Fractional heat conduction with finite wave speed in a thermo-visco-elastic spherical shell

Sur, Abhik; Kanoria, M.

doi:10.1590/s1679-78252014000700005

Cited by 15 publications

(6 citation statements)

References 33 publications

(17 reference statements)

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“…Making use of equations (28) to (32) in equation (34) and using equation (35), we obtain a system of five homogeneous equations as: …”

Section: Boundary Conditionsmentioning

confidence: 99%

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Reflection of Plane Waves at Micropolar Piezothermoelastic Half-space

Kumar¹,

Nidhi²,

Lata³

et al. 2018

CMST

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A problem of reflection at a free surface of micropolar orthotropic piezothermoelastic medium is discussed in the present paper. It is found that there exist five type plane waves in micropolar orthotropic piezothermoelastic medium, namely quasi longitudinal displacement wave (quasi LD wave), quasi thermal wave (quasi T wave), quasi CD-I, quasi CD-II wave and electric potential wave (PE wave). The amplitude ratios corresponding to reflected waves are obtained numerically. The effect of angle of incidence and thermopiezoelectric interactions on the reflected waves are studied for a specific model. Some particular cases of interest are also discussed.

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“…Making use of equations (28) to (32) in equation (34) and using equation (35), we obtain a system of five homogeneous equations as: …”

Section: Boundary Conditionsmentioning

confidence: 99%

“…Sur and Kanoria [32] investigated fractional heat conduction with finite wave speed in a thermoviscoelastic spherical shell. Abo-Dahab [33] analysed the magnetic effect on three plane waves propagation at an interface between solid-liquid media placed under initial stress in the context of the GL model.…”

Section: Introductionmentioning

confidence: 99%

Reflection of Plane Waves at Micropolar Piezothermoelastic Half-space

Kumar¹,

Nidhi²,

Lata³

et al. 2018

CMST

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“…This property is a consequence of the dependence between the heat flux vector and the temperature gradient which is established by the Fourier law. This disadvantage does not appear when the non-local time dependence between the flux vector and the temperature gradient is assumed (Povstenko, 2014;Sur and Kanoria, 2014). This assumption leads to a differential equation and/or boundary conditions with derivatives of a non-integer order.…”

Section: Introductionmentioning

confidence: 99%

Fractional heat conduction in a sphere under mathematical and physical Robin conditions

Kukla

Siedlecka

2018

jtam

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In this paper, the effect of a fractional order of time-derivatives occurring in fractional heat conduction models on the temperature distribution in a composite sphere is investigated. The research concerns heat conduction in a sphere consisting of a solid sphere and a spherical layer which are in perfect thermal contact. The solution of the problem with a classical Robin boundary condition and continuity conditions at the interface in an analytical form has been derived. The fractional heat conduction is governed by the heat conduction equation with the Caputo time-derivative, a Robin boundary condition and a heat flux continuity condition with the Riemann-Liouville derivative. The solution of the problem of non-local heat conduction by using the Laplace transform technique has been determined, and the temperature distribution in the sphere by using a method of numerical inversion of the Laplace transforms has been obtained.

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“…The Kelvin-Voigt model is one of the macroscopic mechanical model often used to describe the viscoelastic behavior of a material. The model represents the delayed elastic response subjected to stress when the deformation is time dependent but recoverable (Sur and kanoria, 2014a;Sur and Kanoria, 2014b). The dynamic interaction of thermal and mechanical fields in solids has great practical applications in modern aeronautics, astronautics, nuclear reactors and high-energy accelerators, for example.…”

Section: Introductionmentioning

confidence: 99%

Three dimensional viscoelastic medium under thermal shock

Sur¹,

Kanoria²

2016

10.5267/j.esm

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This article deals with the thermoelastic interaction in a three-dimensional homogeneous and isotropic viscoelastic medium under the Dual-phase-lag model of generalized thermoelasticity. The resulting non-dimensional coupled equations are applied to a specific problem of a halfspace whose surface is traction-free and is subjected to a time-dependent thermal shock. The analytical expressions for the displacement components, stress, temperature and strain are obtained in the physical domain by employing normal mode analysis. These expressions are also calculated for a copper-like material and have been depicted graphically. Discussions have been made to highlight the effect of viscosity on the studied field. The phenomenon of a finite speed of propagation is observed for each field. Also, if the effect of viscosity is neglected, the results agree with the existing literature.

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Fractional heat conduction with finite wave speed in a thermo-visco-elastic spherical shell

Cited by 15 publications

References 33 publications

Reflection of Plane Waves at Micropolar Piezothermoelastic Half-space

Reflection of Plane Waves at Micropolar Piezothermoelastic Half-space

Fractional heat conduction in a sphere under mathematical and physical Robin conditions

Three dimensional viscoelastic medium under thermal shock

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