Study of the transient thermal wave heat transfer in a channel immersed in a bath of superfluid helium

Zhang, P.; Murakami, Masahide; Wang, Ruzhu

doi:10.1016/j.ijheatmasstransfer.2005.09.031

Cited by 26 publications

(9 citation statements)

References 24 publications

(34 reference statements)

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“…8 and 11), ought not to be confused with the thermal wave phenomenon, commonly known as the second sound in the superfluid helium (He II) [37]. According to the two-fluid model, heat is transferred in a wave mode.…”

Section: Evolution On the Diffusion Timescalementioning

confidence: 99%

On the transition from thermoacoustic convection to diffusion in a near-critical fluid

Shen¹,

Zhang²

2010

International Journal of Heat and Mass Transfer

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Section: Evolution On the Diffusion Timescalementioning

confidence: 99%

On the transition from thermoacoustic convection to diffusion in a near-critical fluid

Shen¹,

Zhang²

2010

International Journal of Heat and Mass Transfer

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“…Such hydrodynamics is a lively topic, with recent emphasis, for instance, on nonlinear features such as the influence of intense heat pulses on the vortex tangle [8][9][10], or in multi-scale formulations allowing to eliminate the fast processes to derive evolution equations for the slow processes [11]. In the present Letter we will focus our attention on a different topic, namely, the behavior of linear heat waves and vortex density waves in the highfrequency domain.…”

mentioning

confidence: 99%

Vortex density waves and high-frequency second sound in superfluid turbulence hydrodynamics

Jou¹,

Mongiovı̀²,

Sciacca³

2007

Physics Letters A

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In this Letter we show that a recent hydrodynamical model of superfluid turbulence describes vortex density waves and their effects on the speed of high-frequency second sound. In this frequency regime, the vortex dynamics is not purely diffusive, as for low frequencies, but exhibits ondulatory features, whose influence on the second sound is here explored.Hydrodynamics of superfluid turbulence, characterized by a tangle of quantized vortex lines [1,2], aims to describe the couplings between pressure and heat perturbations, and the vortex density dynamics [3][4][5][6][7]. Such hydrodynamics is a lively topic, with recent emphasis, for instance, on nonlinear features such as the influence of intense heat pulses on the vortex tangle [8-10], or in multi-scale formulations allowing to eliminate the fast processes to derive evolution equations for the slow processes [11]. In the present Letter we will focus our attention on a different topic, namely, the behavior of linear heat waves and vortex density waves in the highfrequency domain. This has not received much previous attention, but we think it is worthwhile because, whereas at low frequencies the behavior of the vortex distortions is mainly diffusive, at high enough frequencies, the vortex lines behave as an elastic medium, and are able to propagate waves by themselves, i.e. they behave like a viscoelastic medium: diffusive at low frequencies, elastic at high frequencies. Their effect on second sound propagation is of much interest to provide a suitable physical interpretation of the experimental data based on second sound.Collective vortex waves in rotating superfluids have been studied in depth for a long time [12], and the so-called Tkachenko transverse elastic waves in the vortex arrays with crystalline order arising in rotating cylinders have been theoretically discussed since 1966. However, vortex density waves in counterflow situations have not been studied, up to our knowledge.Usually, one considers homogeneous vortex tangles in counterflow situation (i.e. under vanishing barycentric speed) and the evolution of L, the vortex-line density, is assumed to be the well-known Vinen's equation [1,2,6,13] (1)where q is the absolute value of the heat flux q, A and B parameters linked to the dimensionless coefficients appearing in Vinen's equation by the relations A = α v /ρ s T s and B = κβ v [7], ρ s being the density mass of the superfluid component, T the absolute

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“…The heat wave propagation intrinsic to superfluidity, the so-called second sound, may also lead to additional instabilities. To overcome these numerical difficulties, authors have either focused on one-dimensional solutions (Rao et al (1996), Zhang et al (2006)) or proposed simplified multi-dimensional models. For instance, Ramadan and Witt (1994) have modified the momentum equations as the thermo-mechanical and the mutual friction term are larger than the others in balancing each other (hence they can be dropped from the equations) to create a heat flux with the «familiar» |∇T | 1 /3 dependence.…”

Section: Introductionmentioning

confidence: 99%

“…On one hand, the superfluid equations are strongly coupled, mainly from the thermo-mechanical and the mutual friction terms, and coupled algorithms offer suitable solutions (Bottura and Rosso (1999), Zhang et al (2006)). On the other hand, the segregated approach are clearly less memory consuming.…”

Section: Introductionmentioning

confidence: 99%

A PISO-like algorithm to simulate superfluid helium flow with the two-fluid model

Soulaine

Quintard

Allain

et al. 2015

Computer Physics Communications

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This paper presents a segregated algorithm to solve numerically the superfluid helium (He II) equations using the two-fluid model. In order to validate the resulting code and illustrate its potential, different simulations have been performed. First, the flow through a capillary filled with He II with a heated area on one side is simulated and results are compared to analytical solutions in both Landau and GorterMellink flow regimes. Then, transient heat transfer of a forced flow of He II is investigated. Finally, some two-dimensional simulations in a porous medium model are carried out.

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Study of the transient thermal wave heat transfer in a channel immersed in a bath of superfluid helium

Cited by 26 publications

References 24 publications

On the transition from thermoacoustic convection to diffusion in a near-critical fluid

On the transition from thermoacoustic convection to diffusion in a near-critical fluid

Vortex density waves and high-frequency second sound in superfluid turbulence hydrodynamics

A PISO-like algorithm to simulate superfluid helium flow with the two-fluid model

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