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Mathematical Model on Gravitational Electro-Magneto-Thermoelasticity with Two Temperature and Initial Stress in the Context of Three Theories

Author

Listed:
  • Sayed M. Abo-Dahab

    (Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt
    Department of Mathematics, Faculty of Science, Taif University, Taif 888, Saudi Arabia)

  • Alaa A. El-Bary

    (Department of Basic and Applied Science, Arab Academy for Science, Technology and Maritime Transport, Alexandria P.O. Box 1029, Egypt)

  • Yas Al-Hadeethi

    (Department of Physics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Mohamed Alkashif

    (Department of Mathematics, Faculty of Science, Taif University, Taif 888, Saudi Arabia
    Department of Mathematics, Faculty of Science, Assiut University, Assiut 71515, Egypt)

Abstract

The main aim of this paper is to study two temperature thermoelasticity in a generalization form to solve the half-space problem of two dimensions under gravity, perturbed magnetic field, and initial stress. The fundamental equations are solved considering a new mathematical technique under Lord-Şhulman (LS), Green-Naghdi (GN type III) and three-phase-lag (3PHL) theories to investigate displacement, stress components, and temperature distribution. The results obtained by the three theories, i.e., (LS), (GN type III), and (3PHL), considering the absence and the presence of gravity, initial stress, and magnetic field have been compared. The results were numerically calculated and graphically displayed to exhibit the physical meaning of the phenomenon and the external parameters’ effect. A comparison has been presented between the results obtained in the absence and the presence of the external considered parameters and with the previously obtained results by other researchers.

Suggested Citation

  • Sayed M. Abo-Dahab & Alaa A. El-Bary & Yas Al-Hadeethi & Mohamed Alkashif, 2020. "Mathematical Model on Gravitational Electro-Magneto-Thermoelasticity with Two Temperature and Initial Stress in the Context of Three Theories," Mathematics, MDPI, vol. 8(5), pages 1-25, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:735-:d:355017
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    References listed on IDEAS

    as
    1. Manuela Carini & Vittorio Zampoli, 2020. "On Porous Matrices with Three Delay Times: A Study in Linear Thermoelasticity," Mathematics, MDPI, vol. 8(3), pages 1-16, March.
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