Steady state He II heat transfer through random packed spheres

• A temperature independent tortuosity was found.
• A laminar permeability and shape factor were determined.
• The transition regime can be predicted with the laminar and turbulent equations.

Heat flow through superfluid helium (He II) contained in porous media is examined. In particular, heat transfer experiments were performed on He II contained in a bed of polyethylene spheres of uniform size arranged in random packs. Measured results include the steady state temperature drops across the three random packs of spheres (35, 49, and 98 μm diameter) and the associated steady heat inputs. Bath temperatures range from 1.7 to 2.1 K to help grasp the superfluid effects. Two pure flow regimes (laminar and turbulent) are decipherable from the heat flux dependence of the temperature gradient. Turbulent results are fitted to an empirically derived turbulent He II heat equation for large channels with an added tortuosity (extra length traveled) term that accounts for the porous media. An average tortuosity of 1.33 was obtained, which is comparable with values of 1.36–1.41 concluded from published work on classical fluid pressure drop across random packed spheres. Laminar permeability and shape factor results are compared to past studies of He II in porous media and in channel flows. The onset of turbulence is determined through a critical heat flux from which a critical Reynolds number is formulated but, does not describe He II turbulence in the normal fluid component. The addition of the laminar and turbulent heat flow equations into a unifying prediction fits the transition regime data within 25%.