A semi-analytic solution for the heat transfer process between a He II pres
surized bath and a saturated tube-type hear exchanger is presented. The pro
blem is modeled with an extended surface heat transfer formulation analogou
s to that in conventional conduction. The process is governed by Kapitza co
nductance and counter flow within the bulk fluid in the tube. The resulting
nonlinear differential equation may be integrated for the special case of
constant properties, yielding a simple solution applicable to design and an
alysis of practical heat exchangers.