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Journal ArticleDOI

Characterization of the photothermal interaction of a semiconducting solid sphere due to the mechanical damage and rotation under Green-Naghdi theories

TL;DR: In this article, a new mathematical model of a thermoelastic semiconducting solid sphere based on the Green-Naghdi theories was proposed to study the photothermal interaction.
Abstract: The present paper is dealing with a new mathematical model of a thermoelastic semiconducting solid sphere based on the Green-Naghdi theories to study the photothermal interaction. We applied two co...
Citations
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TL;DR: In this paper, a mathematical model based on fractional-order deformations for a one-dimensional, thermoelastic, homogenous, and isotropic solid sphere was constructed.
Abstract: This article constructs a mathematical model based on fractional-order deformations for a one-dimensional, thermoelastic, homogenous, and isotropic solid sphere. In the context of the hyperbolic two-temperature generalized thermoelasticity theory, the governing equations have been established. Thermally and without deformation, the sphere’s bounding surface is shocked. The singularities of the functions examined at the center of the world were decreased by using L’Hopital’s rule. Numerical results with different parameter fractional-order values, the double temperature function, radial distance, and time have been graphically illustrated. The two-temperature parameter, radial distance, and time have significant effects on all the studied functions, and the fractional-order parameter influences only mechanical functions. In the hyperbolic two-temperature theory as well as in one-temperature theory (the Lord-Shulman model), thermal and mechanical waves spread at low speeds in the thermoelastic organization.

4 citations


Cites background from "Characterization of the phototherma..."

  • ...-e constitutive equations with damage mechanics variable [10, 20] are σrr � 1 + τ α 1D α t ( 􏼁 2μerr + λe ( 􏼁 − c TD − T0 ( 􏼁, (3) σψψ � 1 + τ α 1D α t ( 􏼁 2μeψψ + λe 􏼐 􏼑 − c TD − T0 ( 􏼁, (4)...

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  • ...(17) -e following nondimensional variables are used for convenience [5, 9, 10]: r′, u′, a′ 􏼈 􏼉 � coη r, u, a { },...

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  • ...-e hyperbolic two-temperature heat conduction equations take the forms [10, 14, 20] K∇(2)TC � ρCE z zt + τ0 z 2...

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Journal ArticleDOI
TL;DR: In this article , a modified fractional photothermal model was proposed to investigate the interaction of light and heat within a magnetized semiconductor sphere rotating at a constant angular speed, where the Laplace transform was used to obtain solutions for optical excitation induced by physical field variables.
Abstract: By considering the Moore–Gibson–Thompson (MGT) equation, the current work introduces a modified fractional photothermal model. The construction model is based on the proportional Caputo fractional derivative, which is a new definition of the fractional derivative that is simple and works well. In addition, the theory of heat transfer in semiconductor materials was used in the context of optical excitation transfer and plasma processes. The proposed model was used to investigate the interaction of light and heat within a magnetized semiconductor sphere rotating at a constant angular speed. The Laplace transform was used to obtain solutions for optical excitation induced by physical field variables. Using a numerical method, Laplace transforms can be reversed. The figures show the effects of carrier lifetime, conformable fractional operator, and rotation on thermal and mechanical plasma waves, which are shown in the graphs. The theory’s predictions were compared and extensively tested against other existing models.

2 citations

Journal ArticleDOI
25 Aug 2021
TL;DR: In this article, the authors used the diagonalization method for the new modeling of a homogeneous, thermoelastic, and isotropic solid sphere that has been subjected to mechanical damage.
Abstract: This study is the first to use the diagonalization method for the new modelling of a homogeneous, thermoelastic, and isotropic solid sphere that has been subjected to mechanical damage. The fundamental equations were derived using the hyperbolic two-temperature generalized thermoelasticity theory with mechanical damage taken into account. The outer surface of the sphere has been assumed to have been shocked thermally without cubical dilatation. The numerical results for the dynamical and conductive temperatures increment, strain, displacement, and average of the principal stresses components have been represented graphically with different values of the hyperbolic two-temperature parameter and mechanical damage parameters. The two-temperature model parameter and the mechanical damage parameter have significant effects. The propagations of the thermomechanical waves take place at finite speeds in the context of the hyperbolic two-temperature theory as well as in the usual context of the Lord–Shulman theory with one-temperature.

1 citations

References
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Journal ArticleDOI
TL;DR: In this article, a generalized dynamical theory of thermoelasticity is formulated using a form of the heat transport equation which includes the time needed for acceleration of heat flow.
Abstract: In this work a generalized dynamical theory of thermoelasticity is formulated using a form of the heat transport equation which includes the time needed for acceleration of the heat flow. The theory takes into account the coupling effect between temperature and strain rate, but the resulting coupled equations are both hyperbolic. Thus, the paradox of an infinite velocity of propagation, inherent in the existing coupled theory of thermoelasticity, is eliminated. A solution is obtained using the generalized theory which compares favourably with a known solution obtained using the conventional coupled theory.

3,266 citations


"Characterization of the phototherma..." refers background or methods in this paper

  • ...The constitutive equations with damage mechanics variable [35]:...

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  • ...The heat conduction equation based on Green-Naghdi models takes the form [35]:...

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Journal ArticleDOI
TL;DR: In this paper, the authors present the best known elasticity data for silicon, both in depth and in a summary form, so that it may be readily accessible to MEMS designers.
Abstract: The Young's modulus (E) of a material is a key parameter for mechanical engineering design. Silicon, the most common single material used in microelectromechanical systems (MEMS), is an anisotropic crystalline material whose material properties depend on orientation relative to the crystal lattice. This fact means that the correct value of E for analyzing two different designs in silicon may differ by up to 45%. However, perhaps, because of the perceived complexity of the subject, many researchers oversimplify silicon elastic behavior and use inaccurate values for design and analysis. This paper presents the best known elasticity data for silicon, both in depth and in a summary form, so that it may be readily accessible to MEMS designers.

1,741 citations

Journal ArticleDOI
TL;DR: In this article, a universal constitutive equation between the heat flux vector and the temperature gradient is proposed to cover the fundamental behaviors of diffusion, wave, phonon-electron interactions, and pure phonon scattering.
Abstract: A universal constitutive equation between the heat flux vector and the temperature gradient is proposed to cover the fundamental behaviors of diffusion (macroscopic in both space and time), wave (macroscopic in space but microscopic in time), phonon-electron interactions (microscopic in both space and time), and pure phonon scattering The model is generalized from the dual-phase-lag concept accounting for the laging behavior in the high-rate response While the phase lag of the heat flux captures the small-scale response in time, the phase lag of the temperature gradient captures the small-scale response in space The universal form of the energy equation facilitates identifications of the physical parameters governing the transition from one mechanism (such as diffusion or wave) to another (the phonon-electron interaction)

1,435 citations


"Characterization of the phototherma..." refers background in this paper

  • ...For convergence with faster prosses, the value j satisfies the relation jt 4:7[45]....

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  • ...The Laplace transform of any function can be inverted as [45]:...

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Journal ArticleDOI
Andrew C. Tam1
TL;DR: In this article, the theory and applications of photo-acoustic (also called optoacoustic) methods belonging to the more general area of photothermal measurement techniques are reviewed, covering excitation of gaseous or condensed samples with modulated continuous light beams or pulsed light beams.
Abstract: This paper reviews the theory and applications of photoacoustic (also called optoacoustic) methods belonging to the more general area of photothermal measurement techniques. The theory covers excitation of gaseous or condensed samples with modulated continuous light beams or pulsed light beams. The applications of photoacoustic methods include spectroscopy, monitoring deexcitation processes, probing physical properties of materials, and generating mechanical motions. Several other related photothermal methods, as well as particle-acoustics and wave-acoustics methods are also described. This review complements an earlier and narrower review [Rev. Mod. Phys. 53, 517 (1981)] that is mainly concerned with sensitive detection by pulsed photoacoustic spectroscopy in condensed matter.

1,183 citations