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Finite Element Analysis of Generalized Thermoelastic Interaction for Semiconductor Materials under Varying Thermal Conductivity

Author

Listed:
  • Aatef Hobiny

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

  • Ibrahim Abbas

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

Abstract

In this work, we consider the problem of a semiconductor half-space formed of varying thermal conductivity materials with and without Kirchhoff’s transforms. Specifically, we deal with one thermal relaxation time within the context of generalized photothermoelastic theory. It is expected that the thermal conductivity of the material will vary with temperature. The finite element method is used to numerically solve this problem. The Laplace transform and the eigenvalues method are used to determine analytical solutions to the linear problem. Various hypotheses are investigated, both with and without the use of Kirchhoff’s transformations, to consider the influence of thermal conductivity change. To verify the accuracy of the proposed approach, we provide a comparison of numerical and analytical results by ignoring the new parameters and investigating the behaviors of physical quantities for numerical outcomes.

Suggested Citation

  • Aatef Hobiny & Ibrahim Abbas, 2022. "Finite Element Analysis of Generalized Thermoelastic Interaction for Semiconductor Materials under Varying Thermal Conductivity," Mathematics, MDPI, vol. 10(24), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4676-:d:999047
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    References listed on IDEAS

    as
    1. Ahmed E. Abouelregal & Marin Marin, 2020. "The Size-Dependent Thermoelastic Vibrations of Nanobeams Subjected to Harmonic Excitation and Rectified Sine Wave Heating," Mathematics, MDPI, vol. 8(7), pages 1-13, July.
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