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Effects of the Nonlocal Thermoelastic Model in a Thermoelastic Nanoscale Material

Author

Listed:
  • Tareq Saeed

    (Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Mathematics Department, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Ibrahim Abbas

    (Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Mathematics Department, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt)

Abstract

In this work, a novel nonlocal model without energy dissipations is presented to investigate the impacts of the nonlocal thermoelastic parameters in a nanoscale material by the eigenvalue approach. The basic equations are applied under the Green and Naghdi model without energy dissipations. To obtain this model, the theory of the non-local continuum suggested by Eringen is applied. The Laplace transformation technique is used for the basic formulations to obtain the analytical solutions of the thermal stress, the displacement, and the temperature during the nanoscale thermo-electric medium. The inverse of the Laplace transformation is used with the numerical technique to obtain the complete solutions of the studying fields in the time–space domains. The main physical fields are displayed graphically and theoretically discussed under the influence of nonlocal parameters.

Suggested Citation

  • Tareq Saeed & Ibrahim Abbas, 2022. "Effects of the Nonlocal Thermoelastic Model in a Thermoelastic Nanoscale Material," Mathematics, MDPI, vol. 10(2), pages 1-10, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:284-:d:726914
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