Volume 9, Issue 2
Thermoelastic Interaction in an Infinite Long Hollow Cylinder with Fractional Heat Conduction Equation

Ahmed. E. Abouelregal

Adv. Appl. Math. Mech., 9 (2017), pp. 378-392.

Published online: 2018-05

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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

Thermoelasticity, fractional calculus, hollow cylinder, Laplace transform, traction free, heat flux.

  • AMS Subject Headings

74K25, 74G60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-9-378, author = {}, title = {Thermoelastic Interaction in an Infinite Long Hollow Cylinder with Fractional Heat Conduction Equation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {9}, number = {2}, pages = {378--392}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m26}, url = {http://global-sci.org/intro/article_detail/aamm/12154.html} }
TY - JOUR T1 - Thermoelastic Interaction in an Infinite Long Hollow Cylinder with Fractional Heat Conduction Equation JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 378 EP - 392 PY - 2018 DA - 2018/05 SN - 9 DO - http://dor.org/10.4208/aamm.2015.m26 UR - https://global-sci.org/intro/aamm/12154.html KW - Thermoelasticity, fractional calculus, hollow cylinder, Laplace transform, traction free, heat flux. AB -

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.

Ahmed. E. Abouelregal. (2020). Thermoelastic Interaction in an Infinite Long Hollow Cylinder with Fractional Heat Conduction Equation. Advances in Applied Mathematics and Mechanics. 9 (2). 378-392. doi:10.4208/aamm.2015.m26
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