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.