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Steel and Composite Structures   Volume 24, Number 3, June30 2017, pages 297-307
DOI: http://dx.doi.org/10.12989/scs.2017.24.3.297
 
Fractional magneto-thermoelastic materials with phase-lag Green-Naghdi theories
M.A. Ezzat and A.A. El-Bary

 
Abstract     [Full Text]
    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.
 

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