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Effect of fractional parameter on plane waves in a rotating elastic medium under fractional order generalized thermoelasticity
Nantu Sarkar,A. Lahiri +1 more
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TLDR
In this article, a two-dimensional generalized thermoelastic coupled problem for a homogeneous isotropic and thermally conducting rotating medium in the context of the above fractional order generalized thermelasticity with two relaxation time parameters is considered.Abstract:
In ["Theory of fractional order generalized thermoelasticity," Journal of Heat Transfer132, 2010] Youssef has proposed a model in generalized thermoelasticity based on the fractional order time derivatives. The current manuscript is concerned with a two-dimensional generalized thermoelastic coupled problem for a homogeneous isotropic and thermally conducting thermoelastic rotating medium in the context of the above fractional order generalized thermoelasticity with two relaxation time parameters. The normal mode analysis technique is used to solve the resulting non-dimensional coupled governing equations of the problem. The resulting solution is then applied to two concrete problems. The effect of the fractional parameter and the time instant on the variations of different field quantities inside the elastic medium are analyzed graphically in the presence of rotation.read more
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The state of fractional hereditary materials (FHM)
TL;DR: In this article, the authors considered the condition that different histories delivering the same response are such that the fractional derivative of their difference is zero for all times, and provided an approximation formula for the residual stress associated to the difference of the histories above.
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Solutions with Wright functions for time fractional convection flow near a heated vertical plate
TL;DR: In this article, the initial-boundary values problem is determined by means of the Laplace transform technique and are represented by the Wright functions, and a numerical case is analyzed in order to obtain information regarding the influence of the fractional parameters on the temperature and velocity fields.
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Asymptotic analysis of generalized thermoelasticity for axisymmetric plane strain problem with temperature-dependent material properties
TL;DR: In this article, a new formulation for the generalized thermoelasticity in an isotropic elastic medium with temperature-dependent material properties is established, and the generalized axisymmetric plane strain problem is derived.
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Effect of Variable Properties and Moving Heat Source on Magnetothermoelastic Problem under Fractional Order Thermoelasticity
Xiong Chunbao,Guo Ying +1 more
TL;DR: In this article, a one-dimensional generalized magnetothermoelastic problem of a thermo-elastic rod with finite length is investigated in the context of the fractional order thermo elasticity.
References
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Journal ArticleDOI
Linear Models of Dissipation whose Q is almost Frequency Independent-II
TL;DR: In this paper, a linear dissipative mechanism whose Q is almost frequency independent over large frequency ranges has been investigated by introducing fractional derivatives in the stressstrain relation, and a rigorous proof of the formulae to be used in obtaining the analytic expression of Q is given.
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Thermoelasticity and Irreversible Thermodynamics
TL;DR: In this article, a unified treatment of thermoelasticity by application and further developments of the methods of irreversible thermodynamics is presented, along with a new definition of the dissipation function in terms of the time derivative of an entropy displacement.
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A new dissipation model based on memory mechanism
TL;DR: The model of dissipation based on memory introduced by Caputo is generalized and checked with experimental dissipation curves of various materials.
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Fractional heat conduction equation and associated thermal stress
TL;DR: A quasi-static uncoupled theory of thermoelasticity based on the heat conduction equation with a time-fractional derivative of order α is proposed in this article.