Dynamic problem of fractional order thermoelasticity for a thick circular plate with finite wave speeds

Tripathi, J. J.; Kedar, G. D.; Deshmukh, K. C.

doi:10.1080/01495739.2015.1124646

Cited by 15 publications

(8 citation statements)

References 24 publications

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“…Sarkar [19], studied the wave propagation in an initially stressed elasticsolid half-space under time-fractional order twotemperature magneto-thermoelasticity. Tripathi et al [20] discussed a dynamic problem of fractional order thermoelasticity for a thick circular plate with finite wave speeds. Warbhe et al [21], studied fractional order heat conduction and its associated thermal stresses in a thin circular plate with constant temperature distribution.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fractional Order Generalized Thermoelastic Problem in a Thick Circular Plate with Periodically Varying Heat Source

Tripathi¹,

Deshmukh²,

Verma³

2017

International Journal of Thermodynamics

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This paper is concerned with fractional order thermoelastic response due to a heat source whose magnitude varies periodically with time within the context of generalized thermoelasticity with one relaxation time. Traction free boundary conditions are considered and the thick circular plate is subjected to a given axisymmetric temperature distribution. Integral transform technique is used to derive the solution in the transformed domain. Laplace transforms are inverted using a numerical scheme. Mathematical model is prepared for Copper material and results for temperature, displacement and stress distributions are computed and represented graphically.

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Section: Introductionmentioning

confidence: 99%

“…Mathematical model is prepared for Copper material and the numerical inversion of Laplace transform is performed using Gaver-Stehfast algorithm [18][19][20]. All the integrals involved in the problem are evaluated using Romberg integration technique [21] with variable step size.…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Generalized Thermoelastic Problem in a Thick Circular Plate with Periodically Varying Heat Source

Tripathi¹,

Deshmukh²,

Verma³

2017

International Journal of Thermodynamics

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“…Lamba [14] presented mathematical modeling of thermoelastic hollow cylinder subjected to convective boundary condition on the upper and lower plane surface by the application of the fractional order theory. Tripathi [15] studied a dynamic thermoelastic problem of fractional order for a thick circular plate with finite wave speeds. Kukla [16] presented an analytical solution to the problem of timefractional heat conduction in a sphere.…”

Section: Introductionmentioning

confidence: 99%

Application of Fractional Order Theory of Thermoelasticity in an Elliptical Disk and Associated Thermal Stresses

Thakare¹,

Panke²,

Hadke³

2020

International Journal of Applied Mechanics and Engineering

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In this article, a time fractional-order theory of thermoelasticity is applied to an isotropic homogeneous elliptical disk. The lower and upper surfaces of the disk are maintained at zero temperature, whereas the sectional heat supply is applied on the outer curved surface. Thermal deflection and associated thermal stresses are obtained in terms of Mathieu function of the first kind of order 2n. Numerical evaluation is carried out for the temperature distribution, Thermal deflection and thermal stresses and results of the resulting quantities are depicted graphically.

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“…This model is applied to solve a problem of an infinitely long hollow cylinder in the presence of an axial uniform magnetic field. Tripathi et al (2016) attempted the solution of the dynamic problem of fractional order thermoelasticity for a thick circular plate with infinite dimensions in radial directions. El-Bray (2017, 2018) framed a fractional model of the equations of generalized magneto-thermoelasticity for a perfect conducting isotropic thermoelastic media.…”

Section: Introductionmentioning

confidence: 99%

Dual-phase-lag thermoelastic problem in finite cylindrical domain with relaxation time

Mittal¹,

Kulkarni

2018

MMMS

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Purpose The purpose of this paper is to frame a dual-phase-lag model using the fractional theory of thermoelasticity with relaxation time. The generalized Fourier law of heat conduction based upon Tzou model that includes temperature gradient, the thermal displacement and two different translations of heat flux vector and temperature gradient has been used to formulate the heat conduction model. The microstructural interactions and corresponding thermal changes have been studied due to the involvement of relaxation time and delay time translations. This results in achieving the finite speed of thermal wave. Classical coupled and generalized thermoelasticity theories are recovered by considering the various special cases for different order of fractional derivatives and two different translations under consideration. Design/methodology/approach The work presented in this manuscript proposes a dual-phase-lag mathematical model of a thick circular plate in a finite cylindrical domain subjected to axis-symmetric heat flux. The model has been designed in the context of fractional thermoelasticity by considering two successive terms in Taylor’s series expansion of fractional Fourier law of heat conduction in the two different translations of heat flux vector and temperature gradient. The analytical results have been obtained in Laplace transform domain by transforming the original problem into eigenvalue problem using Hankel and Laplace transforms. The numerical inversions of Laplace transforms have been achieved using the Gaver−Stehfast algorithm, and convergence criterion has been discussed. For illustrative purpose, the dual-phase-lag model proposed in this manuscript has been applied to a periodically varying heat source. The numerical results have been depicted graphically and compared with classical, fractional and generalized thermoelasticity for various fractional orders under consideration. Findings The microstructural interactions and corresponding thermal changes have been studied due to the involvement of relaxation time and delay time translations. This results in achieving the finite speed of thermal wave. Classical coupled and generalized thermoelasticity theories are recovered by considering the various special cases for different order of fractional derivatives and two different translations under consideration. This model has been applied to study the thermal effects in a thick circular plate subjected to a periodically varying heat source. Practical implications A dual-phase-lag model can effectively be incorporated to study the transient heat conduction problems for an exponentially decaying pulse boundary heat flux and/or for a short-pulse boundary heat flux in long solid tubes and cylinders. This model is also applicable to study the various effects of the thermal lag ratio and the shift time. These dual-phase-lag models are also practically applicable in the problems of modeling of nanoscale heat transport problems of semiconductor devices and accordingly semiconductors can be classified as per their ability of heat conduction. Originality/value To the authors’ knowledge, no one has discussed fractional thermoelastic dual-phase-lag problem associated with relaxation time in a finite cylindrical domain for a thick circular plate subjected to an axis-symmetric heat source. This is the latest and novel contribution to the field of thermal mechanics.

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Dynamic problem of fractional order thermoelasticity for a thick circular plate with finite wave speeds

Cited by 15 publications

References 24 publications

Fractional Order Generalized Thermoelastic Problem in a Thick Circular Plate with Periodically Varying Heat Source

Fractional Order Generalized Thermoelastic Problem in a Thick Circular Plate with Periodically Varying Heat Source

Application of Fractional Order Theory of Thermoelasticity in an Elliptical Disk and Associated Thermal Stresses

Dual-phase-lag thermoelastic problem in finite cylindrical domain with relaxation time

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