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Then you're not understanding what people are saying. The idea is that you have a closed loop between both tanks - with coils in both tanks. Of course the coil in the smaller tank will be 'smaller'.The copper coil is in the big tank only What better way to get perfect mixing then to just mix the cold water with the warm water...
I.e. - no water is 'mixing'. The cold water from the big tank is sent (via copper tube) to the small tank - where another copper coil cools the water in the small tank - then that same tube is emptied back into the big tank. You only have 1 pump. and one 'tube' - Of course the part of the tube exposed to air needs to be well insulated.