Ihave a water bath that is 3'h x 3'w x 10'l. with water flowing through the water bath (lengthwise) i need to change the water temperature from 10˚c to 40˚c and then back to 10˚c again in 3 complete cycles. so 10-40-10-40-10-30 (it ends at 30˚c).

ideally the process can be completed in 10 min there are 3 water tanks, one at 80˚c, one at 10˚c, and one buffer tank to be used to recycle as much of the warmest water as possible. the buffer tank and the hot water tank will alternate after each use as the recycled water will be heated back up to 80˚c. the water blends the hot and cold water tanks to supply the water temperatures required between 11˚c and 40˚c.

i have 3 questions:

1) what volume do i require the hot and cold water tanks to hold?
2) what flow rate would be required to achieve these temperature changes over a 10 min interval?
3) how much water will not be able to be recycled in each full cycle?