Fundamental solutions to the fractional heat conduction equation in a ball under Robin boundary condition

Povstenko, Yuriy

doi:10.2478/s11533-013-0368-8

Cited by 5 publications

(4 citation statements)

References 27 publications

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“…The present deduced thermoelastic solutions agree with the key derived by Ghonge and Ghadle [41] for an isotropic, homogeneous, elastic sphere. This work combines a fractional-order constitutive model with the standard continuity equation.…”

Section: (Ii)supporting

confidence: 89%

Time-Fractional Cattaneo-Type Thermoelastic Interior-Boundary Value Problem Within A Rigid Ball

DHAMEJA¹,

Khalsa²,

Varghese³

2023

International Journal of Thermodynamics

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The paper discusses the solution of an interior-boundary value problem of one-dimensional time-fractional Cattaneo-type heat conduction and its stress fields for a rigid ball. The interior value problem describes the dependence of the boundary conditions within the ball's inner plane at any instant with a prescribed temperature state, in contrast to the exterior value problem, which relates the known surface temperature to boundary conditions. A single-phase-lag equation with Caputo fractional derivatives is proposed to model the heat equation in a medium subjected to time-dependent physical boundary conditions. The application of the finite spherical Hankel and Laplace transform technique to heat conduction is discussed. The influence of the fractional-order parameter and the relaxation time is examined on the temperature fields and their related stresses. The findings show that the slower the thermal wave, the bigger the fractional-order setting, and the higher the period of relaxation, the slower the heat flux propagates.

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Section: (Ii)supporting

confidence: 89%

Time-Fractional Cattaneo-Type Thermoelastic Interior-Boundary Value Problem Within A Rigid Ball

DHAMEJA¹,

Khalsa²,

Varghese³

2023

International Journal of Thermodynamics

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“…, respectively. Povstenko [30][31][32] has recently investigated the timefractional heat conduction equation with Caputo derivative under mathematical and physical Robin-type boundary conditions. Another equivalent name in use is radiation-type boundary condition [33][34][35][36][37], a specification of a linear combination of the values of a temperature function and its normal derivative on the domain's boundary and can be given as…”

Section: The Plate Under Radiation Boundary Conditionsmentioning

confidence: 99%

Thermoelastic Analysis For A Thick Plate Under The Radiation Boundary Conditions

DHAMEJA¹,

Khalsa²,

Varghese³

2023

International Journal of Thermodynamics

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A fractional Cattaneo model for studying the thermoelastic response for a finite thick circular plate with source function is considered. The thick plate is subjected to radiation-type boundary conditions on the upper and lower surfaces, and its curved surface is kept at zero temperature. The theory of integral transformations is used to solve the generalized fractional Cattaneo-type, classical Cattaneo-Vernotte and Fourier heat conduction model. The analytical expressions of displacement components using thermoelastic displacement potentials; and thermal-stress distribution are computed and depicted graphically. The effects of the fractional-order parameter and the relaxation time on the temperature fields and their thermal stresses are investigated. The findings show that the higher the fractional-order parameter, the higher the thermal response. The greater the relaxation period, the longer the heat flux propagates on thick structures.

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“…The present analysis, and solutions developed, address the time-fractional heat conduction (which can also be considered as an anomalous diffusion equation) with the Robin boundary condition. The Robin boundary condition appears in many applied diffusion problems such as solute rejection [9,14,15], solidification of alloys [16,17], and heat transfer at the boundary by convection (as in this article) [18], and the dominating solutions are numerical [6,[9][10][11][12][15][16][17] considering finite domains [11,[14][15][16][17], while solutions in the semiinfinite domain are rare [9]. Moreover, estimates concerning the existence and uniqueness of the problem solution have been developed in [9,11,19].…”

Section: Introductionmentioning

confidence: 99%

Transient Heat Conduction in a Semi-Infinite Domain with a Memory Effect: Analytical Solutions with a Robin Boundary Condition

Beybalaev,

Aliverdiev,

Hristov

2023

Fractal Fract

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The Robin boundary condition initial value problem for transient heat conduction with the time-fractional Caputo derivative in a semi-infinite domain with a convective heat transfer (Newton’s law) at the boundary has been solved and analyzed by two analytical approaches. The uniqueness and the stability of the solution on the half-axis have been analyzed. The problem solutions by application of the operational method (Laplace transform in the time domain) and the integral-balance method (double integration technique) have been developed analytically.

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Fundamental solutions to the fractional heat conduction equation in a ball under Robin boundary condition

Cited by 5 publications

References 27 publications

Time-Fractional Cattaneo-Type Thermoelastic Interior-Boundary Value Problem Within A Rigid Ball

Time-Fractional Cattaneo-Type Thermoelastic Interior-Boundary Value Problem Within A Rigid Ball

Thermoelastic Analysis For A Thick Plate Under The Radiation Boundary Conditions

Transient Heat Conduction in a Semi-Infinite Domain with a Memory Effect: Analytical Solutions with a Robin Boundary Condition

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