An insulated, thin walled tube, \(60 \mathrm{~m}\) long and \(25 \mathrm{~mm}\) inside diameter, is to deliver \(65^{\circ} \mathrm{C}\) hot water to a house. The water enters the tube at \(70^{\circ} \mathrm{C}\) and at a flow rate of \(0.25 \mathrm{~kg} / \mathrm{s}\). The ambient air temperature in the house is \(15^{\circ} \mathrm{C}\) and the air flows over the tube at a velocity of \(15 \mathrm{~m} / \mathrm{s}\). The insulation thickness is \(25 \mathrm{~mm}\).

a. What are the inside and outside convective heat transfer coefficients, \(h_{i}\) and \(h_{o}\) ?

b. What is the magnitude of the overall resistance to heat transfer, 1/UA?

c. What is the rate of heat loss per unit length of tubing at the entrance?

d. Do we have enough to meet the specification? Prove your answer.