Water, initially at \(25^{\circ} \mathrm{C}\), is slowly flowing through a \(1 \mathrm{~cm}\) diameter tube whose wall temperature remains constant at \(-10^{\circ} \mathrm{C}\). The water velocity is \(0.1 \mathrm{~m} / \mathrm{s}\).

a. Assuming fully developed profiles, how far from the inlet of the tube will the mean temperature of the water reach its freezing point?

b. Once the mean temperature has reached its freezing point, estimate how much ice can we form per unit length of tube? What assumptions do you need to make?