Eigenvalue approach to fractional order generalized thermoelasticity with line heat source in an infinite medium

Gupta, N.; Das, N. C.

doi:10.1080/01495739.2016.1187987

Cited by 11 publications

(4 citation statements)

References 20 publications

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“…To solve Equation ( 24) using the eigenvalue techniques described in [39][40][41][42][43][44][45][46][47][48], Matrix B's characteristic equation is expressed as:…”

Section: Analytical Solutions In the Transform Domainmentioning

confidence: 99%

The Effect of Fractional Derivatives on Thermo-Mechanical Interaction in Biological Tissues during Hyperthermia Treatment Using Eigenvalues Approach

Hobiny

Abbas

2023

Fractal Fract

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This article studies the effects of fractional time derivatives on thermo-mechanical interaction in living tissue during hyperthermia treatment by using the eigenvalues approach. A comprehensive understanding of the heat transfer mechanism and the related thermo-mechanical interactions with the patient’s living tissues is crucial for the effective implementation of thermal treatment procedures. The surface of living tissues is traction-free and is exposed to a pulse boundary heat flux that decays exponentially. The Laplace transforms and their associated techniques are applied to the generalized bio-thermo-elastic model, and analytical procedures are then implemented. The eigenvalue approach is utilized to obtain the solution of governing equations. Graphical representations are given for the temperature, the displacement, and the thermal stress results. Afterward, a parametric study was carried out to determine the best method for selecting crucial design parameters that can improve the precision of hyperthermia therapies.

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“…To solve Equation ( 24) using the eigenvalue techniques described in [39][40][41][42][43][44][45][46][47][48], Matrix B's characteristic equation is expressed as:…”

Section: Analytical Solutions In the Transform Domainmentioning

confidence: 99%

The Effect of Fractional Derivatives on Thermo-Mechanical Interaction in Biological Tissues during Hyperthermia Treatment Using Eigenvalues Approach

Hobiny

Abbas

2023

Fractal Fract

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“…By using the eigenvalue technique as described in [36][37][38][39][40][41][42][43] regarding the solutions of Equation ( 30), the characteristic relation of matrix A may be expressed as…”

Section: Linear Case (With Kirchhoff's Transformation)mentioning

confidence: 99%

The Effects of Variable Thermal Conductivity in Thermoelastic Interactions in an Infinite Material with and without Kirchhoff’s Transformation

Hobiny

Abbas

2022

Mathematics

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In this paper, the problem of an unbonded material under variable thermal conductivity with and without Kirchhoff’s transformations is investigated. The context of the problem is the generalized thermoelasticity model. The boundary plane of the medium is exposed to a thermal shock that is time-dependent and considered to be traction-free. Because nonlinear formulations are difficult, the finite element method is applied to solve the problem without Kirchhoff’s transformations. In a linear case, when using Kirchhoff’s transformations, the problem’s solution is derived using the Laplace transforms and the eigenvalue approach. The effect of variable thermal conductivity is discussed and compared with and without Kirchhoff’s transformations. The graphical representations of numerical results are shown for the distributions of temperature, displacement and stress

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“…In order to investigate the propagation of thermoelastic waves, we need to decouple the equations (19) and (20). As such we transform the equations in the space time domain to a Laplace transform domain of parameter…”

Section: Wave Propagation In a Layermentioning

confidence: 99%

Eigenvalue Approach on Generalized Thermoelastic Interactions of a Layer

Gangopadhyaya¹,

Roy²,

Sahoo³

et al. 2018

IJMTT

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The unified form of the basic equations of generalized thermoelastic interactions for Lord Shulman (LS) and Green Lindsay (GL) models for a layer have been written in the form of a vector matrix differential equation and solved by the eigen value approach technique in the Laplace transform domain in a closed form. The inversions of the physical variables from the transformed domain have been made by using Zakian algorithm for the numerical inversion from the Laplace transform domain. Graphs for the physical variables have been presented for different cases and the results are compared with the existing literature.

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Eigenvalue approach to fractional order generalized thermoelasticity with line heat source in an infinite medium

Cited by 11 publications

References 20 publications

The Effect of Fractional Derivatives on Thermo-Mechanical Interaction in Biological Tissues during Hyperthermia Treatment Using Eigenvalues Approach

The Effect of Fractional Derivatives on Thermo-Mechanical Interaction in Biological Tissues during Hyperthermia Treatment Using Eigenvalues Approach

The Effects of Variable Thermal Conductivity in Thermoelastic Interactions in an Infinite Material with and without Kirchhoff’s Transformation

Eigenvalue Approach on Generalized Thermoelastic Interactions of a Layer

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