This log investigates cooling through our current planned copper braid connection (which is standing in for an intended rigid bar linkage that is WIP)
The question is, can we get [cooling power of cryocooler] out of our baseplate through this copper braid?
Cooner Wire P/N NER 7710836 BOF (oxygen free copper)
Sumitomo CH-104 (manual from Wiki) has 77K coldhead cooling capacity of 34 W, and from the quote, 50K cooling capacity of just under 40 W.
Adequate cooling power of this setup depends on the radiative heat load and conductive losses; for our purposes, we can imagine that tens of Watts will be needed, and circle back to more precise heat budgeting.
Conductive Heat Transfer
Q = A / L * (Uint_T2 - Uint_T1)
Uint_T = the integral of thermal conductivity between T and 4K, see below table [ETP OFE Copper, W/m]. Note these are values from literature not from our copper braid's spec sheet (no such properties available from vendor).
Table of Thermal Conductivity integral values, between T and 4K. Unit = W/m. Source: Ekin, Appendix 2.1
20K = 14000, 40K = 40600, 50K = 50800, 60K = 58700, 70K = 65100, 80K = 70700, 100K = 80200, 120K = 89100, 140K = 97600
A = 6.71e-5 m^2
L = 0.5 m (estimate)
T2 = 123 K (intended workpiece temperature)
T1 = ? (coldhead temperature, unknown, we will pick a value and calculate)
Q(T1_80K) = 6.71e-5 m^2 / 0.5 m * (89100 W/m - 70700 W/m) = 2.46 W
Q(T1_20K) = 6.71e-5 m^2 / 0.5 m * (89100 W/m - 14000 W/m) = 10.07 W
It appears that the copper braid's capacity for conductive heat transfer will constrain the tens of Watts of cryocooler capacity. This is even before we consider imperfections in the clamping interfaces and similar real losses.
Fixes for this constraint might involve adding parallel linkages (increasing area) or shortening the strap length.
It would be interesting to compare this to the anticipated capacity of the flexible strap in the original design - future work.