Aregenerator is used to preheat milk before it is pasteurized. the regenerator is a shell-and-tube heat exchanger with one shell pass and two tube passes. cold milk enters the regenerator at a temperature of 10oc and hot milk, which has recently completed the pasteurization process, enters at 75oc. after leaving the regenerator, the heated milk enters a second heat exchanger that further raises its temperture to 75oc. this system is used in a pasteurization process in which the flow rate of the milk is 7.5 kg/s. the manufacturer of the heat exchanger specifies that for this flow rate, the overall heat transfer coefficient is 2500 w/m2-k. use the properties of water for the milk. if an effectiveness of 0.5 is desired, find

(a) the required heat transfer area

(b) the rate of heat recovery

(c) the fluid outlet temperatures

the hot fluid in the secondary heat exchanger derives its energy from the combustion of natural gas, and the burner has an efficiency of 95%. the facility operates continuously and the cost of natural gas is $0.010/mj.

(d) what is the annual savings in energy associated with the use of the regenerator.