That's a loaded question. Depends on the starting temperatures of both the milk and the water in the external vat. Here are some notes from when I was designing that setup. FYI - Based on these calculations, I ended up going with a 6000 watt element to move things along faster. We start with water that is as hot as possible in the vat, not the 100F mentioned in my notes. We also let the milk come up to room temperature around 70F to jump start the process. That is below the threshold where bad bacteria will start to grow. Between 70F and rippening temperature you need to heat quickly and add starter bacteria to outcompete unwanted bacteria. You also need to be VERY careful of lag time/temperature. When your milk is finished heating you will need to quickly drain the external vat or the milk will overheat. Anyway, here are my ramblings. The actual application was implemented differently, but the math is still the same:
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OK it's been way too long since my college physics days so my thermodynamics is a little rusty.
I am designing my milk "vat". I am planning on using a 70 gallon poly stock tank heated with hot water heating elements as my water bath. I will use a 142 quart stainless stockpot with batches of 30 gallons of milk. I will initially fill the tank up manually with hot water say 100F and the milk will be around 40F.
So, thinking out loud, if I fill the tank up to the 65 gallon level after the milk pot is in place. That would be 30 gallons of displacement for the milk and 35 gallons of actual hot water. So the average fluid (water & milk) temperature would be (35/65)x100 + (30/65)x40 = 72.3F. Let's say 72F. I am trying to decide on the size and number of heating elements. The 110 v 1500W elements are easier to deal with for controllers but may not heat fast enough.
It takes one BTU of energy to raise one pound of water, one degree F. Assuming water & milk are both 8.5 lb/gal So 65 gallons x 8.5 = 553 pounds. It will take 553 BTUs to increase 65 gallons by one degree.
For an electric heating element 1 kw/hr = 3413 BTUs. Obviously, this assumes 100% of the energy goes to heating the water and none of it is lost.
A 1.5kw produces 5119 BTUs/hr. So 5119/553 = 9.25 degree rise per hour
From 72F to 90F = 18 degree rise or about 2 hours to heat to rippening temp. Too long
Two 1500w would give 18.5 degrees per hour. One hour for “make ready”, but probably too slow for heating to 125F for thermophilics.
A 4500w would give 27.75 degrees per hour or about 39 minutes to “make ready”.
