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Finite Element Analysis of Thermal-Diffusions Problem for Unbounded Elastic Medium Containing Spherical Cavity under DPL Model

Author

Listed:
  • Aatef D. Hobiny

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

  • Ibrahim A. Abbas

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt)

Abstract

In this work, the thermo-diffusions interaction in an unbounded material with spherical cavities in the context dual phase lag model is investigated. The finite element technique has been used to solve the problem. The bounding surface of the inner hole is loaded thermally by external heat flux and is traction-free. The delay times caused in the microstructural interactions, the requirement for thermal physics to take account of hyperbolic effects within the medium, and the phase lags of chemical potential and diffusing mass flux vector are interpreted. A comparison is made in the case of the presence and the absence of mass diffusions between coupled, Lord-Shulman and dual phase lag theories. The numerical results for the displacement, concentration, temperature, chemical potential and stress are presented numerically and graphically.

Suggested Citation

  • Aatef D. Hobiny & Ibrahim A. Abbas, 2021. "Finite Element Analysis of Thermal-Diffusions Problem for Unbounded Elastic Medium Containing Spherical Cavity under DPL Model," Mathematics, MDPI, vol. 9(21), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2782-:d:670746
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    References listed on IDEAS

    as
    1. Madureira, Rodrigo L.R. & Rincon, Mauro A. & Aouadi, Moncef, 2021. "Numerical analysis for a thermoelastic diffusion problem in moving boundary," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 630-655.
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    Cited by:

    1. Nicolae Pop & Marin Marin & Sorin Vlase, 2023. "Mathematics in Finite Element Modeling of Computational Friction Contact Mechanics 2021–2022," Mathematics, MDPI, vol. 11(1), pages 1-5, January.

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