Two-dimensional problem for thermoviscoelastic materials with fractional order heat transfer

Hendy, Mohamed H.; Amin, Magdy M.; Ezzat, Magdy A.

doi:10.1080/01495739.2019.1623734

Cited by 39 publications

(11 citation statements)

References 59 publications

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“…El-Karamany and Ezzat (2016) built the heat transfer in anisotropical and isotropic materials with two delays and the functions of the kernel within the context of a newly and expanding theory of thermo-equilibrium. Hendy et al (2019) solved the thermo-viscoelastic two-dimensional problem by using the state–space approach (Ezzat, 2008). Ezzat et al (2014, 2016) evaluated the thermal behavior of living tissue subjected to instant surface heating.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional thermo-mechanical fractional responses to biological tissue with rheological properties

Ezzat

Lewis

2021

HFF

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Purpose The system of equations for fractional thermo-viscoelasticity is used to investigate two-dimensional bioheat transfer and heat-induced mechanical response in human skin tissue with rheological properties. Design/methodology/approach Laplace and Fourier’s transformations are used. The resulting formulation is applied to human skin tissue subjected to regional hyperthermia therapy for cancer treatment. The inversion process for Fourier and Laplace transforms is carried out using a numerical method based on Fourier series expansions. Findings Comparisons are made with the results anticipated through the coupled and generalized theories. The influences of volume materials properties and fractional order parameters for all the regarded fields are examined. The results indicate that volume relaxation parameters, as well as fractional order parameters, play a major role in all considered distributions. Originality/value Bio-thermo-mechanics includes bioheat transfer, biomechanics, burn injury and physiology. In clinical applications, knowledge of bio-thermo-mechanics in living tissues is very important. One can infer from the numerical results that, with a finite distance, the thermo-mechanical waves spread to skin tissue, removing the unrealistic predictions of the Pennes’ model.

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Section: Introductionmentioning

confidence: 99%

Two-dimensional thermo-mechanical fractional responses to biological tissue with rheological properties

Ezzat

Lewis

2021

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“…Fractional calculus is a mathematical problem to study integral and differential of arbitrary order. Fractional calculus has many applications, such as physical system modeling [1][2][3], control theory [4][5][6], and so on. In control theory, as fractional calculus is more and more applied to the design and analysis of controllers and filters, the research on approximation methods of fractional order systems or operator models has attracted more and more attention [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Rational Implementation of Fractional Calculus Operator Based on Quadratic Programming

2021

Mathematical Problems in Engineering

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When fractional calculus operators and models are implemented rationally, there exist some problems such as low approximation accuracy of rational approximation function, inability to specify arbitrary approximation frequency band, or poor robustness. Based on the error criterion of the least squares method, a quadratic programming method based on the frequency-domain error is proposed. In this method, the frequency-domain error minimization between the fractional operator s ± r and its rational approximation function is transformed into a quadratic programming problem. The results show that the construction method of the optimal rational approximation function of fractional calculus operator is effective, and the optimal rational approximation function constructed can effectively approximate the fractional calculus operator and model for the specified approximation frequency band.

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“…Hendy et al. [17] studied two‐dimensional problem for thermo viscoelastic materials with fractional order heat transfer. Yu et al.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal response of multi‐field coupling elastic medium based on fractional order strain

Wang

Huang

2021

Z Angew Math Mech

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In this work, a three‐dimensional model of the generalized thermoelasticity with fractional order stain and nonlocal effect is established. Nonlocal effect is used to depict size‐dependence feature and fractional order strain is considered to describe memory‐dependence properties. The Laplace and double Fourier transform techniques are applied to the three‐dimensional half‐space model subjected to thermal shock and traction free surface. A complex inversion formula of the transform with the techniques of the Fourier expansion been applied to obtain the inverses of double Fourier transforms, and Laplace transforms. Numerical results for the temperature, stress, strain and displacement are represented graphically based on various values of the fractional order strain parameter and elastic nonlocal parameter. The fractional order strain and nonlocal parameter has a limited effect on the thermal waves while it has significant effects on the mechanical waves.

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Two-dimensional problem for thermoviscoelastic materials with fractional order heat transfer

Cited by 39 publications

References 59 publications

Two-dimensional thermo-mechanical fractional responses to biological tissue with rheological properties

Two-dimensional thermo-mechanical fractional responses to biological tissue with rheological properties

Rational Implementation of Fractional Calculus Operator Based on Quadratic Programming

Nonlocal response of multi‐field coupling elastic medium based on fractional order strain

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