I've used the following model for cooling of the coldplate and testmass in Megastat:
,
where , and e_cp and e_bp are the emissivities of the coldplate and baseplate, respectively. The first term is conductive cooling of the cold plate via copper braid, and the second term is radiative heating of the coldplate from the baseplate (roughly room temp). In the model, the coefficient c is the fit parameter.
,
where and e_is and e_tm are the emissivities of the inner shield and test mass, respectively. This equation considers radiative cooling of the test mass from the surrounding inner shield. Here, the fit parameter is e_tm.
Attachment 1 (top plot) shows the results of the fitting. For conductive cooling of the coldplate, the best fit parameter is c=0.62. This means that 62% of the calculated conductive cooling power is actually being delivered to cool the coldplate, according to this model. Another way to look at it is that the constant factors (A, l of copper braid) that are used in the model need a correction of 0.62. Regardless, the model predicts a plateau temperature a few degrees cooler than the data shows. This means there must be a heat source we are not considering that delivers extra heating power at lower temperatures.
The testmass cooldown best fit parameter is e_tm = 1. I supplied bounds on e_tm from 0 to 1, since it is an emissivity value; the fit hits the upper limit. This is consistent with Koji's result that the calculated test mass emissivity is over 1. It is not clear why/how the test mass is cooled so quickly, since the black paint realistically has an emissivity between 0.5-1. Just like for the coldplate, the current model predicts a plateau temperature lower than what the data shows.
The bottom plot of Attachment 1 shows the difference between the fits and the data. The coldplate model does fairly well at high temperatures, but starts to break down around 100K. Then, other effects must be kicking in that we are failing to consider.
Next I plan to simplify further and model cooling power as a polynomial of T, and fit for its coefficients. Hopefully this can give insight into the temperature dependence of cooldown curve. |