Thermal Conductivity of Liquid He-4 near the Superfluid Transition in Restricted Geometries

We present measurements of the thermal conductivity near the superfluid transition of He-4 in confined geometries. The confinements we have studied include: cylindrical geometries with radii L=.5 and 1.0 microns, and parallel plates with 5 micron spacing. For L=1.0 microns, measurements at six pressures were conducted, whereas only SVP measurements have been done for other geometries. For the 1-D confinement in cylinders, the data are consistent with a universal scaling for all pressures at and above T(sub lambda). There are indications of breakdown of scaling and universality below T(sub lambda). For the 2-D confinement between parallel plates, the preliminary results indicate that the thermal conductivity is finite at the bulk superfluid transition temperature. Further analyses are needed to compare the 2-D results with those in bulk and 1-D confinement.