Refined Lord–Shulman Theory for 1D Response of Skin Tissue under Ramp-Type Heat

Sobhy, Mohammed; Zenkour, Ashraf M.

doi:10.3390/ma15186292

Cited by 10 publications

(5 citation statements)

References 49 publications

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“…where ∇ 2 = ∂ 2 ∂x 2 + ∂ 2 ∂z 2 ; θ = T − T 0 , wherein T is the temperature over the reference temperature T 0 ; = ρ is the medium density; c e is the certain heat at constant strain, K is the parameter of thermal conductivity; e = e kk = u k,k is the volumetric strain where u i is the components of displacement; γ = α t (3λ + 2µ) is the parameter of thermoelastic coupling in which λ, µ are Lame's constants and α t is the coefficient of thermal expansion; and D 1 , D m 1 are the operators of time-derivative, which can be written as [33][34][35][36][37][38][39][40],…”

Section: Basic Governing Equationsmentioning

confidence: 99%

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A Modified Two-Relaxation Thermoelastic Model for a Thermal Shock of Rotating Infinite Medium

Aljadani

Zenkour

2022

Materials

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A unified form of thermoelasticity theory that contains three familiar generalized thermoelasticity. The Lord–Shulman theory, Green–Lindsay theory, and the classical one can be outlined in this form. The field quantities of a rotating/non-rotating half-space with and without the effect of the decay parameter can be obtained due to the unified thermoelasticity theory. The present medium is subjected to a time-dependent thermal shock taking into account that the magnitude of the thermal shock wave is not totally fixed but decaying over time. A special case of a thermal shock waveform with constant magnitude may be considered. The field quantities such as temperature, displacements, and stresses of the present problem are analytically obtained. Some plots of these field variables are presented in two- and three-dimensional illustrations in the context of refined theories.

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Section: Basic Governing Equationsmentioning

confidence: 99%

“…It must be mentioned that three terms having exponentials of growing in nature in the space variables x were omitted in the present approach. The following results are given by inserting Equation (36) into Equations ( 22) and ( 23)…”

Section: Solution Of the Problemmentioning

confidence: 99%

A Modified Two-Relaxation Thermoelastic Model for a Thermal Shock of Rotating Infinite Medium

Aljadani

Zenkour

2022

Materials

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“…Here, the classical Fourier's law is replaced by an approximation to a modification of the law with two different translations for the heat flux vector and the temperature gradient. In the last few years, some of the important investigations in thermoelastic media under the purview of DPL theory are performed by Zenkour [4][5][6][7], Zenkour and El-Shahrany [8], Kutbi and Zenkour [9] and Zenkour et al [10].…”

Section: Introductionmentioning

confidence: 99%

“…In the last few years, some of the important investigations in thermoelastic media under the purview of DPL theory are performed by Zenkour [4–7], Zenkour and El‐Shahrany [8], Kutbi and Zenkour [9] and Zenkour et al. [10].…”

Section: Introductionmentioning

confidence: 99%

Nonlocal and dual‐phase‐lag effects in a transversely isotropic exponentially graded thermoelastic medium with voids

Barak,

Poonia,

Devi

et al. 2024

Z Angew Math Mech

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The aim of the present work is to examine the thermally induced disturbances in a transversely isotropic nonlocal exponentially graded (nonhomogeneous) thermoelastic half‐space with voids within the framework of dual‐phase‐lag (DPL) theory. It is supposed that the material's properties are graded in z‐direction. By employing normal mode technique, the exact expressions of the temperature field, the change in volume fraction field, displacement and stress components are obtained. The obtained results are computed numerically for a magnesium crystal‐like material and depicted graphically to display the effects of material's anisotropy, non‐homogeneity parameter, generalized theories, nonlocal parameter, void parameter and time on the variations of different physical fields. Certain limiting cases of interest have been deduced from the present investigation.

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“…Kumar et al [ 26 ] display the heat damage that skin tissue sustained while being exposed to a moving thermal source and the DPL theory of biological heat transport is used to model the issue based on a memory-dependent derivative. Recently, Sobhy and Zenkour [ 27 ] presented a theory of skin tissue response that considered accounting for the effect of higher-order time derivatives based on the Lord and Shulman model.…”

Section: Introductionmentioning

confidence: 99%

Refined Dual-Phase-Lag Theory for the 1D Behavior of Skin Tissue under Ramp-Type Heating

2023

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In this article, a mathematical analysis of thermoelastic skin tissue is presented based on a refined dual-phase-lag (DPL) thermal conduction theory that considers accounting for the effect of multiple time derivatives. The thin skin tissue is regarded as having mechanically clamped surfaces that are one-dimensional. Additionally, the skin tissue undergoes ramp-type heating on its outer surface, whereas its inner surface keeps the assessed temperature from vanishing. Some of the previous generalized thermoelasticity theories were obtained from the proposed model. The distributions of temperature, displacement, dilatation, and stress are attained by applying the Laplace transform and its numerical reversal approaches. The outcomes are explicitly illustrated to examine the significant influences on the distributions of the field variables. The refined DPL bioheat conduction model in this study predicts temperature, and the findings revealed that the model is located among the existing generalized thermoelastic theories. These findings offer a more thorough understanding of how skin tissue behaves when exposed to a particular boundary condition temperature distribution.

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Refined Lord–Shulman Theory for 1D Response of Skin Tissue under Ramp-Type Heat

Cited by 10 publications

References 49 publications

A Modified Two-Relaxation Thermoelastic Model for a Thermal Shock of Rotating Infinite Medium

A Modified Two-Relaxation Thermoelastic Model for a Thermal Shock of Rotating Infinite Medium

Nonlocal and dual‐phase‐lag effects in a transversely isotropic exponentially graded thermoelastic medium with voids

Refined Dual-Phase-Lag Theory for the 1D Behavior of Skin Tissue under Ramp-Type Heating

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