I have been following the fine work of the MFMP team and analyzing the data. These guys are doing excellent work and I congratulate them for sharing their data on a real time basis for everyone to view. I wish that we had the same cooperation from the other experimenters, but I understand why they are reluctant.
The purpose for this post is to see if anyone among us can explain the unusual power output as a function of the outer glass temperature of the test cylinder. I believe that it has been the assumption that the outer glass surface should behave as a radiation source in a more or less black body manner. This implies that the radiation should be proportional to the 4th power of the temperature at that surface according to the Stefan-Boltzmann equation. I began my analysis assuming that this would be likely, but find that it does not seem to be true. I performed a curve fitting operation on some of the recent data that the guys submitted on line and found that the power leaving the cell very much matches a second order equation over a wide range of input values. My actual function is as follows: P(Out) = .001656 * T * T - .6284 * T + 40.3. Here P(Out) is in units of watts and T is Kelvin degrees. This function does a good job of matching the point pairs from 0 watts to 100 watts of output. The temperature varies from approximately 300 to 450 Kelvin over that output range. It is apparent that the function that I am posting does not work over a much larger range than that in actual use since an entry of 0 degrees Kelvin would result in an output of 40.3 watts which is nonsense. I started my review by assuming the forth order function. I thought of a cute trick of taking the derivative of the expected function to eliminate the fixed incoming radiation that must be subtracted to obtain accurate output radiation power calculations. Then I took the ratio of the derivatives for each adjacent pair of power points to eliminate the proportional constant. My procedure was a bit tricky to perform, but eventually I got the bugs worked out of my results. At that point I was expecting to see the ratio of adjacent derivatives follow a cubic function of their temperature ratios. This expectation was not demonstrated to my satisfaction. I was seeking useful results so I plotted the derivative of the power output versus temperature and saw that the curve followed a linear path instead of third order. With this result as a reference I performed a curve fit of power out versus temperature using a second order function and got very reasonable results. Am I missing something here? Why does the temperature on the surface of the glass cylinder not obey the Stefan-Boltzmann relationship? Does this suggest that the major heat transport mechanism is convection into the air instead of radiation? Is it possible that the IR radiation is escaping the demonstration device and the calibrations are mainly derived from the direct gas heating of the glass? Dave
