> The formula for heat transfer is:
>
> Q/t = kA (Th-Tc)/d
>
> Q/t is the rate of heat transfer, like Btu's per hour, k is the thermal
> conductivity of the conducting material (like your copper pot), A is
> the area the heat is being transferred across (square inches or square
> feet usually), Th (the h should really be a subscript) is the
> temperature on the hot side (inside your pot of broth), Tc (the c
> should really be a subscript) is the temp on the cold side (in your
> tub), and d is the thickness of the pot wall (probably in inches).
>
> Basically, all the formula says is that the rate of heat transfer is
> increased if the pot wall is a good conductor, like copper, by
> increasing the temperature differential between the contents of the pot
> and the contents of the tub, by increasing the area over with the
> transfer is taking place or by decreasing the thickness of the wall in
> between.
>
> So all of the factors you mentioned come into play here.
>
> For you scientific/mathematical types, since the temp of the broth is
> constantly falling, this formula becomes a differential equation to
> account for the fact that as the broth temp falls (and, if you want to
> get really detailed, the temp of the water in the tub rising, maybe),
> Th keeps changing. Fun stuff, for us nerds!
>

As I recall, altitude also plays some small part in this, as does static vs
moving liquids.

Larry T