Extended irreversible thermodynamics of liquid helium II

Constitutive equations for heat conduction in nanosystems and nonequilibrium processes: an overview

“…In steady states, the heat transfer in turbulent liquid helium [85,[89][90][91][92] may be described by an equation analogous to Eq. (6), taking the form…”

“…In EIT, superfluid helium is considered as a single fluid with the heat flux as an internal variable [85]. In the more usual two-fluid model by Landau and Tisza [86][87][88][89], instead, it is considered to be composed of a normal viscous component and a superfluid one.…”

Refrigeration of an Array of Cylindrical Nanosystems by Flowing Superfluid Helium

“…We aim to consider heat removal from the system by means of forced He II convection with net velocity v. The basic equations for the specific volume (volume per unit mass) V = ρ −1 , the velocity v, the specific internal energy and heat flux q are [15][16][17][18] (1) has been written in terms of the volume V instead of the usual density ρ for future purposes. Since we want to avoid quantum turbulence, we will take L = 0 in Eq.…”

Effective thermal conductivity of superfluid helium: laminar, turbulent and ballistic regimes

“…where S is the entropy per unit volume, σ q is the production term of the heat flux, p is the pressure, and λ 1 and η can be interpreted as the heat conductivity and the shear viscosity when applied to a classical fluid [24]. The thermal conductivity λ 1 is related to the velocity of second sound w 2 by the relation ζ := λ 1 /τ 1 = w 2 2 ρC v , where C v is the constant volume specific heat, and τ 1 the relaxation time of the heat flux.…”

“…The dynamical equations in the stationary situation, neglecting the nonlinear terms, for zero net mass flow are [24,25] (5)…”