In this work a one-fluid model of liquid helium II, based on extended irreversible thermodynamics, is further developed, in order to describe the action of quantized vortices on second sound propagation. The vortex array is described by means of a pressure tensor ${\mathbf{P}}_{\omega }^V,$ which may be related to some parameters describing the vorticity. The influence of the vortices on the heat flux is taken to be given by the contraction of this pressure tensor and the heat flux. Two situations with different geometries of the vortices are examined: superfluid in a rotating cylinder and thermal counterflow. In both of them, previously known results are recovered from this more general perspective. Finally, a generalization of Vinen’s equation for the evolution of the vortex line density including fractal effects is proposed on dimensional grounds, and its relation to recent experiments is briefly discussed.

• Received 27 June 2002

DOI:https://doi.org/10.1103/PhysRevB.66.224509