A 2D problem of time-fractional heat order for two-temperature thermoelasticity under hydrostatic initial stress

doi:10.1080/15376494.2016.1255826

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A 2D problem of time-fractional heat order for two-temperature thermoelasticity under hydrostatic initial stress

Journal Article•DOI•

A 2D problem of time-fractional heat order for two-temperature thermoelasticity under hydrostatic initial stress

Nantu Sarkar¹, Kh. Lotfy²•Institutions (2)

University of Calcutta¹, Zagazig University²

12 Mar 2018-Mechanics of Advanced Materials and Structures (Taylor & Francis)-Vol. 25, Iss: 4, pp 279-285

TL;DR: In this article, the authors solved the problem of thermoelastic interactions in a half-space medium under hydrostatic initial stress in the context of a fractional order heat conduction model with two-temperature theory.

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Abstract: The present study solves the problem of thermoelastic interactions in a half-space medium under hydrostatic initial stress in the context of a fractional order heat conduction model with two-temperature theory. The analytical solutions of the field variables are obtained by using the normal mode analysis. The obtained solutions are then applied to a specific problem for a thermally insulated surface which is acted upon by a load. The distributions of the two temperatures, displacements, and the stress components inside the half-space are studied. The graphical results depict that the fractional parameter has significant effects on all the studied field variables. Comparisons are made within the theory in the presence and absence of the hydrostatic initial stress. Thus, we can conclude that the fractional order generalized thermoelasticity model may be an improvement on studying elastic materials.

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Journal Article•DOI•

Memory response on wave propagation in a thermoelastic plate due to moving band-type thermal loads and magnetic field

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Abhik Sur, Sudip Mondal, Mridula Kanoria¹•Institutions (1)

University of Calcutta¹

17 Feb 2021-Mechanics Based Design of Structures and Machines

TL;DR: The main concern of as mentioned in this paper is to deal with the thermoelastic interaction in a thick plate subjected to a moving heat source and being enlightened by memory-dependent derivative (MDD).

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Abstract: The main concern of this article is to deal with the thermoelastic interaction in a thick plate subjected to a moving heat source and being enlightened by memory-dependent derivative (MDD). Due to ...

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25 citations

Journal Article•DOI•

On thermoelectric materials with memory-dependent derivative and subjected to a moving heat source

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Mohamed H. Hendy¹, Sayed I. El-Attar¹, Magdy A. Ezzat², Magdy A. Ezzat³•Institutions (3)

Northern Borders University¹, Alexandria University², Qassim University³

01 Feb 2020-Microsystem Technologies-micro-and Nanosystems-information Storage and Processing Systems

TL;DR: In this article, a generalized thermoelasticity with memory-dependent derivative (MDD) heat conduction law for a thermoelectric half-space was developed.

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Abstract: We develop a model of generalized thermoelasticity with memory-dependent derivative (MDD) heat conduction law for a thermoelectric half-space. Some urgent theories take after as most remote point cases. The Laplace transform and state-space procedures are utilized to urge the overall account for any arrangement of limit conditions. The general solution acquired is connected to the particular issue of a half-space exposed to a uniform magnetic field, a moving heat source with consistent speed and ramp-type heating. The inverse Laplace transforms are registered numerically. The impacts of various estimations of the figure-of-merit quantity, heat source speed, MDD parameters, the magnetic number and the ramping time parameter are thought about.

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13 citations

Journal Article•DOI•

Interaction of thermal and mechanical waves in axisymmetric generalized thermoelasticity of rotating disk

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Yaser Kiani¹•Institutions (1)

Shahrekord University¹

04 May 2021-Waves in Random and Complex Media

TL;DR: In this paper, a numerical solution for the coupled thermomechanical response of a rotating annular disk which is subjected to the combined action of thermal and mechanical loads is proposed.

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Abstract: This study proposes a numerical solution for the coupled thermomechanical response of a rotating annular disk which is subjected to the combined action of thermal and mechanical loads. The annular ...

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10 citations

Cites methods from "A 2D problem of time-fractional hea..."

...Lotfy and Sarkar [18] proposed a novel generalizedmodel of photothermal theorywith two-temperature thermoelasticity theory basedonmemory-dependent derivative theory....
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...Thermoelastic interactions in a half-space medium under hydrostatic initial stress in the context of a fractional order heat conduction model with two-temperature theory is performed by Sarkar and Lotfy [19]....
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...Lotfy and Allan [11] performed an investigation on the effects of rotation and magnetic field in a twodimensional thermoelastic medium....
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...Lotfy [17] performed an investigation on the heat conduction of a semi-conductor medium containing a spherical cavity....
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...For the case of viscoelastic materials, Lotfy [13] performed an investigation on the transient disturbances created by an internal line heat source that suddenly starts moving uniformly inside a visco-elastic half-space....
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Journal Article•DOI•

Plane Harmonic Waves in Thermoelastic Materials with a Memory-Dependent Derivative

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M. Bachher

01 Jan 2019-Journal of Applied Mechanics and Technical Physics

TL;DR: In this paper, the Lord-Shulman theory of generalized thermoelasticity based on a memory-dependent derivative is employed to study the propagation of plane harmonic waves in a two-dimensional semi-infinite thermo-elastic medium.

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Abstract: The Lord-Shulman theory of generalized thermoelasticity based on a memory-dependent derivative is employed to study the propagation of plane harmonic waves in a two-dimensional semi-infinite thermoelastic medium. The numerical solution is analyzed for various values of the time delay parameter.

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6 citations

Journal Article•DOI•

Three-dimensional thermal shock problem in the frame of memory-dependent generalized thermoelasticity

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Nantu Sarkar¹, Mohamed I. A. Othman²•Institutions (2)

University of Calcutta¹, Zagazig University²

01 Mar 2021-Indian Journal of Physics

TL;DR: In this article, the Lord-Shulman theory of generalized thermoelasticity based on a memory-dependent derivative is employed to study the thermo-elastic response in a three-dimensional elastic half-space medium whose free surface is assumed to be traction-free and subjected to a thermal shock.

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Abstract: The Lord–Shulman theory of generalized thermoelasticity based on a memory-dependent derivative is employed to study the thermoelastic response in a three-dimensional elastic half-space medium whose free surface is assumed to be traction-free and subjected to a thermal shock. The numerical solutions for the field variables are presented graphically and analyzed for various values of the time delay parameter. The predictions of the new model are discussed and compared with the Lord–Shulman model (without memory-dependent derivative).

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5 citations

References

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Journal Article•DOI•

Fractional order theory of thermoelasticity

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Hany H. Sherief¹, Ahmed M. A. El-Sayed¹, A. M. Abd El-Latief¹•Institutions (1)

Alexandria University¹

15 Jan 2010-International Journal of Solids and Structures

TL;DR: In this paper, a new theory of thermoelasticity is derived using the methodology of fractional calculus, and a uniqueness theorem for this model is proved and a variational principle and a reciprocity theorem are derived.

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445 citations

"A 2D problem of time-fractional hea..." refers background in this paper

...[2] introduced a fractional order theory of thermoelasticity....
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Journal Article•DOI•

Theory of two-temperature-generalized thermoelasticity

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Hamdy M. Youssef¹•Institutions (1)

Alexandria University¹

01 Jun 2006-Ima Journal of Applied Mathematics

TL;DR: In this article, a new theory of generalized thermoelasticity has been constructed by taking into account the theory of heat conduction in deformable bodies, which depends on two distinct temperatures, the conductive temperature and the thermodynamic temperature, where the difference between these two temperatures is proportional to the heat supply.

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Abstract: In this paper, a new theory of generalized thermoelasticity has been constructed by taking into account the theory of heat conduction in deformable bodies, which depends on two distinct temperatures, the conductive temperature and the thermodynamic temperature, where the difference between these two temperatures is proportional to the heat supply. The uniqueness theorem is obtained for equations of two-temperature-generalized linear thermoelasticity for a homogeneous and isotropic body.

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377 citations

"A 2D problem of time-fractional hea..." refers background in this paper

...Youssef [3] deduced a theory of fractional order generalized thermoelasticity....
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...[19] H. M. Youssef, Theory of two-temperature-generalized thermoelasticity, IMA J. Appl....
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...The governing equations of linear, © Taylor & Francis Group, LLC homogenous, and isotropic fractional order generalized thermoelasticity WHIS (Montanaro [12], Youssef [19], and Ezzat et al. [5]) as follows: σi j = −p(δi j + ωi j)+ 2μei j + (λekk − γ θ ) δi j, (1) ei j = 12 (ui, j + uj,i), (2) ωi j = 12 (uj,i − ui, j), (3) σi j, j = ρüi, (4) k∇2φ = ∂ ∂t ( 1 + τ α 0 α!...
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...homogenous, and isotropic fractional order generalized thermoelasticity WHIS (Montanaro [12], Youssef [19], and Ezzat et al....
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...[6] H. M. Youssef, State-space approach to fractional order twotemperature generalized thermoelastic medium subjected to moving heat source, Mech....
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Journal Article•DOI•

Theory of Fractional Order Generalized Thermoelasticity

[...]

Hamdy M. Youssef¹•Institutions (1)

Alexandria University¹

01 Jun 2010-Journal of Heat Transfer-transactions of The Asme

300 citations

"A 2D problem of time-fractional hea..." refers background in this paper

...Youssef [3] deduced a theory of fractional order generalized thermoelasticity....
[...]

Journal Article•DOI•

Magneto-thermoelasticity with thermoelectric properties and fractional derivative heat transfer

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Magdy A. Ezzat¹•Institutions (1)

Alexandria University¹

01 Jan 2011-Physica B-condensed Matter

TL;DR: In this article, a new model of the magneto-thermoelasticity theory has been constructed in the context of a new consideration of heat conduction with fractional derivative.

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Abstract: In this work, a new model of the magneto-thermoelasticity theory has been constructed in the context of a new consideration of heat conduction with fractional derivative. A one-dimensional application for a conducting half-space of thermoelectric elastic material, which is thermally shocked in the presence of a magnetic field, has been solved using Laplace transform and state-space techniques (Ezzat, 2008 [1]). According to the numerical results and its graphs, a conclusion about the new theory of magneto-thermoelasticity has been constructed. The theories of coupled magneto-thermoelasticity and of generalized magneto-thermoelasticity with one relaxation time follow as limited cases. The result provides a motivation to investigate conducting thermoelectric materials as a new class of applicable materials.

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175 citations

"A 2D problem of time-fractional hea..." refers background in this paper

...Ezzat [10] also studied magnetothermoelasticity with thermoelectric properties and fractional derivative heat transfer....
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Journal Article•DOI•

Reflection of plane waves from an elastic solid half-space under hydrostatic initial stress without energy dissipation

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Mohamed I. A. Othman¹, Yaqin Song¹•Institutions (1)

Xi'an Jiaotong University¹

15 Aug 2007-International Journal of Solids and Structures

TL;DR: In this paper, the basic governing equations for isotropic and homogeneous generalized thermoelastic half-space under hydrostatic initial stress are formulated in the context of the Green and Naghdi theory of types II and III.

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147 citations

"A 2D problem of time-fractional hea..." refers methods in this paper

...Reflection of plane waves from an elastic solid half-space under hydrostatic initial stress without energy dissipation was investigated by Othman and Song [15]....
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...Song, Reflection of planewaves froman elastic solid half-space under hydrostatic initial stress without energy dissipation, Int....
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