A cooling drum consists of a (horizontally) rotating, large stainless steel cylinder. The cylinder has a diameter D and a width of W. The cooling at the inside of the drum is so effective that the outside temperature is homogeneous and constant at T °C.

This drum is used to produce a foil of X mm thick (and Y m wide) out of a polymer mixture. The mixture is distributed over the whole width onto the drum and removed as a foil after half a revolution. The mixture is at a temperature of T1 °C and has a density of M kg/m3, a heat capacity of H J / kg K and a heat conductivity of Q W / m K.

Using a rotation frequency of K Hz, the foil is cooled down sufficiently for further processing. The surroundings are at T2 °C.

Consider melting heat to be incorporated in the specific heat given

Assume that the polymer layer is flat and horizontal

The highest temperature in the foil at removal is a prerequisite.

a. Make a schematic drawing of the process

b. Make a complete list of relevant physical quantities (symbol, dimension, description)

c. Calculate the production rate of foil (kg/s and linear metre per second)

d. Determine the temperature profile in the foil at the moment of removal.

e. Estimate the amount of heat removed by the cooling water and via the top surface to the surroundings. What do you conclude?

Now the production is to be doubled and one considers the following possibilities:

1. Double rotation frequency

2. Double thickness of foil

3. Double external drum diameter

4. Double drum width

f. What are the consequences of each measure (apart) for the process (in terms of production rate, critical temperature and other process variables). Use the method of scaling factors.

g. How would you advise to scale up the process? (in the same terms)