Rapid phase transformation under local non-equilibrium diffusion conditions

Соболев, С. Л.

doi:10.1179/1743284715y.0000000051

Cited by 32 publications

(26 citation statements)

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“…Understanding how heat is carried, distributed, stored, and converted in various systems has occupied the minds of many scholars for quite a long time [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. This is not due only to purely academic reasons: its practical importance in the fabrication and characterization of nanoscale systems has been recognized as one of the most critical programs in process industries [15][16][17][18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

“…One of them, of a theoretical nature, refers to the so-called "paradox" of propagation of thermal signals with infinite speed, which is predicted by the PHCE [1,2,4,5,6]. The second, more closely related to experimental observations, deals with the propagation of second sound, ballistic phonon propagation, and phonon hydrodynamics in solids at low temperatures, where heat transport departs dramatically from the usual parabolic description [5][6][7][9][10][11][14][15][16][17][18][19][20][21][22][23][24][25][26]. The most simple and well known modification of the Fourier law (MFL) for the one-dimensional (1-D) case is given by [1,2,[5][6][7][8][9][10][11][12][13][14][15] x T t q q          (1) where q is the heat flux, T is the temperature, λ is the thermal conductivity.…”

Section: Introductionmentioning

confidence: 99%

“…Glasses are out-of-equilibrium systems in which thermal equilibrium is reached by work exchanged through thermal fluctuations and viscous dissipation exchange that happens at widely different timescales simultaneously. The "active" systems, from phase transformations [12,19,25] to bio systems [31,32,40,47], move actively by consuming energy from internal or external energy sources and their behavior is thus intrinsically out of equilibrium. The effective temperature of the active systems is usually defined also on the basis of the FDT.…”

Section: Introductionmentioning

confidence: 99%

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Hyperbolic heat conduction, effective temperature, and third law for nonequilibrium systems with heat flux

Соболев

2018

Phys. Rev. E

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Some analogies between different nonequilibrium heat conduction models, particularly random walk, the discrete variable model, and the Boltzmann transport equation with the single relaxation time approximation, have been discussed. We show that, under an assumption of a finite value of the heat carrier velocity, these models lead to the hyperbolic heat conduction equation and the modified Fourier law with relaxation term. Corresponding effective temperature and entropy have been introduced and analyzed. It has been demonstrated that the effective temperature, defined as a geometric mean of the kinetic temperatures of the heat carriers moving in opposite directions, acts as a criterion for thermalization and is a nonlinear function of the kinetic temperature and heat flux. It is shown that, under highly nonequilibrium conditions when the heat flux tends to its maximum possible value, the effective temperature, heat capacity, and local entropy go to zero even at a nonzero equilibrium temperature. This provides a possible generalization of the third law to nonequilibrium situations. Analogies and differences between the proposed effective temperature and some other definitions of a temperature in nonequilibrium state, particularly for active systems, disordered semiconductors under electric field, and adiabatic gas flow, have been shown and discussed. Illustrative examples of the behavior of the effective temperature and entropy during nonequilibrium heat conduction in a monatomic gas and a strong shockwave have been analyzed.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hyperbolic heat conduction, effective temperature, and third law for nonequilibrium systems with heat flux

Соболев

2018

Phys. Rev. E

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“…Other authors claim that a jump condition for the temperaure should be utilized at the interface [30,31,46]. Based on a diffuse interface model, Hennessy et al [29] show that, when the MCE is used to model the melting of nanoparticles, the jump condition avoids the phenomenon of supersonic melting [25,35,47], which may appear when (5) is used. In the case of nanoparticle melting, the onset of supersonic phase change is due to the spherical geometry of system and the fact that less energy is required to melt the surface of smaller solid cores.…”

Section: Boundary and Initial Conditionsmentioning

confidence: 99%

The one-dimensional Stefan problem with non-Fourier heat conduction

Calvo-Schwarzwälder

Myers

Hennessy

2020

International Journal of Thermal Sciences

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We investigate the one-dimensional growth of a solid into a liquid bath, starting from a small crystal, using the Guyer-Krumhansl and Maxwell-Cattaneo models of heat conduction. By breaking the solidification process into the relevant time regimes we are able to reduce the problem to a system of two coupled ordinary differential equations describing the evolution of the solid-liquid interface and the heat flux. The reduced formulation is in good agreement with numerical simulations. In the case of silicon, differences between classical and nonclassical solidification kinetics are relatively small, but larger deviations can be observed in the evolution in time of the heat flux through the growing solid. From this study we conclude that the heat flux provides more information about the presence of non-classical modes of heat transport during phase-change processes.

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“…In Sec. 5, it will be shown how the singular behaviour of the jump conditions prevent the onset of unphysical "supersonic" melting [38,42,43], whereby the speed of the melt front exceeds the speed of heat propagation.…”

Section: Boundary Conditionsmentioning

confidence: 99%

Modelling ultra-fast nanoparticle melting with the Maxwell–Cattaneo equation

Hennessy

Calvo-Schwarzwälder

Myers

2019

Applied Mathematical Modelling

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The role of thermal relaxation in nanoparticle melting is studied using a mathematical model based on the Maxwell-Cattaneo equation for heat conduction. The model is formulated in terms of a two-phase Stefan problem. We consider the cases of the temperature profile being continuous or having a jump across the solid-liquid interface. The jump conditions are derived from the sharp-interface limit of a phase-field model that accounts for variations in the thermal properties between the solid and liquid. The Stefan problem is solved using asymptotic and numerical methods. The analysis reveals that the Fourier-based solution can be recovered from the classical limit of zero relaxation time when either boundary condition is used.However, only the jump condition avoids the onset of unphysical "supersonic" melting, where the speed of the melt front exceeds the finite speed of heat propagation. These results conclusively demonstrate that the jump condition, not the continuity condition, is the most suitable for use in models of phase change based on the Maxwell-Cattaneo equation. Numerical investigations show that thermal relaxation can increase the time required to melt a nanoparticle by more than a factor of ten. Thus, thermal relaxation is an important process to include in models of nanoparticle melting and is expected to be relevant in other rapid phase-change processes.can be compared against experimental data and used to assess new theories of nanoscale heat transport and phase change. From a practical perspective, nanoparticles play fundamental roles in novel drug delivery systems [3], materials with modified properties [4,5], and for improving the efficiency of solar collectors [6].Many current and future applications of nanoparticles require quantitative knowledge of how they respond to their thermal environment and their behaviour during melting.The thermal response of a nanoparticle differs from that of a macroscopic body for two main reasons.Firstly, the large ratio of surface to bulk atoms leads to many key thermophysical properties, such as melt temperature [7-9], latent heat [10][11][12], and surface energy [13] becoming dependent on the size of the nanoparticle. Secondly, the mechanism of thermal transport changes between the macroscale and the nanoscale. At the macroscale, heat is transported by a diffusive process that is driven by frequent collisions between thermal energy carriers known as phonons. Diffusive transport of heat across macroscopic length scales is well described by Fourier's law. On nanometer length scales, thermal energy is transported by a ballistic process driven by infrequent collisions between phonons. The finite time between phonon collisions results in a wave-like propagation of heat with finite speed [14,15]. Since Fourier's law leads to an infinite speed of heat propagation, it is not suitable for describing ballistic energy transport.Recent theoretical studies of nanoparticle melting have investigated the role of size-dependent material properties [16][17][18][19][20][21][22] u...

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Rapid phase transformation under local non-equilibrium diffusion conditions

Cited by 32 publications

References 95 publications

Hyperbolic heat conduction, effective temperature, and third law for nonequilibrium systems with heat flux

Hyperbolic heat conduction, effective temperature, and third law for nonequilibrium systems with heat flux

The one-dimensional Stefan problem with non-Fourier heat conduction

Modelling ultra-fast nanoparticle melting with the Maxwell–Cattaneo equation

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