Applesauce is pasteurized by being heated with 200F (average temp) water from 35F to 170^oF at a rate of 300,000 pounds per hour using a plate heat exchanger (plate size 5 ft X 2ft) and held in the holding tube for 20 sec. The product is then cooled with 0F (average temp) glycol to 35^oF and sent to packaging.

You are requested to consider the suggestion that hot product stream be cooled through regeneration by using it to preheat the incoming raw product prior to pasteurization by reconfiguring and adding more plates to the existing plate heat exchanger.

a. Develop an analytical equation to find the total heat exchanger area and the pressure drop, given a plate spacing and a flow pattern of the plate heat exchanger that will minimize the annualized cost if the process operates at 8,000 hours/year.

Given:

1. Heat capacity of product = 0.9 BTU/(lb. ^oF), 2. Assume temperature effect on viscosity is proportional to water, 3. Cost of utilities: heating = $10.00/106 BTU, cooling = $20.00/106 BTU, electricity= $0.07 KW,

4. Minimum acceptable incremental rate of return = 20 %

5. 10 Year equipment life

6. Straight line depreciation

7. Salvage value 10% of initial cost

8. Income tax rate 25%

9. Capital Gains tax 20%

10. Inflation 3%

11. Assume that total installed cost of heat exchange and pump is 2.5 times the delivered cost.