Effect of a general body force on a 2D generalized thermoelastic body with a cylindrical cavity

Sherief, Hany H.; El‐Maghraby, Nasser M.; Zaky, Mohamed F.

doi:10.1002/mma.5774

Cited by 6 publications

(4 citation statements)

References 20 publications

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“…Temperature variation in biological tissues was first noticed by Richardson et al [54]. In the present study, the mathematical model used for thermal conduction in living tissues is the generalized thermoelasticity theory with one relaxation time [30,[55][56][57]. Laplace and inverse Laplace transforms are used to solve the problem.…”

Section: Mathematical Formulationsmentioning

confidence: 95%

Mathematical modeling of heat transfer in tissues with skin tumor during thermotherapy

Sherief,

Zaky,

Abbas

et al. 2024

PLoS ONE

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The study of thermal therapy to tumors and the response of living cells to this therapy used to treat tumor is very important due to the complexity of heat transfer in biological tissues. In the past few years, there has been a growing interest among clinicians, mathematicians, and engineers regarding the use of computational and mathematical methods to simulate biological systems. Numerous medical proceedings also employ mathematical modeling and engineering techniques as a means to guarantee their safety and evaluate the associated risks effectively. This manuscript provides an analytical solution used for the first time to study the mechanism of biological thermal response during heat therapy on spheroidal skin tumor. The proposed method used a generalized thermoelasticity model with one relaxation time. The influence of relaxation times on the responses of diseased and healthy tissues is studied and interpreted graphically. Also, the impact of different laser irradiance on the thermal profile of the malignant tumor cells over a period of 2 minutes is interpreted graphically. To investigate the transfer of heat within biological tissues during the thermal therapy, the Laplace transform and inverse Laplace transform methods were applied. A comparison of the present generalized thermoelasticity model and different models based on Pennes bioheat transfer PBT shows that our proposed model yields more realistic and accurate predictions. The current model can be used to explain various therapeutic methods.

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Section: Mathematical Formulationsmentioning

confidence: 95%

Mathematical modeling of heat transfer in tissues with skin tumor during thermotherapy

Sherief,

Zaky,

Abbas

et al. 2024

PLoS ONE

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“…The stability of this theory has been studied by Sherief in 1987 who proved also the uniqueness of the theory [8]. Some works in the context of these two theories and their extensions can be found in [9][10][11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 97%

Dynamic response of a long cylinder under thermal shock in micropolar thermoelasticity

Sherief,

Abbas,

Zaky

et al. 2023

PLoS ONE

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In this manuscript, the dynamic response of a long cylinder subjected to an asymmetric thermal shock is investigated within the framework of generalized micropolar thermoelasticity. The displacement and micro-rotation are assumed to vanish at the surface. Laplace transformation techniques are used to solve the problem. The solution is obtained in the transformed field using an innovative direct approach. Furthermore, we obtain the inverse transformations using a numerical method based on Fourier expansion. The obtained results are carefully presented through graphical representations and discussed extensively across different relaxation time values. It is evident that the relaxation time parameter significantly influences all the distributions. The displacement distributions are always continuous, whereas all other functions, including temperature variation, stress distribution, and micro-rotation, exhibit discontinuity at the wave front. The results obtained hold significant importance in various technological applications and in the manufacturing of mechanical components.

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“…Sadeghi and Kiani [5] have discussed and solution for Magneto generalized thermoelasticity of a layer via the Green-Lindsay and Lord-Shulman Green-Lindsay theories. Sharif and others [6][7][8][9][10] are presented a number of research papers as an application of Lord and Shulman's theory.…”

Section: Introductionmentioning

confidence: 99%

The Influence of a Non-local thermoelasticity with Diffusion under Hydrostatic Pressure

Khader,

Marrouf,

Esmail

et al. 2023

Preprint

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This article is demonstrating the diffusion theory of thermoelasticity on a two-dimensional half-space problem. The surface is exposed to thermal shocks and hydrostatic loads. Chemical potential must be a known time function. The solution is obtained with the direct method using Laplace's techniques and Fourier's exponential transform. Local and non-local thermoelasticity were discussed and the influence of the non-local parameter on the generalized theory of thermoelastic diffusion was investigated. Chemical potential, concentration temperature, stress, and displacement distributions are computed numerically and represented by graphical.

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Effect of a general body force on a 2D generalized thermoelastic body with a cylindrical cavity

Cited by 6 publications

References 20 publications

Mathematical modeling of heat transfer in tissues with skin tumor during thermotherapy

Mathematical modeling of heat transfer in tissues with skin tumor during thermotherapy

Dynamic response of a long cylinder under thermal shock in micropolar thermoelasticity

The Influence of a Non-local thermoelasticity with Diffusion under Hydrostatic Pressure

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