Since the cistern is an isolated source without regular makeup water, you have to think of the problem as a shell and tube heat exchanger
q= M Cp Dt Where
Q = specific heat of water 4.18
M = mass flow rate pumped water in lbs mass per hour in this case 5 gpm x 60 minutes =300 gph x 8.34 lbs/gal=2502 lbs mass/hour or 60048 lbs mass per day
Cp= specific heat 4.18 divided by Delta temp Dt inlet and outlet of heat exchanger
Dt= T2 - T1 outlet - inlet of heat exchanger
1 BTU is the energy to raise 1 lb mass of water 1 degreee
Its easier to convert to lb/mass per hour simply because thats the way I learned it many years ago. You need to make some assumptions too. Without the heat being added to the cistern water being removed the differential temps are a moving target and the efficiency of the heat exchanger is not 100% due to tube fouling and other stuff.
Further as the concrete container acts as an insulator temp in the heat sink cistern will gradually increase.
After 1 day or 7200 gallons pump throughput you should begin to see a temp increase depending on system efficicency.
7200 gallons is a pretty big cistern and thats just 1 day at 5 gallons a minute.
Also you're going to see a higher dewpoint as temperatures rise under the house in that space leading to all sorts of nasty molds and maybe rot.
Cooling water requires treatment. Bleach maybe? I don't know, I didn't work in chemistry. we used sulphuric acid and other stuff location dependent.
Bottom line line is it would work at least for while until your heat sink became elevated in temperature or what I would call saturated. Then use it in the winter for heat I guess. LOL
I just don't think your heat sink is big enough for it to last a long time.
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