Heat transport in superfluid filled capillaries

Effective thermal conductivity of superfluid helium: laminar, turbulent and ballistic regimes

“…Indeed, in Section 3.1. we obtain expression (23) which is proportional to b for very small value of b. Expression (23) takes into account the transition between laminar and ballistic regimes, and for b very small we find expression (25), which is equivalent to the experimental proposal in the ballistic regime in cylindrical channel [4,6]. Further studies are required to handle the so called "near wall shock wave" in the proximity of the hot walls [20,21].…”

“…Inspiring in the so-called phonon hydrodynamics in the rarefied regime, one admits a heat flux slip flow along the walls, instead of the non slip condition. For this reason we choose (17) q w = −C ∂q(y, z) ∂z z=b where C is a non-negative parameter, which in kinetic theory of rarefied gases ma be identified as C = 2 − f f [4,6]. More arguments on the interesting subject of no-slip condition can be find in Ref.…”

“…The properties of superfluid helium to flow through very thin capillaries with very low viscosity, or the high thermal conductivity which does not allow it to boil have been known since the first half of the last century [1][2][3][4][5][6][7].…”

“…Ballistic regime: The phonon mfp increases when temperature is lowered (for low temperatures, for example, it behaves as T −4.3 [4]), in such a way that for sufficiently low temperatures, it becomes comparable to (or higher than) the smallest size of the pipe (below some 0.7 K is of the order of 0.5 mm and for lower temperatures it is still larger) [4,6]. In this case, the predominant collisions are not the phonon-phonon collisions, but the phonon-walls collisions [4]. Thus, in these situations the walls play a crucial role.…”

“…Thus, in these situations the walls play a crucial role. The expression relating ∇T andQ in this case is [4,6] (4)…”