I've made simplifications to the testmass cooling model. Assuming 2 possible cooling mechanisms, radiative and conductive, the ODE must be a function of only and . If conductive cooling/heating of the testmass is treated as negligible, as we previously assumed, then:
, where a is the fit parameter. I include in the equation because it would appear as a constant in any radiative transfer model. I use the measured coldplate/inner shield temperature data for . Note that , and here and throughout I use a temperature-dependent .
The best fit parameter is a = 0.014, and the result of this fit can be seen in Attachment 1. The disagreement between the best-fit model and data suggest that cooling is not only dependent on , i.e. it cannot be radiative alone. I added back a conductive heating/cooling component:
, where a and b are the parameters of the fit.
The result of the fit can be seen in Attachment 2. The best fit parameters [a, b] = `[0.022, -0.0042].` This model matches the data much better than the purely radiative model, but the negative sign on b is non-physical (I think) since should always be < 0, so the sign of the conductive term should also be < 0. I'm not sure how to interpret this result, but it almost seems like there is conductive heating to the test mass even though physically this shouldn't be the case. |