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Steel and Composite Structures Volume 24, Number 3, June30 2017 , pages 297-307 DOI: https://doi.org/10.12989/scs.2017.24.3.297 |
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Fractional magneto-thermoelastic materials with phase-lag Green-Naghdi theories |
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M.A. Ezzat and A.A. El-Bary
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| Abstract | ||
| A unified mathematical model of phase-lag Green-Naghdi magneto-thermoelasticty theories based on fractional derivative heat transfer for perfectly conducting media in the presence of a constant magnetic field is given. The GN theories as well as the theories of coupled and of generalized magneto-thermoelasticity with thermal relaxation follow as limit cases. The resulting nondimensional coupled equations together with the Laplace transforms techniques are applied to a half space, which is assumed to be traction free and subjected to a thermal shock that is a function of time. The inverse transforms are obtained by using a numerical method based on Fourier expansion techniques. The predictions of the theory are discussed and compared with those for the generalized theory of magneto-thermoelasticity with one relaxation time. The effects of Alfven velocity and the fractional order parameter on copper-like material are discussed in different types of GN theories. | ||
| Key Words | ||
| generalized magneto-thermoelasticity; caputo fractional derivatives; phase-lag Green-Naghdi theories; laplace transforms; numerical results | ||
| Address | ||
| (1) M.A. Ezzat: Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt; (2) A.A. El-Bary: Arab Academy for Science and Technology, P.O. Box 1029, Alexandria, Egypt. | ||