Thought I'd show one graph based on the more sophisticated model to give insight as to what the effects of finite 'conduction', the production of heat by yeast and the differences in fermenter material might be expected to make. These results are from running an imperfect model and as such should be used to gain insight, not predict actual behavior of real systems.
The assumptions are:
1) 20L Wort in full fermentation at temp 30 °C is placed in a cylindrical fermenter at time t = 0
2) The fermentation produces 0.5 watts/L i.e. 10 watts total heat
3) The volume of the wort in the fermenter has height equal to 3 times its radius
4) The glass fermenter walls are 3 mm thick and the glass has conductivity of 0.58 W/m-K
5) The stainless steel fermenter walls are 1.5 mm thick and the metal has conductivity 80 times that of glass.
6) There is no conduction through the bottom of the fermenter
7) The fermenters sit in a constant temperature water bath at 20°C
8) The thermal coupling between portions of the volume of fermenting beer are 10 times that of conductive coupling alone. This increase is assumed to be due to convection.
The graph shows the temperatures at thee points in the fermenting wort volume
1) On the axis i.e. at the center of the fermenter
2) At the distance from the center which divides the mass of the beer into 2 equal halves. This is 70.7% of the radius
3) At the interior surface of the fermenter wall.
The obvious conclusions are those that I have noted in earlier posts the main one being that the conductivity of the fermenter has a large effect on the time it takes the beer to come to equilibrium and on the equilibrium temperature drop across the fermenter wall.
