For the conditions of Problem 8.70, how long must the annulus be if the water flow rate is \(0.35 \mathrm{~kg} / \mathrm{s}\) instead of \(0.02 \mathrm{~kg} / \mathrm{s}\) ?

Data From Problem 8.70:-

Water at \(\dot{m}=0.02 \mathrm{~kg} / \mathrm{s}\) and \(T_{m, i}=20^{\circ} \mathrm{C}\) enters an annular region formed by an inner tube of diameter \(D_{i}=25 \mathrm{~mm}\) and an outer tube of diameter \(D_{o}=100 \mathrm{~mm}\). Saturated steam flows through the inner tube, maintaining its surface at a uniform temperature of \(T_{s, i}=100^{\circ} \mathrm{C}\), while the outer surface of the outer tube is well insulated. If fully developed conditions may be assumed throughout the annulus, how long must the system be to provide an outlet water temperature of \(75^{\circ} \mathrm{C}\) ? What is the heat flux from the inner tube at the outlet?