AHA, I have found the error.
Ok, so Fourier's Law tells us how much heat can be transfered per second!!! (dQ/dt = Watts / second)
surface area with 8 inches (typical diameter of a stove top and close enough for a propane burner used with a turkey fryer) = 0.2032 meters
surface area of a circle = Pi * (radius ^2)
3.1416 * (0,1016 ^2)
3.1416 * 0.010322 = 0.0324m^2
For stainless steel:
dQ/dt= k * A * (dT/dx) (thermal conductivity times surface area times temperature difference divided by distance between objects)
dQ/dt= 15 * 0.0324m^2 * (80C / 0.05m) (0.05m = 2 inches, I'm including some leeway for wether it's a propane burner or a stove top).
dQ/dt= 777.6W/s
Basically, a stainless steel pot of 8 inches in diameter placed on a stove top 5cm from it can transfer a maximum of 777W/s.
Aluminium:
replace k (15) by 237
12286W/s
So, what does this mean? It basically tells us how many watts the material can transfer in a second...
Well, everybody using a turkey fryer and a stainless steel pot are waisting a bunch of energy, although probably protecting their wort from burning, since the average stove element is about 2000Watts, I have no clue how many Watts a turkey fryer is...
Also, that means that people using stove tops are better off with aluminium as well, seeing how they will get the most from their burner.
The big problem now is how not to burn the wort, yet use the energy efficiently.
BTW: The amount of Joules needed to heat up water is: 4.184 J / (g * K)
So, let's say for 7 gallons of pure water:
4.184 J * (7gallons *3.78 l/g * 1000g/l) * (373 - 293K)
4.184J * 26460g * 80K = 8856691,2Joules...
1 Watt = 1 Joule per second...
Let's say the stove top has a 2000W element, someone using Stainless steel would be limited by the pot, thus the maximum amount of wattage would be 777W.
8856691,2 Joules / (777 joules / second) = 11398s = 3.16 hours!!
Now, that same person, trying to boil with an aluminium pot on the same stove top would reach the limit of the element, thus 2000W would be transfered!
8856691,2 Joules / (2000 joules / second) = 4428s = 1.23 hours!
Now, for those of you doing things like extract brewing with only 3.5 gallons to boil, the numbers would be:
4.184J * (3.5g * 3,78l/g * 1000g/l) * 80degrees K
4428345.6Joules
Stainless steel: 5699s = 1.58hours
Aluminium: 2214s = 0.61hours
Soooooo, what can we conclude?
Aluminium does transfer heat in a greater quantity per second. For someone using a stove top, the difference is about 2.57 times faster, and this is limited by the wattage of the element.
I still don't have absolute faith in my calculations, and I would like some people to tell us their setup (aluminium or stainless steel), what kind of burner they use, how much water they are boiling and how long it takes to boil.
BTW: Sorry if this is such a long post...
