Effective thermal conductivity of superfluid helium in short channels

Abstract

The aim of this paper is to explore how the effective thermal conductivity of small channels filled with superfluid helium II in the laminar regime separates from the classical Landau expression as the channel becomes shorter. The Landau expression is valid for fully developed Poiseuille flow for the normal component, and therefore is suitable for long channels. By taking into account entrance effects, we show a transition from a heat flux proportional to ∆T /l (Landau regime) for long channels, to a heat flux proportional to l^(1/3) (∆T /l)^(2/3) for short channels.