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Application of fractional order theory to a functionally graded perfect conducting thermoelastic half space with variable Lamé’s Modulii

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Abstract

In this work, the model of fractional magneto-thermoelasticity is applied to a one-dimensional thermal shock problem for a functionally graded half-space whose surface is assumed to be traction free and subjected to an arbitrary thermal loading. The Lamé’s modulii is taken as functions of the vertical distance from the surface of thermoelastic perfect conducting medium in the presence of a uniform magnetic field. Laplace transform and the perturbation techniques are used to derive the solution in the Laplace transform domain. Numerical inversion of the Laplace transform is carried out to obtain the temperature, displacement, stress and induced magnetic and electric field distributions. Numerical results are represented graphically and discussed.

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Acknowledgements

The authors wish to acknowledge the approval and the support of this research study by the grant no. SCI-2016-1-6-F-6842 from the Deanship of Scientific Research in Northern Border University, Arar, KSA.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Northern Border University, Arar, Kingdom of Saudi Arabia

    Mohamed H. Hendy & Magdy M. Amin

  2. Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt

    Magdy A. Ezzat

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  1. Mohamed H. Hendy
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  2. Magdy M. Amin
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  3. Magdy A. Ezzat
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Correspondence to Magdy A. Ezzat.

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Hendy, M.H., Amin, M.M. & Ezzat, M.A. Application of fractional order theory to a functionally graded perfect conducting thermoelastic half space with variable Lamé’s Modulii. Microsyst Technol 23, 4891–4902 (2017). https://doi.org/10.1007/s00542-017-3409-6

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