Search results for "Extended thermodynamics"
showing 6 items of 6 documents
Gibbs equation in the nonlinear nonequilibrium thermodynamics of dilute nonviscous gases
2003
AbstractThis paper deals with the derivation of the Gibbs equation for a nonviscous gas in the presence of heat flux. The analysis aims to shed some light on the physical interpretation of thermodynamic potentials far from equilibrium. Two different definitions for the chemical potential and thermodynamic pressure far from equilibrium are introduced: nonequilibrium chemical potential and nonequilibrium thermodynamic pressure at constant heat flux q and nonequilibrium chemical potential and nonequilibrium thermodynamic pressure at constant J = Vq, where V is the specific volume.
Refrigeration bound of heat-producing cylinders by superfluid helium
2019
In this paper we go ahead in our studies on refrigeration of nanosystems by superfluid helium, as an appealing subject for future applications to computers or astronautical precision nanodevices. We first recall the effective thermal conductivity in laminar counterflow superfluid helium through arrays of mutually parallel cylinders and we discuss the conditions for the appearance of quantum turbulence around the heat-producing cylinders. We then consider the cooling of an array of heat-producing cylindrical nanosystems by means of superfluid-helium counterflow. We discuss the upper bound on heat removal set by avoidance of quantum turbulence and avoidance of phase transition to normal He I,…
A Continuum Theory of Superfluid Turbulence based on Extended Thermodynamics
2009
A thermodynamical model of inhomogeneous superfluid turbulence previously formulated is extended in this paper to nonlinear regimes. The theory chooses as fundamental fields the density, the velocity, the energy density, and two extra variables, in order to include the specific properties of the fluid in consideration: the averaged vortex line length per unit volume and a renormalized expression of the heat flux. The relations which constrain the constitutive quantities are deduced from the second principle of thermodynamics using the Liu method of Lagrange multipliers. Using a Legendre transformation, it is shown that the constitutive theory is determined by the choice of only two scalar f…
Hydrodynamics of superfluid 4He without dissipative effects
2013
This review paper is the first of a series of papers focusing on the singular behavior of superfluids. Here, we will consider the laminar flow of superfluid $^4$He. It is shown that the properties of helium II can be explained both considering it as a two-fluid mixture or as a single fluid with extremely high thermal conductivity and extremely small viscosity. More specifically, in this paper is shown that the anomalous effects in helium II are, in a large measure, a consequence of entropy conservation. Indeed, it will be shown that these effects can be explained imposing entropy conservation in a two-fluid mixture as well as in a single fluid described by extended thermodynamics. Firstly, …
HYDRODYNAMICAL MODELS OF SUPERFLUID TURBULENCE
2011
This review paper puts together some of our results concerning the application of non equilibrium Thermodynamics to superfluid liquid helium. Two of the most important situations of this quantum fluid are rotating superfluid and superfluid turbulence, both characterized by the presence of quantized vortices (vortex lines whose core is about 1 Angstrom and the quantum of circulation is $h/m$, $h$ being the Plank's constant and $m$ the mass of helium atom). In the first part of the work a non-standard model of superfluid helium, which considers heat flux as independent variable, is briefly recalled, and compared with the well known two-fluid model, in absence of vortices, proposed by Tisza an…
Extended Thermodynamics of Turbolent Superfluids:Nonlinear Costitutive Theory
2008
In this paper we extend to nonlinear regimes a thermodynamical model of inhomogeneous superfluid turbulence previously formulated. The theory chooses as fundamental fields the density, the velocity, the energy density, the heat flux and the averaged vortex line length per unit volume. The relations which constrain the constitutive quantities are deduced from the entropy principle, using the Liu method of Lagrange multipliers. Using a Legendre transformation, in the paper it is shown that the constitutive theory is determined by the choice of only two scalar functions of the intrinsic Lagrange multipliers.