Pasteurization and Preheating: Calculating Heat Transfer Rates and Cooling Duty

[tweety1234]

Homework Statement

Milk is pasteurised by heating it to 72C for 15 seconds. The hot pasteurised milk
is cooled by using it to preheat incoming cool milk. Milk enters a pasteurising system at 2C and a flow rate of 3000 litres per hour The incoming milk enters a preheating plate heat exchanger, then flows to a second plate heat exchanger where
it is heated to $$72^{0} C$$ using hot water at an initial temperature of 95C and
flow rate of 2200 litres per hour . The hot milk is returned on the hot side of the preheating
plate heat exchanger, where it is cooled to 10C.
Ignoring any heat losses, and assuming heat capacity does not change signicantly
with temperature, calculate:
(a) the temperature of the milk exiting the preheater,
(b) the exit temperature of the hot water,
(c) the heat transfer rate across the rst and second heat exchangers,
(d) the cooling duty (in kW) required to bring the pasteurised milk to a final
temperature of 4C.

I have drawn a diagram for this question, can someone please check it and tell me if it is correct? Also I need help working out the temperature of the milk coming out of the pre heater,

I know i have to use Q = mct
Heat capacity of water $$4.21 KJ kg^{-1} K^{-1}$$
Heat capacity of milk $$3.92 kJ kg^{-1} K^{-1}$$
Density of water $$961 kg m^{-3}$$

Density of milk $$990 kg m^{-3}$$^[-3

 

[tweety1234]

Can someone please let me know If I am doing this correctly? I have used the density given to calculate the mass of milk, going into the feed. which I also use to calculate the energy content of the milk.

$$Q = m \\\ C_{p} \deta T$$the energy content of milk going into the pre-heater $$= 2^{o}C \times 2970kg \times 3.92 KJ kg^{-1} K^{-1}$$

And I can also work out the energy content of the water, but how does I use this work out the temperature of the milk coming out of the pre-heater?

Also do I have to change my temperatures to kelvin, in the energy calculation? Because as I understand it, a change in 1C = 1K , and in the equation we are using delta T. Could someone clarify?

thank you.