Engine oil at a rate of \(0.05 \mathrm{~kg} / \mathrm{s}\) flows through a \(3 \mathrm{~mm}\) diameter tube that is \(30 \mathrm{~m}\) long. The oil has an inlet temperature of \(40^{\circ} \mathrm{C}\) while the tube wall temperature is maintained at \(100^{\circ} \mathrm{C}\) by steam condensing on its outer surface.

a. Estimate the average heat transfer coefficient for internal flow of the oil.

b. Determine the outlet temperature of the oil.