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Thermoelastic Interaction in an Infinite Long Hollow Cylinder with Fractional Heat Conduction Equation

Part of: Thin bodies, structures Equilibrium (steady-state) problems

Published online by Cambridge University Press:  09 January 2017

Ahmed. E. Abouelregal
Ahmed. E. Abouelregal*
Affiliation:
Department of Mathematics, Faculty of Science, Mansoura University, P.O. Box 35516, Egypt Department of Mathematics, College of Science and Arts, Aljouf University, Al-Qurayat, Saudi Arabia
*
*Corresponding author. Email:[email protected] (A. E. Abouelregal)
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Abstract

In this work, we introduce a mathematical model for the theory of generalized thermoelasticity with fractional heat conduction equation. The presented model will be applied to an infinitely long hollow cylinder whose inner surface is traction free and subjected to a thermal and mechanical shocks, while the external surface is traction free and subjected to a constant heat flux. Some theories of thermoelasticity can extracted as limited cases from our model. Laplace transform methods are utilized to solve the problem and the inverse of the Laplace transform is done numerically using the Fourier expansion techniques. The results for the temperature, the thermal stresses and the displacement components are illustrated graphically for various values of fractional order parameter. Moreover, some particular cases of interest have also been discussed.

Keywords

Thermoelasticityfractional calculushollow cylinderLaplace transformtraction freeheat flux

MSC classification

Secondary: 74K25: Shells 74G60: Bifurcation and buckling
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 2 , April 2017 , pp. 378 - 392
Copyright
Copyright © Global-Science Press 2017 

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