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Transient Finite-Speed Heat Transfer Influence on Deformation of a Nanoplate with Ultrafast Circular Ring Heating

Author

Listed:
  • Mohsen Fayik

    (Department of Mathematics, Faculty of Education, Alexandria University, Souter St. El-Shatby, Alexandria 21526, Egypt)

  • Sharifah E. Alhazmi

    (Mathematics Department, Al-Qunfudhah University College, Umm Al-Qura University, Al-Qunfudhah 28821, Mecca, Saudi Arabia)

  • Mohamed A. Abdou

    (Department of Mathematics, Faculty of Education, Alexandria University, Souter St. El-Shatby, Alexandria 21526, Egypt)

  • Emad Awad

    (Department of Mathematics, Faculty of Education, Alexandria University, Souter St. El-Shatby, Alexandria 21526, Egypt)

Abstract

The present study provides a theoretical estimate for the thermal stress distribution and the displacement vector inside a nano-thick infinite plate due to an exponentially temporal decaying boundary heating on the front surface of the elastic plate. The surface heating is in the form of a circular ring; therefore, the axisymmetric formulation is adopted. Three different hyperbolic models of thermal transport are considered: the Maxwell-Cattaneo-Vernotte (MCV), hyperbolic Dual-Phase-Lag (HDPL) and modified hyperbolic Dual-Phase-Lag (MHDPL), which coincides with the two-step model under certain constraints. A focus is directed to the main features of the corresponding hyperbolic thermoelastic models, e.g., finite-speed thermal waves, singular surfaces (wave fronts) and wave reflection on the rear surface of the plate. Explicit expressions for the thermal and mechanical wave speeds are derived and discussed. Exact solution for the temperature in the short-time domain is derived when the thermalization time on the front surface is very long. The temperature, hydrostatic stress and displacement vector are represented in the space-time domain, with concentrating attention on the thermal reflection phenomenon on the thermally insulated rear surface. We find that the mechanical wave speeds are approximately equal for the considered models, while the thermal wave speeds are entirely different such that the modified hyperbolic dual-phase-lag thermoelasticity has the faster thermal wave speed and the Lord-Shulman thermoelasticity has the slower thermal wave speed.

Suggested Citation

  • Mohsen Fayik & Sharifah E. Alhazmi & Mohamed A. Abdou & Emad Awad, 2023. "Transient Finite-Speed Heat Transfer Influence on Deformation of a Nanoplate with Ultrafast Circular Ring Heating," Mathematics, MDPI, vol. 11(5), pages 1-25, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1099-:d:1077156
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    References listed on IDEAS

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    1. Ibrahim H. El-Sirafy & Mohamed A. Abdou & Emad Awad, 2014. "Generalized Lagging Response of Thermoelastic Beams," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-13, April.
    2. Metzler, Ralf & Klafter, Joseph, 2000. "Boundary value problems for fractional diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(1), pages 107-125.
    3. Giampaolo D’Alessandro & Filippo de Monte, 2020. "Multi-Layer Transient Heat Conduction Involving Perfectly-Conducting Solids," Energies, MDPI, vol. 13(24), pages 1-25, December.
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