Effects of fractional and two-temperature parameters on stress distributions for an unbounded generalized thermoelastic medium with spherical cavity

Molla, Abul Kashim; Mondal, Nasiruddin; Mallik, Sadek Hossain

doi:10.1080/25765299.2019.1621511

Cited by 7 publications

(2 citation statements)

References 54 publications

(54 reference statements)

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“…In the limitless media, Mukhopadhyay and Kumar investigated the universal thermoelastic interactions with the cavity [19]. Many authors used spherical cavities to solve problems involving thermoelastic mediums [20][21][22][23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Influence of the fractional-order strain on an infinite material with a spherical cavity under Green-Naghdi hyperbolic two-temperature thermoelasticity theory

Youssef¹,

Alghamdi²

2023

J., eng., them. sci.

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In this work, a novel mathematical model of thermoelastic, homogenous, isotropic, and infinite medium with a spherical cavity has been constructed. Under the hyperbolic two-temperature Green-Naghdi theory of thermoelasticity type-I and type-III with fractional-order strain, the governing equations have been established. The bounding surface of the cavity has been thermally loaded by a ramp-type heat and is connected to a rigid foundation which prevents volumetric strain. Different values of the fractional-order and two-temperature parameters have shown numerical results for the dynamical and conductive temperature increment, strain, displacement, and average of principal stresses, which are graphically applicable to all the functions studied. The fractional-order parameter has significant effects on stress and strain distributions, while it has a limited effect on the dynamical and conductive temperatures increment. The hyperbolic two-temperature parameter has significant effects on all studied functions based on Green-Naghdi models of type-1 and type-II. Moreover, the ramp-time heat parameter has a significant impact on all the studied functions under all the studied models of thermoelasticity.

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Section: Introductionmentioning

confidence: 99%

Influence of the fractional-order strain on an infinite material with a spherical cavity under Green-Naghdi hyperbolic two-temperature thermoelasticity theory

Youssef¹,

Alghamdi²

2023

J., eng., them. sci.

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“…Mukhopadhyay and Kumar studied the general thermoelastic interactions with the cavity in the unlimited medium [25]. Many authors solved problems of thermoelastic medium with spherical cavity [26][27][28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

The Fractional Strain Influence on a Solid Sphere under Hyperbolic Two-Temperature Generalized Thermoelasticity Theory by Using Diagonalization Method

Youssef

El-Bary

Al-Lehaibi

2021

Mathematical Problems in Engineering

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This article constructs a mathematical model based on fractional-order deformations for a one-dimensional, thermoelastic, homogenous, and isotropic solid sphere. In the context of the hyperbolic two-temperature generalized thermoelasticity theory, the governing equations have been established. Thermally and without deformation, the sphere’s bounding surface is shocked. The singularities of the functions examined at the center of the world were decreased by using L’Hopital’s rule. Numerical results with different parameter fractional-order values, the double temperature function, radial distance, and time have been graphically illustrated. The two-temperature parameter, radial distance, and time have significant effects on all the studied functions, and the fractional-order parameter influences only mechanical functions. In the hyperbolic two-temperature theory as well as in one-temperature theory (the Lord-Shulman model), thermal and mechanical waves spread at low speeds in the thermoelastic organization.

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Waves in generalized thermo-viscoelastic infinite continuum with cylindrical cavity due to three-phase-lag time-nonlocal heat transfer

Molla

Mondal

Mallik

2020

Journal of Thermal Stresses

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Effects of fractional and two-temperature parameters on stress distributions for an unbounded generalized thermoelastic medium with spherical cavity

Abstract: Effects of fractional and two-temperature parameters on stress distributions for an unbounded generalized thermoelastic medium with spherical cavity,

Cited by 7 publications

References 54 publications

Influence of the fractional-order strain on an infinite material with a spherical cavity under Green-Naghdi hyperbolic two-temperature thermoelasticity theory

Influence of the fractional-order strain on an infinite material with a spherical cavity under Green-Naghdi hyperbolic two-temperature thermoelasticity theory

The Fractional Strain Influence on a Solid Sphere under Hyperbolic Two-Temperature Generalized Thermoelasticity Theory by Using Diagonalization Method

Waves in generalized thermo-viscoelastic infinite continuum with cylindrical cavity due to three-phase-lag time-nonlocal heat transfer

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