Non-equilibrium thermodynamics, heat transport and thermal waves in laminar and turbulent superfluid helium

Relationships between rational extended thermodynamics and extended irreversible thermodynamics

“…In nanosystems, the small size of the system, which becomes comparable to the mean free path of the heat carriers, means that classical transport equations, valid in the diffusive regime, are no longer valid, because heat transport takes place in a situation intermediate between diffusive and ballistic regime; it is well known this is a very active topic, very inspiring in the theory and applications of transport theory and thermodynamics. In superfluid helium, the macroscopically coherent quantum effects lead to a long relaxation time and a long coherence length for the heat flux and to a quantization of the circulation of vortices [10,11,29,34]; when the heat flux exceeds some threshold, related to a critical value (of the order of 100) of the quantum heat number Re q = qd(ρTsκ) −1 , with κ the quantum of vorticity, given by κ = h/m, with h Planck's constant and m the atomic mass of helium, and d the diameter of the tube where heat is flowing, quantized vortices appear. These vortices exert a friction force on the helium flow and contribute to the thermal resistance of the system.…”

“…Recently, it has also considered polyatomic ideal gases [17,42] and dense gases [43], by loosening the too-tight original structure of the theory, excessively limited by the proximity to ideal monatomic gases, and becoming slightly more phenomenological, which gives it higher flexibility. By contrast, EIT has not paid so much attention to the detailed structure of the nonlinear terms, but it has considered ideal gases (monatomic or not, as well as photon gases, phonon gases and electron gases), dense gases (incorporating the transport of intermolecular potential energy) [6], superfluids [29,34], nuclear matter, fast solidification fronts in alloys and mixtures [35], and polymer solutions and blends [10,[21][22][23][24][25]28] and ecological systems [16]. In such systems, the detailed structure of the evolution equations becomes unmanageable, and one tries to have some phenomenologically satisfactory expressions rather than exact expressions of the equations.…”

“…From the three basic ideas mentioned in the first paragraph, the several developments of extended thermodynamics may differ in: (a) the concrete fluxes taken into account; (b) the techniques being used in the exploitation of the second law; (c) the connections with the microscopic level of description; (d) the range of systems being analysed. In fact, the bibliography related to extended thermodynamics is considerably wide: it includes at least 18 monographs [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and 17 review papers [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] but the diversity of approaches makes it difficult to give them a wide well-recognizable form beyond their mutual differences. The aim of this paper is to foster the contact between them.…”

Heat rectification in He II counterflow in radial geometries

“…Heat transport in superfluid He II is not described by Fourier's law but it requires a much more general law, considering the long relaxation time τ 1 of the heat flux q (first term of Equation (2)), nonlocal effects (fourth term of Equation (2)) related to the long coherent length of the superfluid (a macroscopic quantum coherence), and nonlinear effects (third term and last term of Equation (2)) related to quantized vortices forming a turbulent tangle of lines described by the vortex length per unit volume L [22][23][24]. Such generalized equation takes the form [24,25]:…”

Kelvin Waves Structure Analysis of a Horizontal Axis Wind Turbine Tip Vortices

“…The method was used in a wide range of applications to characterize the vortex physics, structures, and energy exchanges such as airplane wakes (Jacquin et al 2003), laminar and turbulent flows (Arendt et al 1998;Mongiovi et al 2018), vortex mass transport (Weber and Ghaffari 2014), environmental and lakes investigations (Bouffard, and Lemmin 2013) and the dynamics of tornadoes.…”