Contribution of the normal component to the thermal resistance of turbulent liquid helium

Previous results for the velocity profile of the normal component of helium II in counterflow are used to evaluate the viscous contribution to the effective thermal resistance. It turns out that such a contribution becomes considerably higher than the usual Landau estimate, because in the presence of vortices the velocity profile is appreciably different from the Poiseuille parabolic profile. Thus, a marked increase of the contribution of the normal component to the thermal resistance with respect to the viscous Landau estimate does not necessarily imply that the normal component is turbulent. Furthermore, we examine the influence of a possible slip flow along the walls when the radius of the tube becomes comparable to the phonon mean-free path; this implies a reduction of the thermal resistance with respect to that obtained for non-slip boundary conditions.