A thin-walled tube with a diameter of \(12 \mathrm{~mm}\) and length of \(25 \mathrm{~m}\) is used to carry exhaust gas from a smoke stack to the laboratory in a nearby building for analysis. The gas enters the tube at \(200^{\circ} \mathrm{C}\) and with a mass flow rate of \(0.006 \mathrm{~kg} / \mathrm{s}\). Autumn winds at a temperature of \(15^{\circ} \mathrm{C}\) blow directly across the tube at a velocity of \(2.5 \mathrm{~m} / \mathrm{s}\). Assume the thermophysical properties of the exhaust gas are those of air.

(a) Estimate the average heat transfer coefficient for the exhaust gas flowing inside the tube.

(b) Estimate the heat transfer coefficient for the air flowing across the outside of the tube.

(c) Estimate the overall heat transfer coefficient \(U\) and the temperature of the exhaust gas when it reaches the laboratory.