Transition to ballistic regime for heat transport in helium II

Michele Sciacca; Antonio Sellitto; David Jou

doi:10.1016/j.physleta.2014.06.041

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arXiv · 1405.3596

Transition to ballistic regime for heat transport in helium II

Michele Sciacca·Antonio Sellitto·David Jou

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Abstract

The size-dependent and flux-dependent effective thermal conductivity of narrow capillaries filled with superfluid helium is analyzed from a thermodynamic continuum perspective. The classical Landau evaluation of the effective thermal conductivity of quiescent superfluid, or the Gorter-Mellinck regime of turbulent superfluids, are extended to describe the transition to ballistic regime in narrow channels wherein the radius $R$ is comparable to (or smaller than) the phonon mean-free path $\ell$ in superfluid helium. To do so we start from an extended equation for the heat flux incorporating non-local terms, and take into consideration a heat slip flow along the walls of the tube. This leads from an effective thermal conductivity proportional to $R^2$ (Landau regime) to another one proportional to $R\ell$ (ballistic regime). We consider two kinds of flows: along cylindrical pipes and along two infinite parallel plates.

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Michele Sciacca, Antonio Sellitto, David Jou. 2014-05-12. Transition to ballistic regime for heat transport in helium II. https://doi.org/10.1016/j.physleta.2014.06.041

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