  Future superconducting radio frequency (SRF) cavities, as part of Project X
at Fermilab, will be cooled to superfluid helium temperatures by a cryogenic
distribution system supplying cold supercritical helium. To reduce vapor
fraction during the final Joule-Thomson (J-T) expansion into the superfluid
helium cooling bath, counter-flow, plate-fin heat exchangers will be utilized.
Due to their compact size and ease of fabrication, plate-fin heat exchangers
are an effective option. However, the design of compact and high-effectiveness
cryogenic heat exchangers operating at liquid helium temperatures requires
consideration of axial heat conduction along the direction of flow, in addition
to variable fluid properties. Here we present a numerical model that includes
the effects of axial conduction and variable properties for a plate fin heat
exchanger. The model is used to guide design decisions on heat exchanger
material choice and geometry. In addition, the J-T expansion process is modeled
with the heat exchanger to analyze the effect of heat load and cryogenic supply
parameters.
