Transient helium II heat transfer through random packed spheres

In this study time dependant heat flow through superfluid helium (He II) contained in porous media is examined. Using a porous insulation instead of fully epoxy-impregnated insulation could potentially increase cooling efficiency by allowing an intimate contact of He II with the conductor. The present work focuses on understanding heat transfer in He II contained in a bed of polyethylene spheres of uniform size arranged in a random pack. Measured results include the transient temperature decay across the bed of packed spheres (diameters of 35, 49 and 98 microns) when heat addition is removed on one side of the porous media while the other is held at bath temperature. Bath temperatures range from 1.7 to 2.1 K. Two flow regimes (transitional and turbulent) are decipherable from the dependence of the temperature gradient on the heat flux. Past steady state, turbulent He II heat transfer experiments in the same media have concluded that the Gorter-Mellink exponent varies from 3.3 to 3.4 in this temperature range. Transient results compare favorably to a one-dimensional numerical solution that considers a variable Gorter-Mellink exponent and a piece-wise determination of the heat flux.