A hydrodynamical model describing the superfluid phase transition of 4He close to $\lambda$-line is presented. In the work, which generalizes a phase field model of lambda 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 $\psi$, 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 satisfy the second law of thermodynamics.

Fabrizio, M., Mongiovi, M.S. (2013). Phase transition and lambda-line in liquid helium. JOURNAL OF NON-EQUILIBRIUM THERMODYNAMICS, 38(38), 185-200 [10.1515/jnetdy-2013-0004].

### Phase transition and lambda-line in liquid helium

#### Abstract

A hydrodynamical model describing the superfluid phase transition of 4He close to $\lambda$-line is presented. In the work, which generalizes a phase field model of lambda 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 $\psi$, 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 satisfy the second law of thermodynamics.
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Fabrizio, M., Mongiovi, M.S. (2013). Phase transition and lambda-line in liquid helium. JOURNAL OF NON-EQUILIBRIUM THERMODYNAMICS, 38(38), 185-200 [10.1515/jnetdy-2013-0004].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/98213
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