, Volume 49, Issue 9, pp 2125–2137 | Cite as

Effects of heat flux on λ-transition in liquid 4He

  • Maria Stella MongiovìEmail author
  • Lidia Saluto
New Trends in Fluid and Solid Mechanical Models


This paper is concerned with the derivation of a phase field model for λ-transition in 4He, when the liquid is subject to pressure and heat flux. As parameter that controls the transition, a field f that is the geometrical mean between the density of the fluid and that of the superfluid is used. The resulting model, that is a generalization of previous papers on the same subject, chooses as field variables the density, the velocity, the temperature and the heat flux, in addition to this field f. The restrictions on the constitutive quantities are obtained by using the Liu method of Lagrange multipliers. New results with respect to previous models are the presence of non-local terms to describe inhomogeneities in the field variables and dissipative effects of mechanical and thermal origin, and the fact that the model describes the behaviour of the liquid also far from the λ-transition region.


Liquid helium Phase transitions Mean phase-field model Superfluids 



The authors acknowledge the financial support of the Università of Palermo (under Grant Fondi 60 % 2012-ATE-0106).


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Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Dipartimento di Energia, Ingegneria dell’Informazione e Modelli Matematici (DEIM)Università di PalermoPalermoItaly

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