Steel and Composite Structures

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Fractional magneto-thermoelastic materials with phase-lag Green-Naghdi theories

  • Ezzat, M.A. (Department of Mathematics, Faculty of Education, Alexandria University) ;
  • El-Bary, A.A. (Arab Academy for Science and Technology)
  • Received : 2016.12.10
  • Accepted : 2017.03.30
  • Published : 2017.06.30
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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.

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References

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