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Smart Structures and Systems Volume 18, Number 4, October 2016 , pages 707-731 DOI: https://doi.org/10.12989/sss.2016.18.4.707 |
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Modeling of fractional magneto-thermoelasticity for a perfect conducting materials |
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M.A. Ezzat and A.A. El-Bary
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| Abstract | ||
| A unified mathematical model of the equations of generalized magneto-thermoelasticty based on fractional derivative heat transfer for isotropic perfect conducting media is given. Some essential theorems on the linear coupled and generalized theories of thermoelasticity e.g. the Lord- Shulman (LS) theory, Green-Lindsay (GL) theory and the coupled theory (CTE) as well as dual-phase-lag (DPL) heat conduction law are established. Laplace transform techniques are used. The method of the matrix exponential which constitutes the basis of the state-space approach of modern theory is applied to the non-dimensional equations. The resulting formulation is applied to a variety of one-dimensional problems. The solutions to a thermal shock problem and to a problem of a layer media are obtained in the present of a transverse uniform magnetic field. According to the numerical results and its graphs, conclusion about the new model has been constructed. The effects of the fractional derivative parameter on thermoelastic fields for different theories are discussed. | ||
| Key Words | ||
| generalized magneto-thermoelasticity; fractional calculus; laplace transforms; state space approach; numerical results | ||
| Address | ||
| M.A. Ezzat: Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt A.A. El-Bary: Arab Academy for Science and Technology, P.O. Box 1029, Alexandria, Egypt | ||