Effective thermal conductivity of helium II: from Landau to Gorter-Mellink regimes

TL;DR

This paper models the size- and flux-dependent effective thermal conductivity of helium II across different flow regimes, extending classical theory to turbulent conditions by incorporating vortex dynamics and wall effects.

Contribution

It introduces a unified model that transitions from Landau's classical regime to the Gorter-Mellink turbulent regime by including vortex line density and wall influences.

Findings

Extended classical Landau model to turbulent regime

Derived vortex line density considering wall effects

Predicted flux-dependent thermal conductivity behavior

Abstract

The size-dependent and flux-dependent effective thermal conductivity of narrow channels filled with He II is analyzed. The classical Landau evaluation of the effective thermal conductivity of quiescent He II is extended to describe the transition to fully turbulent regime, where the heat flux is proportional to the cubic root of the temperature gradient (Gorter-Mellink regime). To do so we use an expression for the quantum vortex line density $L$ in terms of the heat flux considering the influence of the walls. From it, and taking into account the friction force of normal component against the vortices, we compute the effective thermal conductivity.