Heat transfer and flow of He II in narrow channels Original Research Article

Heat transfer and fluid flow of He II in a long, narrow channel connected to a bath that supplies a constant supply of heat have been investigated by numerical simulations by using the simplified model of Kitamura et al. [Cryogenics 37 (1) (1997) 1]. Such channels are used to cool compact, stable, low-temperature magnets. The fluid flow is driven by natural convection and the mutual friction between the normal fluid and the superfluid. In this model, the thermomechanical effect and the Goter–Mellink mutual friction balance each other. A consequence of this balance is that the velocity and temperature distributions of He II can be characterized by a dimensionless, dependent parameter equal to the ratio of the fluid speeds of internal convection to the total fluid flow. After a sudden application of heat flux, the internal convection dominates over the total fluid flow until the establishment of steady-state temperature gradients. This predicts that the time required to set up the steady-state total fluid flow is proportional to the total heat capacity in the channel.