Thermal diffusivity of rods, tubes, and spheres by the flash method

Salazar, A.; Garrido, Florencio; Celorrio, R.

doi:10.1063/1.2183584

Cited by 32 publications

(27 citation statements)

References 6 publications

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“…Subsequently, Salazar et al [3] used this method to calculate the in-plane effective thermal diffusivity of unidirectional fiber-reinforced composites. Salazar and co-workers also extended this classical flash method to study the surface temperature resulting from nonplanar samples, such as solid cylinders [4], hollow cylinders [5,6], and spheres [7]. Recently, Madariaga and Salazar [8] exploited this elegant method to express the surface temperature of multilayered spherical samples with continuously varying in-depth thermal conductivity.…”

Section: List Of Symbols λmentioning

confidence: 95%

Multiple Scattering of Thermal Waves from a Subsurface Cylindrical Inclusion in Semi-infinite Functionally Graded Materials Using Non-Fourier Model

et al. 2009

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In this study, a theoretical method is applied to investigate the multiple scattering of thermal waves and temperature field resulting from a subsurface cylindrical inclusion in a semi-infinite functionally graded material (FGM). The adiabatic boundary condition at the semi-infinite surface is considered. The thermal waves are excited at the surface of semi-infinite functionally graded materials by modulated optical beams. The model includes the multiple scattering effects of the cylindrical thermal wave generated by the line heat source. According to the wave equation of heat conduction, a general solution of scattered thermal waves is presented. Numerical calculations illustrate the effect of subsurface inclusion on the temperature and phase change at the sample surface under different physical and geometrical parameters. It is found that the temperature above the conducting cylindrical inclusion decreases because of the existence of the inclusion. The effect of the inclusion on the temperature and phase change at the surface is also related to the non-homogeneous parameter of FGMs, the wave frequency of thermal waves, and the distance between the inclusion and the semi-infinite surface. Finally, the effect of the relaxation time of buried inclusion on the temperature and phase change at the surface is examined.

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Section: List Of Symbols λmentioning

confidence: 95%

Multiple Scattering of Thermal Waves from a Subsurface Cylindrical Inclusion in Semi-infinite Functionally Graded Materials Using Non-Fourier Model

et al. 2009

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“…Subsequently, Salazar et al used this method to calculate the in-plane effective thermal diffusivity of unidirectional fiber-reinforced composites [17] and the surface temperature of multilayered cylindrical samples [18]. Salazar et al [19] also extended this classical flash method to be used with non-planar samples, such as solid cylinders, hollow cylinders, and spheres. Recently, Madariaga and Salazar [20] exploited this elegant method to express the surface temperature of multilayered spherical samples with continuously varying in-depth thermal conductivity.…”

Section: Nomenclature λmentioning

confidence: 97%

Scattering of Thermal Waves and Non-steady Effective Thermal Conductivity of Unidirectional Fibrous Composites with Functionally Graded Interface

Fang

2008

Int J Thermophys

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In this paper, a thermal wave method is applied to investigate the non-steady effective thermal conductivity of unidirectional fibrous composites with a functionally graded interface, and the analytical solution of the problem is obtained. The Fourier heat conduction law is applied to analyze the propagation of thermal waves in the fibrous composite. The scattering and refraction of thermal waves by a cylindrical fiber with an inhomogeneous interface layer in the matrix are analyzed, and the results of the single scattering problem are applied to the composite medium. The wave fields in different material layers are expressed by using the wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary conditions of the layers. The theory of Waterman and Truell is employed to obtain the effective propagating wave number and the non-steady effective thermal conductivity of composites. As an example, the effects of a graded interface on the effective thermal conductivity of composites are graphically illustrated and analyzed. Analysis shows that the non-steady effective thermal conductivity under higher frequencies is quite different from the steady thermal conductivity. In the region of intermediate and high frequencies, the effect of the properties of the interface on the effective thermal conductivity is greater. Comparisons with the steady thermal conductivity obtained from other methods are also presented.

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“…For decades, research in photothermal techniques has been restricted to samples with flat surfaces. Specifically, with the increasing applications of photothermal radiometry (PTR) to the characterization of materials with curved surfaces, studies on nonflat (e.g., cylindrical or spherical) solids [6][7][8][9][10][11][12][13] have been reported in recent years. In this study, we present a generalized theoretical model of a multilayered spherical structure using the Green function method.…”

Section: Introductionmentioning

confidence: 99%

“…(a) Assumed thermal-conductivity depth profiles of two inhomogeneous solid spheres with different thermal gradients, Q (mm −1 ); (b1, b2) thermal-wave responses of two inhomogeneous spheres and comparison with results obtained with the quadrupole method; (c1, c2) normalized amplitude and phase at different azimuthal angles, θ ; and (d1, d2) the normalized amplitude and phase of spherical solids with various diameters at θ = 0 • the thermal-wave responses of the two inhomogeneous spheres, diameters = 2 mm with different Q, and the results obtained by the quadrupole method (line)[11] are shown for comparison. Different depth profiles with different Q factors imply different effective thicknesses of the inhomogeneous layer, which result in different peak or valley positions in both amplitude and phase channels.…”

mentioning

confidence: 96%

Modeling of Thermal-Wave Fields in Radially Inhomogeneous Spherical Solids Using the Green Function Method

Zhang¹,

Xie

Wang³

et al. 2012

Int J Thermophys

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A theoretical model for evaluating solid multilayered spherical solids heated by a frequency-modulated light beam using the Green function method is presented. The specific thermal-wave Green function corresponding to the composite structure has been derived. The characteristics of the thermal-wave field with respect to the thermophysical, geometrical, and measurement parameters are presented. Unlike the quadrupole method, the Green function method is capable of evaluating thermalwave fields at any point of multilayered structures with arbitrary intensity distributions of the incident laser beams. This study establishes applications of thermal-wave fields in both cylindrical and spherical samples using the Green function method and is of importance in characterizing radially inhomogeneous spherical solids.

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Thermal diffusivity of rods, tubes, and spheres by the flash method

Cited by 32 publications

References 6 publications

Multiple Scattering of Thermal Waves from a Subsurface Cylindrical Inclusion in Semi-infinite Functionally Graded Materials Using Non-Fourier Model

Multiple Scattering of Thermal Waves from a Subsurface Cylindrical Inclusion in Semi-infinite Functionally Graded Materials Using Non-Fourier Model

Scattering of Thermal Waves and Non-steady Effective Thermal Conductivity of Unidirectional Fibrous Composites with Functionally Graded Interface

Modeling of Thermal-Wave Fields in Radially Inhomogeneous Spherical Solids Using the Green Function Method

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