Existence and stability results for thermoelastic dipolar bodies with double porosity

Marín, Marín; Nicaise, Serge

doi:10.1007/s00161-016-0503-4

Cited by 80 publications

(43 citation statements)

References 23 publications

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“…Lotfy et al [17] investigated the response of a semiconductor medium of variable thermal conductivity due to laser pulses with two temperatures through the photothermal process. Many researchers [18][19][20][21][22][23][24][25][26] have solved various problems under generalized thermoelastic models. In the Laplace domain, the eigenvalues approach gave an analytical solution without any supposed restrictions on the factual physical variables.…”

Section: Introductionmentioning

confidence: 99%

Photo-Thermal Interactions in a Semiconducting Media with a Spherical Cavity under Hyperbolic Two-Temperature Model

Alzahrani

Abbas

2020

Mathematics

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This article highlights the study of photo-thermoelastic interaction in an unbounded semiconductor medium containing a spherical cavity. This problem is solved using the new hyperbolic two-temperature model. The bounding surface of the cavity is traction free and loaded thermally by exponentially decaying pulse boundary heat flux. In addition, the carrier density is prescribed on the inner surface of the cavity in terms of the recombination speed. The techniques of Laplace transforms are used to get the analytical solutions of the problem in the transformed domain by the eigenvalues method. The inversions of Laplace transformations have been carried out numerically. The outcomes also display that the analytical schemes can overcome the mathematical problem to analyze this problem. Numerical outcomes for a semiconductor material are performed and demonstrated graphically. According to the numerical results, this new hyperbolic two-temperature model of thermoelasticity offers finite speed of the thermal wave and mechanical wave propagation.

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Section: Introductionmentioning

confidence: 99%

Photo-Thermal Interactions in a Semiconducting Media with a Spherical Cavity under Hyperbolic Two-Temperature Model

Alzahrani

Abbas

2020

Mathematics

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“…El-Naggar et al [20] studied the effects of the initial stress, magnetic field, voids, and rotation on plane waves in generalized thermoelasticity. Marin and Marin et al [21][22][23] used various models to study the dipolar bodies. Abbas [24] studied the nonlinear transient thermal stress analysis of a thick-walled FGM cylinder with temperature-dependent material properties.…”

Section: Introductionmentioning

confidence: 99%

The Effect of Fractional Time Derivative of Bioheat Model in Skin Tissue Induced to Laser Irradiation

et al. 2020

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This work uses the “fractional order bio-heat model” (Fob) model of heat conduction to offer a new interpretation to study the thermal damages in a skin tissue caused by laser irradiation. The influences of fractional order and the thermal relaxation time parameters on the temperature of skin tissue and the resulting thermal damage are studied. In the Laplace domain, the analytical solutions of temperature are obtained. Using the equation of Arrhenius, the resulting thermal injury to the tissues is assessed by the denatured protein ranges. The numerical results of the thermal damages and temperature are presented graphically. A parametric analysis is dedicated to the identifications of suitable procedures for the selection of significant design variables to achieve an effective thermal in the therapy of hyperthermia.

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“…In this sense, it is enough to list a few studies, such as Mindlin [19], Green and Rivlin [20], or Fried and Gurtin [21], which have a good recognition among researchers. Then the number of approaches of these media with dipolar structure has increased considerably [22][23][24][25][26][27][28][29][30][31][32]. Our study is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

On the decay of exponential type for the solutions in a dipolar elastic body

Marín

Ellahi

Vlase

et al. 2020

Journal of Taibah University for Science

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Our study is concerned with a generalization of the principle of Saint-Venant in the context of the theory of elastic bodies with a dipolar structure. It is an extension of the form of this principle proposed by Toupin in the case of classical linear elasticity. We consider a straight cylinder which is occupied by an dipolar elastic body that is only loaded at one end and our main finding proves that the internal energy in a portion of this cylinder, that is located at a given distance regarding the end that is loaded, is exponentially decreasing, regarding the respective distance. ARTICLE HISTORY

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Existence and stability results for thermoelastic dipolar bodies with double porosity

Cited by 80 publications

References 23 publications

Photo-Thermal Interactions in a Semiconducting Media with a Spherical Cavity under Hyperbolic Two-Temperature Model

Photo-Thermal Interactions in a Semiconducting Media with a Spherical Cavity under Hyperbolic Two-Temperature Model

The Effect of Fractional Time Derivative of Bioheat Model in Skin Tissue Induced to Laser Irradiation

On the decay of exponential type for the solutions in a dipolar elastic body

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