Heat Conduction by Helium II Contained in Small Channels

Helium-II heat-flow experiments have been carried out with the helium contained in small channels (tubes < 10 μ in diameter $d$) having simple geometries and with the temperature differences limited to ∼ 5 × ${10}^{-3\mathrm{}}$ K° or less. In this domain, the heat current density is found to be proportional to the temperature gradient and the differential thermohydrodynamic equations of London and Zilsel should be valid. Comparison with the London-Zilsel theory shows good agreement for most of our data with regard to the absolute magnitude of the thermal conductivity $\kappa$ and its dependence on temperature. The experimental $\kappa$ values have a weaker dependence on the channel size than the theoretically predicted square of $d$, and this size dependence is a function of temperature. Our data for the largest channels ($d\sim 8$ μ) and at the larger heat current densities depart significantly from the London-Zilsel predictions. This difference is not explainable on the basis of a Gorter-Mellink mutual friction, but is consistent with a dissipative flow for the superfluid depending linearly on its velocity. This superfluid dissipative flow is comparable to that reported in other helium-flow experiments.