diameter tube. Determine the required tube length and the required power for the smaller tube in order to achieve the same heat transfer rate as for the larger tube.