A tube bank uses an aligned arrangement of \(15-\mathrm{mm}-\) diameter tubes with \(S_{T}=S_{L}=30 \mathrm{~mm}\). There are 10 rows of tubes with 50 tubes in each row. Consider an application for which cold water flows through the tubes, maintaining the outer surface temperature at \(40^{\circ} \mathrm{C}\), while flue gases at \(427^{\circ} \mathrm{C}\) and a velocity of \(5 \mathrm{~m} / \mathrm{s}\) are in cross flow over the tubes. The properties of the flue gas may be approximated as those of atmospheric air at \(427^{\circ} \mathrm{C}\). What is the total rate of heat transfer per unit length of the tubes in the bank?