Temperature Rise in a 30 Gallon Kettle

Submitted by Dan K on Thu, 05/22/2008 - 12:51.

Below are the explanation and calculations behind the chart:

Equipment and conditions:
30 gallon stainless steel kettle with stainless steel lid
70,000 BTU ring style burner running at full tilt
Slight breeze

Data for 28 gallons:

Time Temperature
0 min 74oF
5 85
8 88
10 92
16 102
26 116
34 128
37 134
44 143
48 149
54 156
59 162
65 170
67 172

After the data was recorded, it was entered into an ExcelTM spreadsheet and a temperature vs. time graph was plotted. A linear regression plot line was then added to see what the equation of the data line was. The regression line fit the data points very well. The reason that the data fell on a linear path is because the heat transfer acts as steady state under the given conditions. This is a direct result of the large ?T between the flame and the water. Propane can burn in excess of 3500oF and the water only ranges from 74 to 212oF, which gives less than a 6% difference in ?T. That is most likely less than the human error that went into the data points to begin with.

The R2=.997 (for the statistically inclined) which indicated a very good linear relationship between the data. More specifically, 97.7% of the variability in temperature has been explained by the time variable by assuming a linear relationship.

Since the slope of the regression line (1.4396) is inversely proportional to the volume, a general equation for the rise in heat transfer can be easily calculated.

To find the new slope for any given volume:

(old slope)(old volume/new volume)
ex. 16 gallons: new slope = (1.4396)(28/16) = 2.519

So the new equation for the temperature rise for the same kettle with 16 gallons would be:

y = (2.519)X + initial temperature of the water (let's say 60oF)

So the new data would be as follows:

Time Temperature
0 min 60oF
5 72.6
10 85.2
15 97.8
20 110.4
25 123
30 135.6
35 148.2
40 160.8
45 173.4
50 186
55 198.6
60 211.2

The experiment was done again to test the equation for 16 gallons and the time varied less than 5% at the end of one hour. The variance is made up from several factors such as the wind speed, pressure of the propane tank, and ambient air temperature. The results may have been lucky but the equation seemed to hold true.

The chart that I made from this data hangs in my garage next to my system. I have fired up the burner, left for the estimated amount of time, returned at the predicted time, and have never been off by much more than 5 minutes from time that the chart gave. It may not be perfect, but it is a hell of a lot better than worrying about overshooting the temperature (which means checking the kettle's temperature more than I want to).

© 2000 by Dan Kiplinger
Please do not reproduce this information (other than for personal use) without written permission from the author via KLOB. Thank you.