Water flows at \(0.20 \mathrm{~kg} / \mathrm{s}\) through a thick-walled tube. The inside diameter of the tube is \(25 \mathrm{~mm}\) in diameter and the tube is \(5 \mathrm{~m}\) long. The outside diameter of the tube is \(30 \mathrm{~mm}\) and the tube material has a thermal conductivity, \(k_{w}=12 \mathrm{~W} / \mathrm{m} \mathrm{K}\). The water enters at a temperature of \(25^{\circ} \mathrm{C}\) and hot air flows across the tube at a velocity, \(v_{\infty}=50 \mathrm{~m} / \mathrm{s}\), and a temperature, \(T_{\infty}=250^{\circ} \mathrm{C}\). What is your estimate of the outlet temperature of the water? What is the controlling resistance? To increase the rate of heat transfer substantially, how would you design and/or operate the system differently?