Thermal wave oscillations and thermal relaxation time determination in a hyperbolic heat transport model

Ordoñez-Miranda, José; Alvarado‐Gil, J. J.

doi:10.1016/j.ijthermalsci.2009.03.008

Cited by 76 publications

(28 citation statements)

References 28 publications

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“…Figure 1 depicts the volumetric heat source consists of parts of four ellipsoidal. The maximum heat flux intensity at the origin, in general, is defined by (14) The temperature gradient at the front and rear are different and as well as non-symmetric profile along the Z-direction. The fractions in heat deposited are accounted in the general expression of heat flux density distribution in eq.…”

Section: Heat Source Representationmentioning

confidence: 99%

“…The pulse duration is such that any phase transformation occurs in non-equilibrium condition and finite time is required for attaining equilibrium strongly depends on laser-material interaction [13]. Hence, understanding of lag behaviour in heat transfer may minimize any unwanted material change, produce limited HAZ and minimize induced thermal stress using ultra-short pulse laser [14]. To account for the finite speed of thermal wave, Fourier equation is upgraded from parabolic to hyperbolic that analyse the transient phase of the ultra-short pulse laser heating process when laser pulse duration approaches to femtosecond or picosecond level and the mechanism of radiation absorption becomes important [15].…”

Section: Introductionmentioning

confidence: 99%

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Microscale heat transfer in fusion welding of glass by ultra-short pulse laser using dual phase lag effects

Bag

2018

IOP Conf. Ser.: Mater. Sci. Eng.

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Abstract. The heat transfer in microscale has very different physical basis than macroscale where energy transport depends on collisions among energy carriers (electron and phonon), mean free path for the lattice (~ 10 -100 nm) and mean free time between energy carriers. The heat transport is described on the basis of different types of energy carriers averaging over the grain scale in space and collations between them in time scale. The physical bases of heat transfer are developed by phonon-electron interaction for metals and alloys and phonon scattering for insulators and dielectrics. The non-Fourier effects in heating become more and more predominant as the duration of heating pulse becomes extremely small that is comparable with mean free time of the energy carriers. The mean free time for electron -phonon and phonon-phonon interaction is of the order of 1 and 10 picoseconds, respectively. In the present study, the mathematical formulation of the problem is defined considering dual phase lag i.e. two relaxation times in heat transport assuming a volumetric heat generation for ultra-short pulse laser interaction with dielectrics. The relaxation times are estimated based on phonon scattering model. A three dimensional finite element model is developed to find transient temperature distribution using quadruple ellipsoidal heat source model. The analysis is performed for single and multiple pulses to generate the time temperature history at different location and at different instant of time. The simulated results are validated with experiments reported in independent literature. The effect of two relaxation times and pulse width on the temperature profile is studied through numerical simulation.

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Section: Heat Source Representationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Microscale heat transfer in fusion welding of glass by ultra-short pulse laser using dual phase lag effects

Bag

2018

IOP Conf. Ser.: Mater. Sci. Eng.

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“…By implementation of a generalized, hyperbolic heat conduction law, suggested by the linear theory of heat conduction in media with thermal memory [8][9][10][11][12][13][14][15][16][17], a generalized model of thermoelastic deformation is described by the following system of partial differential equations [19,20] …”

Section: Theory Of Thermoelasticity In Solids Including Thermal Memorymentioning

confidence: 99%

“…The development of these experimental techniques has caused the advance of different detection schemes, but theoretical models as well-the ones that help interpret and analyze various experimental data. Classical theories of the PA thermoelastic bending [3][4][5][6][7] have ignored implicitly, until now, the fact that the heat propagation velocity in solids is finite and that the thermal relaxation time does not equal zero [8][9][10][11][12][13][14][15][16][17][18][19][20][21], thus neglecting the presence of thermal memory properties [11,12] because they use classical heat conduction theory. There are several exceptions among models coping with the direct PA effect [18] and PT thermoelastic bending [19,20], which are based on some of the generalized theories of thermoelasticity [14][15][16][17], removing the nonphysicality of classical Fourier's theory of heat conduction [8].…”

Section: Introductionmentioning

confidence: 99%

Photothermal Thermoelastic Bending for Media with Thermal Memory

et al. 2012

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Photothermal thermoelastic bending depends on an optically generated dynamic thermal field distribution within a sample. A generalized description of the distribution is proposed, including the effects of a finite heat propagation velocity and a finite, non-zero time of thermal relaxation (known as thermal memory effects in generalized heat conduction theory), and finally the generated thermoelastic bending is calculated by using both a thin solid-plate approximation and a decoupling system of thermoelastic equations. The comparison between this model and the classical one, which does not account for thermal memory influence, has been made. If the sample is thicker than the value of its minimal thermal diffusion length, the difference between the two models becomes insignificant. Otherwise, it has been shown that the two models tend to overlap at low and high modulation frequencies of the excitation light, while in the mid-frequency range, some deviations become more apparent and thermal memory properties of the sample must be taken into account. The suggested model enables evaluation of thermal memory properties for such a solid.M. Nesic (B) · S. Galovic · M. Popovic

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“…In this case it has been shown that, depending on the thermal wave penetration inside the material, the effective thermal properties could show a complex behavior influenced by the modulation frequency of the heating source [26,28]. The generalization of this approach for two-layer systems under the hyperbolic heat transport equation has been studied [38]; however, the role of the interface thermal resistance as well as the thermal relaxation time on the effective thermal properties has not been fully explored.…”

Section: Introductionmentioning

confidence: 99%

Effective Thermal Properties of Multilayered Systems with Interface Thermal Resistance in a Hyperbolic Heat Transfer Model

Ordoñez-Miranda¹,

Alvarado‐Gil²

2010

Int J Thermophys

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One-dimensional thermal wave transport in multilayered systems with an interface thermal resistance is studied under the framework of the CattaneoVernotte hyperbolic heat conduction model, considering modulated heat excitation under Dirichlet and Neumann boundary conditions. For a single semi-infinite layer, analytical formulas useful in the measurement of its thermal relaxation time as well as additional thermal properties are presented. For a composite-layered system, in the thermally thin regime, with the Dirichlet boundary condition, the well known effective thermal resistance formula is obtained, while for the Neumann problem, only the heat capacity identity is found. In contrast, in the thermally thick case, an analytical expression for both Dirichlet and Neumann conditions is obtained for the effective thermal diffusivity of the whole system in terms of the thermal properties of the individual layers and their interface thermal resistance. The limits of applicability of this equation, in the thermally thick regime, are shown to provide useful and simple results in the characterization of layered systems and that they can be reduced to the results obtained using the Fourier approach. The role of the thermal relaxation time, the interface thermal resistance, and the implications of these results in the possibility of enhancement in heat transport are discussed.

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Thermal wave oscillations and thermal relaxation time determination in a hyperbolic heat transport model

Cited by 76 publications

References 28 publications

Microscale heat transfer in fusion welding of glass by ultra-short pulse laser using dual phase lag effects

Microscale heat transfer in fusion welding of glass by ultra-short pulse laser using dual phase lag effects

Photothermal Thermoelastic Bending for Media with Thermal Memory

Effective Thermal Properties of Multilayered Systems with Interface Thermal Resistance in a Hyperbolic Heat Transfer Model

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