Dry, compressed air at \(T_{m, i}=75^{\circ} \mathrm{C}, p=10 \mathrm{~atm}\), with a mass flow rate of \(\dot{m}=0.001 \mathrm{~kg} / \mathrm{s}\), enters a \(30-\mathrm{mm}-\) diameter, 5 -m-long tube whose surface is at \(T_{s}=25^{\circ} \mathrm{C}\).

(a) Determine the thermal entry length, 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. For these conditions the fully developed heat transfer coefficient is \(h=3.58 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\).

(b) In an effort to reduce the capital cost of the installation it is proposed to use a smaller, \(28-\mathrm{mm}\) diameter tube. Determine the thermal entry length, the mean temperature of the air at the tube outlet, the heat transfer rate, and the required power for the smaller tube. For laminar flow conditions it is known that the value of the fully developed heat transfer coefficient is inversely proportional to the tube diameter.