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Two-temperature fractional Green–Naghdi of type III in magneto-thermo-viscoelasticity theory subjected to a moving heat source

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Abstract

In this work, we construct a mathematical model of two-temperature Green–Naghdi (III) magneto-thermo viscoelasticty theory based on the fractional order of heat transfer. Some essential theorems of coupled and generalized thermo-viscoelasticity can be easily obtained. The Laplace transform and state-space techniques are used to obtain the general solution for any set of boundary conditions. The resulting formulation is applied to the specific problem of a perfect electrically conducting viscoelastic half-space subjected to a moving heat source with constant velocity and ramp-type heating. The inverse transforms are obtained by using a numerical method based on Fourier expansion techniques. The effects of the heat source speed, the two-temperature parameter, Alfven velocity and the ramping time parameter on a polymethyl methacrylate (Plexiglas) material are discussed.

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Acknowledgements

The authors gratefully acknowledge the approval and the support of this research study by the Grant No. SCI-2017-1-8-F-7354 from the Deanship of Scientific Research in Northern Border University, Arar, KSA.

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Author notes

  1. Magdy A. Ezzat

    Present address: Department of Mathematics, Faculty of Science and Arts, Qassim University, Al Bukairyah, Saudi Arabia

Authors and Affiliations

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

    Mohamed H. Hendy & Sayed I. El-Attar

  2. Department of Mathematics, Faculty of Science, Al Arish University, Al Arish, Egypt

    Mohamed H. Hendy

  3. 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. Sayed I. El-Attar
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Correspondence to Magdy A. Ezzat.

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Hendy, M.H., El-Attar, S.I. & Ezzat, M.A. Two-temperature fractional Green–Naghdi of type III in magneto-thermo-viscoelasticity theory subjected to a moving heat source. Indian J Phys 95, 657–671 (2021). https://doi.org/10.1007/s12648-020-01719-1

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