Page 250 - Modelling in Transport Phenomena A Conceptual Approach

230 CHAPTER 7. UNSTEADY-STATE MACROSCOPIC BALANCES

One way of cooling the beer is obviously putting it into a freezer. However, your
friend insists that placing a can of beer in a pot in the kitchen sink, and letting
cold water run over it into the pot and then into the sink shortens the cooling time.
He claims that the overall heat transfer coefficient for this process is much greater
than that for a can of beer sitting idly in the freezer in still air. He supports this
idea by presenting the following data of Horwitz (1981):

freezer Tap Water
Cooling medium temperature ( "C) - 21 13
Initial temperature of beer ("C) 29 29
Final temperature of beer ("C) 15 15
Time elapsed (min) 21.1 8.6
Surface area of can = 0.03m2
Quantity of beer in can = 0.355 kg
Heat capacity of beer = 4.2 kJ/ kg. K

a) Do you think that your friend is right? Show your work by calculating the heat
transfer coefficient in each case. Ignore the cost and availability of water.

b) Calculate the time required to cool the beer from 29°C to 4°C in the freezer.
c) Suppose that you first cool the beer to 15°C by the running water and then
place the beer in the freezer. Calculate the time required to cool the beer from
29 "C to 4°C in this case.
(Answer: a) (h) (freezer) = 12.9W/m2.K, (h) (tap water) = 200W/m2.K
b) 44.5min c) 32min)

7.16 M kg of a liquid is to be heated from TI to T2 in a well stirred, jacketed
tank by steam condensing at T, in the jacket. The heat transfer area, A, the
heat capacity of tank contents per unit mass, 6'p, and the overall heat transfer
coefficient, U, axe known. Show that the required heating time is given by

Indicate the assumptions involved in the derivation of Eq. (1).

7.17 In Problem 7.16, assume that hot water, with a constant mass flow rate m
and inlet temperature Tin, is used as a heating medium instead of steam.
is
a) Show that the outlet temperature of hot water, Tout, given by