Analysis of the wave propagation processes in heat transfer problems of the hyperbolic type

Babenkov, Mikhail B.; Иванова, Е. А.

doi:10.1007/s00161-013-0315-8

Cited by 26 publications

(9 citation statements)

References 24 publications

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“…Compared to the classic Fourier's law (i.e., τ 0 = 0), the Cattaneo's law has a hyperbolic nature giving rise to the so-called 'second sound' effect and having a finite signal propagation speed. While often being quantitatively indistinguishable from the Fourier's law, the Cattaneo's law becomes critical at small time-space scales and/or large heat pulse amplitudes as the latter is the case in laser cleaning (see, e.g., [8,43] and references therein) and numerous other applications [10], etc. Since the plate is thin in the x 3 -direction, it is legitimate to approximate the equation for Q 3 in (A.7) via the Fourier's law and obtain .8) or, equivalently,…”

Section: A1 Thermoelastic Plate As a 3d Prismatic Bodymentioning

confidence: 99%

Long-time behavior of quasilinear thermoelastic Kirchhoff–Love plates with second sound

2019

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We consider an initial-boundary-value problem for a thermoelastic Kirchhoff & Love plate, thermally insulated and simply supported on the boundary, incorporating rotational inertia and a quasilinear hypoelastic response, while the heat effects are modeled using the hyperbolic Maxwell-Cattaneo-Vernotte law giving rise to a 'second sound' effect. We study the local wellposedness of the resulting quasilinear mixed-order hyperbolic system in a suitable solution class of smooth functions mapping into Sobolev H k -spaces. Exploiting the sole source of energy dissipation entering the system through the hyperbolic heat flux moment, provided the initial data are small in a lower topology (basic energy level corresponding to weak solutions), we prove a nonlinear stabilizability estimate furnishing global existence & uniqueness and exponential decay of classical solutions.

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Section: A1 Thermoelastic Plate As a 3d Prismatic Bodymentioning

confidence: 99%

Long-time behavior of quasilinear thermoelastic Kirchhoff–Love plates with second sound

2019

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“…In this paper, we analyze the analogy between mass and energy transfer for dynamical processes, where more open questions still exist. Wave energy transfer plays a key role in many different processes: electromagnetic, acoustic, seismic, and so forth [12][13][14][15][16][17][18][19][20][21]. Electromagnetic waves (radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays) propagate through space, carrying electromagnetic radiant energy [22].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of matter and energy

Кривцов

2022

Z Angew Math Mech

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We propose and examine a potential analogy between mass transfer (in space) and energy transfer (in solids). We adapt classical equations of matter dynamics to describe the dynamics of energy transfer. Such fundamental quantities as the effective mass, momentum, moment of inertia and other quantities typical for bodies of matter are introduced for “bodies” of energy. Along with this, two new concepts of “carrier” and “phantom” are proposed. A carrier is a medium which enables energy transfer. A phantom is a virtual body of matter having its mass distribution equivalent to the energy distribution in the carrier. Using an inhomogeneous chain of particles as a sample system, we show that the phantom motion satisfies the Newton's second law of dynamics. For certain systems, we derive constitutive equations for the net force, which results in a closed system of dynamics equations. We further show that with the relevant properties of the chain it is possible to obtain the dynamics equation for the phantom motion in a gravitational field. We use similar methods to study energy dispersion. To analyze phantom evolution, we introduce the velocities of phantom transfer and dispersion. We show that, depending on the ratio of these velocities, the phantom can behave either as a wave or as a particle. Furthermore, we discuss potential application of energy dynamics to other branches of physics, such as quantum mechanics, electrodynamics and general relativity. We introduce the idea that a body of matter itself can be a phantom in some other carrier, which is a different entity than matter. Possible associations of the phantom/carrier model with current models of physical space are discussed. Based on the presented concept, we propose plausible qualitative answers to several open questions in modern physics.

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“…This leads to a change in the type of differential equations, as for example in refs. [15][16][17][18][19][20]. Such models allow describing rapid transient processes.…”

Section: Introductionmentioning

confidence: 99%

The chemical interaction charged particles with target material under surface treatment of metal with particle beam

Parfenova

Knyazeva

2022

Z Angew Math Mech

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The paper presents a nonlinear coupled nonisothermal model of the process of material implementation into the target surface under conditions of surface treatment by a particle beam in the form of one or few consecutive pulses. The model takes into account the interaction of impurity diffusion, heat propagation, and mechanical disturbances, as well as the chemical reaction between the introduced impurity and the target material. The problem is solved numerically using an implicit symmetric difference scheme of the second‐order approximation in time and spatial coordinates. The results of solution are obtained for different time intervals. It was found that the interaction of different processes leads to the appearance of distortions in the front of waves. The distributions of temperature and impurity concentration have a wave character. The increment of the reaction product in the dynamics for different numbers of pulses is presented. The interaction mechanisms of the studied processes do not change and do not depend on the number of pulses. However, a more complicated picture is observed under treatment by several successive pulses due to the appearance of new extremes and distortions.

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Analysis of the wave propagation processes in heat transfer problems of the hyperbolic type

Cited by 26 publications

References 24 publications

Long-time behavior of quasilinear thermoelastic Kirchhoff–Love plates with second sound

Long-time behavior of quasilinear thermoelastic Kirchhoff–Love plates with second sound

Dynamics of matter and energy

The chemical interaction charged particles with target material under surface treatment of metal with particle beam

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