Abstract.
A hydrodynamic model describing the superfluid phase transition of 
He close to
the λ-line is presented. In the work, which generalizes a phase
field model of λ-transition previously formulated by the
same authors, the independent fields are the density, the
temperature, the velocity, the heat flux, and a scalar function
f, linked to the modulus of the wave-function ψ, solution
of the Ginzburg–Landau equation. In this framework, the heat flux
is given by a modified Maxwell–Cattaneo equation. The restrictions
on the constitutive quantities are obtained from the entropy
principle, using the Liu method of Lagrange multipliers. A maximum
theorem is proved that allows the model to satisfy the second law of
thermodynamics.
© 2013 by Walter de Gruyter Berlin Boston
