Consider a continuous-flow device described below used to pasteurize liquid milk, whose properties approach those of water. Milk at 20°C enters a preheater tube at a volumetric flow rate of 6 L/min. The inner diameter of the tube is 1.5 cm. The tube winds through a steam chest, which heats the milk. The outer tube wall temperature is maintained at 115°C using pressurized steam. Since the thermal conductivity through the metal is high, the temperature difference across the wall is small, so it may be assumed that the inside wall temperature is also at 115°C. The heated milk then enters an adiabatic holding tube, which provides sufficient fluid residence time so that most of the microorganisms in the milk are destroyed at ∼70°C.
a. Develop an energy-balance model to predict the steady-state temperature profile of the milk as it moves down the pipe.
b. Is the milk in turbulent or laminar flow?

c. What are the Prandtl, Nusselt, and Stanton numbers for milk in the pipe? What is the film temperature to be used for estimating thermophysical properties? What is the average heat-transfer coefficient for the milk flowing inside the tube?
d. How long must the tube be to achieve the exit temperature of 70°C?