Consider the in-line tube bank of Problem \(7.69(D=\) \(10 \mathrm{~mm}, L=1 \mathrm{~m}\), and \(S_{T}=S_{L}=15 \mathrm{~mm}\) ), with condensing steam used to heat atmospheric air entering the tube bank at \(T_{i}=25^{\circ} \mathrm{C}\) and \(V=5 \mathrm{~m} / \mathrm{s}\). In this case, however, the desired outlet temperature, not the number of tube rows, is known. What is the minimum value of \(N_{L}\) needed to achieve an outlet temperature of \(T_{o} \geq\) \(75^{\circ} \mathrm{C}\) ? What is the corresponding pressure drop across the tube bank?

Data From Problem 7.69:-

A preheater involves the use of condensing steam at \(100^{\circ} \mathrm{C}\) on the inside of a bank of tubes to heat air that enters at \(1 \mathrm{~atm}\) and \(25^{\circ} \mathrm{C}\). The air moves at \(5 \mathrm{~m} / \mathrm{s}\) in cross flow over the tubes. Each tube is \(1 \mathrm{~m}\) long and has an outside diameter of \(10 \mathrm{~mm}\). The bank consists of 196 tubes in a square, aligned array for which \(S_{T}=\) \(S_{L}=15 \mathrm{~mm}\). What is the total rate of heat transfer to the air? What is the pressure drop associated with the airflow?