Fermenter heat transfer area
The following calculation is based on a simple cylinder. A jacket would transfer heat through
the sides and sometimes through the bottom as well.
Note how the ratio of fermenter volume to area that could be jacketed
increases as the tank size increases.
Another way to look at this is that area depends on dimensions squared
while volume depends on dimensions cubed.
Small tanks have plenty of heat transfer area, but large tanks do not.
The usual way to obtain sufficient area for heat transfer is with coils.