Air at \(p=1 \mathrm{~atm}\) enters a thin-walled \((D=10-\mathrm{mm}\) diameter) long tube \((L=2 \mathrm{~m})\) at an inlet temperature of \(T_{m, i}=100^{\circ} \mathrm{C}\). A constant heat flux is applied to the air from the tube surface. The air mass flow rate is \(\dot{m}=270 \times 10^{-6} \mathrm{~kg} / \mathrm{s}\).

(a) If the tube surface temperature at the exit is \(T_{s, o}=\) \(160^{\circ} \mathrm{C}\), determine the heat rate entering the tube. Evaluate properties at \(T=400 \mathrm{~K}\).

(b) If the tube length of part (a) were reduced to \(L=\) \(0.2 \mathrm{~m}\), how would flow conditions at the tube exit be affected? Would the value of the heat transfer coefficient at the tube exit be greater than, equal to, or smaller than the heat transfer coefficient for part (a)?

(c) If the flow rate of part (a) were increased by a factor of 10 , would there be a difference in flow conditions at the tube exit? Would the value of the heat transfer coefficient at the tube exit be greater than, equal to, or smaller than the heat transfer coefficient for part (a)?