In homebrewing on of the key steps when brewing with extract is to rapidly chill the wort from boiling temperatures to about 80F in 30 min. This is needed to reduce risk of environmental contamination, oxidation, and control of formation of Dimethyl Sulfide This isn't too hard for small batches of beer, and most people use ice baths for their brew pots, however, as you get to larger sized batches, most people resort to wort chillers run from tap water to reduce temperature. Usually this works great from getting from boiling to 90F, but the temperature gradient usually is too low to allow for rapid chilling from 90F to 80F. In order to optimize this process, one might like a nice set of physical equations for modeling heat exchange rather than some rule of thumb engineering models for heat exchangers. If one were to model this process from a physicists point of view, what would be the resulting set of equations?
Netwon's Law of Cooling I think is exactly what you want to look at. Roughly, heat exchange is porportional to the difference in temperature between the beer and the cooling apparatus (be it water or something else) and also to the contact area between the two.
A secondary effect is the mixing of the beer. If the cold beer sits at the outer walls, the temperature difference is reduced and the middle will never cool. The reverse goes for the cooling liquid.