Design and Analysis of Continuous Heat Exchanger for Dilution Refrigerators

We present the tentative design and numerical analysis of a compact footprint (diameter < 5 cm and length < 10 cm) continuous tube-in-tube heat exchanger (TTHx) operating at sub-K temperatures for dilution refrigerators with a base temperature of 10 mK and cooling power of 10 μW or higher at 20 mK. A 70/30 Cu-Ni alloy is used for inner and outer tube construction and then wound spirally. We include the effect of Kapitza resistance, viscous heating due to impedance, and axial and radial conduction. We find that the axial conductivity of both outgoing dilute and incoming concentrated streams has a significant effect on the temperature profile along the length of the TTHx. Radial conduction uniformly distributes the boundary heat flux from Kapitza resistance and leads to a uniform temperature in the entire cross-section of dilute and concentrated streams. Our analysis shows that by keeping the inlet stream thermalized with the Still, i.e., the temperature of 700 mK, and flow rate below 200 μmol/sec, the no-load outlet temperature of the concentrated stream can be kept below 100 mK at the exit of TTHx, which is necessary to reach the no-load temperature of 30 mK or below using copper or silver sintered heat exchanger and 10 mK in the mixing chamber. Moreover, by performing explicit calculations with or without viscous heating, we find viscous effects to be negligible in the operating temperature range of TTHx.