Dispersion relations for the hyperbolic thermal conductivity, thermoelasticity and thermoviscoelasticity

Vitokhin, Evgeniy Yu.; Иванова, Е. А.

doi:10.1007/s00161-017-0574-x

Cited by 17 publications

(3 citation statements)

References 36 publications

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“…Especially, Lord and Shulman (Lord and Shulman 1967) concretized the CV heat conduction equation for the elastic medium known as ''LS'' model. (Vitokhin and Ivanova 2017) Moreover, (Khisaeva and Ostoja-Starzewski 2006) examined the damping mechanism of the Euler-Bernoulli nanobeam model during the flexural vibration. (Sharma 2011) studied the vibration for a silicon beam including the frequency shift and dissipation induced by the phase-lagging time.…”

Section: Introductionmentioning

confidence: 99%

Thermoelastic attenuation of circular-cross-sectional micro/nanoring including single-phase-lag time

Kim

2021

Int J Mech Mater Des

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In this work, the thermoelastic dissipation (TED) for circular-cross-sectional micro/nanoring model is studied including the single-phase-lag (SPL) time based on the non-Fourier heat conduction model. The toroidal solid ring is simple to manufacture and thus the potential is high for future development. Also, the present model is more precise than the 1D or 2D beam or rectangular-cross-sectional ring because the governing equation is established by 3D coordinate system. Moreover, the SPL shows the delay time of heat-flux and is especially important in cryogenic or ultrafast-vibration environments. In this regard, characteristics of the TED is mainly analyzed according to the lagging time, geometrical shape, mode number and temperature, etc. Using the experimental data in literatures, the effectiveness of this work is verified to represent the investigations. The spectra of the TED with the phenomenon of multiple peaks are presented, and then the results can be grouped and compared with previous works. Moreover, the temperature distribution is graphically described to explain the SPL mechanism.

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Section: Introductionmentioning

confidence: 99%

Thermoelastic attenuation of circular-cross-sectional micro/nanoring including single-phase-lag time

Kim

2021

Int J Mech Mater Des

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“…A lot of research about convective heat transfer were conducted numerically [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Numerical study of the low-Reynolds flows in the vertical heated caverns

et al. 2019

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The object of research is the critical geometry of a three-dimensional air flow in a cavern between two vertical heated plates. In this rate the convection's contribution to heat transfer will be limited due to thermal conductivity at a fixture temperature drop. A three-dimensional RANS approach closed by the k-w SST turbulence model in conjunction with the energy equation. The model validated and verified by comparison with the experimental results. The results of the work applied in developing of ventilated façades.

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“…Dispersion relations for the Lord-Schulman thermoelasticity equations have been found and studied for arbitrary values of the heat flux relaxation time. [12][13][14] The speed of quasi-thermal and quasi-acoustic fronts of thermoelastic waves are summarized in the works. [12,14,15] The major work on different neoclassic theories of the thermoelasticity can be found in Jou, Casas-Vazquez and Lebon's book.…”

Section: Introductionmentioning

confidence: 99%

A comparison of the finite‐difference and finite‐volume methods for a numerical solution of a hyperbolic thermoelasticity problem utilizing the implicit and explicit schemes

Matias

Vitokhin

2019

Z Angew Math Mech

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A numerical solution for a coupled hyperbolic thermoelasticity problem of the Lord-Shulman type is presented. An infinite layer with free boundaries that are kept at a constant temperature is irradiated by a short laser impulse. In this case the problem can be studied in the one-dimensional formulation. An impact of the laser impulse on a medium is modeled by an internal heat source. The laser impulse intensity decays with a distance from an irradiated surface according to the Bouguer law. The layer is in an unperturbed state at the initial moment of time. The material properties of copper are taken to be the thermo-mechanical properties of the layer.Two approaches for the boundary value problem are considered: the finite-difference method (FDM) and the finite-volume method (FVM). In the first case the system of two second-order PDE is investigated, in the second case a system of integral balance equations and an integral thermal conductivity equation are composed. To integrate these equations both the explicit and implicit schemes are used. The obtained results are compared with each other and with an analytical solution. A numerical error is estimated for different time and space step sizes. The features inherent in various ways of integration of the coupled hyperbolic thermoelastic problem with the thermal excitation are found. K E Y W O R D SEuler implicit scheme, explicit leap-frog scheme, finite-difference method, finite-volume method, tridiagonal matrix algorithm, Lord-Shulman hyperbolic thermoelasticity, Maxwell-Cattaneo equation, relaxation constant, trust region algorithm

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Dispersion relations for the hyperbolic thermal conductivity, thermoelasticity and thermoviscoelasticity

Cited by 17 publications

References 36 publications

Thermoelastic attenuation of circular-cross-sectional micro/nanoring including single-phase-lag time

Thermoelastic attenuation of circular-cross-sectional micro/nanoring including single-phase-lag time

Numerical study of the low-Reynolds flows in the vertical heated caverns

A comparison of the finite‐difference and finite‐volume methods for a numerical solution of a hyperbolic thermoelasticity problem utilizing the implicit and explicit schemes

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