Photothermal wave propagation in media with thermal memory

Galović, S.; Kostoski, D.

doi:10.1063/1.1540741

Cited by 62 publications

(48 citation statements)

References 37 publications

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“…It is important to observe that for low frequencies (ωτ 1) the parameter χ tends to unity and the parameter p approaches its classical value p c = (1 + i)/μ [16,17]. On the other hand, for high frequencies (ωτ 1), the parameter χ tends to 1/ √ 2ωτ and the parameter p → (1 + i2ωτ )/2 √ ατ , whose real part is independent of the modulation frequency and, therefore, it predicts that the hyperbolic thermal waves are able to travel larger distances than the parabolic ones predicted by Fourier's law.…”

Section: Mathematical Formulation and Solutionsmentioning

confidence: 99%

“…3 establishes that the heat flux q(x, t) at a certain time t depends on the history of the temperature gradient established in the whole time interval from −∞ to t. This indicates that the heat flux has thermal memory, a consequence of the finite value of the thermal relaxation time [17]. In this way, Eq.…”

Section: Introductionmentioning

confidence: 97%

“…In these situations Fourier equation provides an adequate approach. However, in modern applications such as in analysis and processing of materials using ultrashort laser pulses and high speed electronic devices, the finite value of the relaxation time is necessary to be considered [6,17,[19][20][21].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Mathematical Formulation and Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

See 1 more Smart Citation

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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“…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 paper we present a general photothermal mathematical model for thermal gradient materials [8]. The case of constant thermal diffusivity and linear variable heat capacity on inhomogeneous coatings is discussed, which is good approximation of thermal inhomogeneous thin layers [9].…”

Section: Introductionmentioning

confidence: 99%

Phototermal Spectra of Inhomogeneous Coatings

2009

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In this paper we demonstrate a theoretical study for photothermal measurements on inhomogeneous coatings. First, a general photothermal mathematical model for thermal gradient materials is presented. Then, we discuss the effects of inhomogeneous thermal properties in photothermal amplitude and phase spectra of coatings. Finally, a method for quantitative depth profiling that makes use of prior knowledge about the type of profile existing in a sample to reduce the instabilities associated with the mathematically ill conditioned task is demonstrated.

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Photothermal wave propagation in media with thermal memory

Cited by 62 publications

References 37 publications

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

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

Photothermal Thermoelastic Bending for Media with Thermal Memory

Phototermal Spectra of Inhomogeneous Coatings

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