Complicated problem for pasteurization

[kriskkk]

So I'm finishing my set up and I am installing 2 rectangular stainless steel tanks (filled with water) attached with coils to preheat and then pasteurize my semi-sweet cider bottles.
The first tank will be at around 45 degrees Celsius and the second one at around 75C.
Calculating the PUs onces the bottles are at the right temperature will not be that difficult and the coils will turn on and off to keep the temperatures at the required degrees since once i submerge the bottles, the water in the tanks will lose heat.
The biggest question, (since I am filling the bottles at around 4 degrees Celcius) is how can I calculate the time it will take for the cider in the bottles to reach that temperature of , let's say 65-68 C.
Is there a formula that can give me the required time to reach a certain target temperature (for the cider) or even an estimate once the bottles are in those tanks?
My thermodynamics laws are a bit rusty and I can't seem to find an equation that gives me the time required, assuming that the water in the tanks will remain almost constant since the coils will turn back on every time the water loses it's target temperature.
Thanks for the help!

 

[Vale71]

Place a test bottle in the bath, uncork it, stick a thermometer probe in it and start measuring.
Calculating the time is really hard as the size, shape and wall thickness of the bottle will all have a difficult to predict effect on heat transfer.

 

[kriskkk]

Place a test bottle in the bath, uncork it, stick a thermometer probe in it and start measuring.
Calculating the time is really hard as the size, shape and wall thickness of the bottle will have a difficult to predict effect on heat transfer.

The issue is that I want to determine the final size of the stainless steel bath to see how many bottles I want to submerge at a time/
If i have 2,000 bottles to pasteurize on a given day, should I build a 50X50 or 1mX1m tank to fulfill the 2,000 bottles within 12 hours for example.
I can't do a home test since the coils will have sensors to reheat to the water at target temperature once the bottles are submerged.

 

[Vale71]

I was going to say "Use your mash tun to run a simulation" but then I realized you don't have to own one if you're only doing cider...
Can't you rig something up for a test? It doesn't need to able able to hold more than the one test bottle, the important thing is it can hold the set temperature.

 

[ajdelange]

A big factor in the time required is how fast you want to warm up. You can set up a bath at the desired limit temperature, immerse the bottles in that and wait forever fot them to come to exactly that temperature but knowing that they will never get hotter or you can plunge them into boiling water and see them go to the desired temperature much faster and then sail right past that to approach boiling assymptotically.

I'd suggest putting a large pot of water on the stove, boiling it, lowering a bottle of the cider into that and recording temperature rise over time. From the resulting curve you ought to be able to deduce the thermal mass and thermal conductivity of a bottle and from that determine how long it will take to warm a bottle to a desired temperature in a bath at another (higher) temperature.