Compressed air at \(p=20\) atm enters a \(20-\mathrm{mm}\) diameter tube at \(T_{m, i}=20^{\circ} \mathrm{C}\) and a mass flow rate of \(\dot{m}=6 \times 10^{-4} \mathrm{~kg} / \mathrm{s}\). The air is warmed by a constant surface heat flux so that its exit mean temperature is \(T_{m, o}=50^{\circ} \mathrm{C}\). Determine the required surface heat flux and the temperature of the tube wall at the tube exit for \(L=0.15,1.5\), and \(15 \mathrm{~m}\).