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Four-Phase Lags in a Generalized Thermoelastic Rotational Diffusive Plate with Laser Pulse Emission

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Abstract

Here, we study the effect of rotation and diffusion on a thermoelastic plate with four-phase lag. The normal mode method was used to get the exact solution of the displacement, stress, and temperature functions. The last-mentioned functions were plotted and comprised in three cases, presence and absence of rotation, in addition to the context of three cases, and finally in the presence and absence of laser pulse.

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REFERENCES

  1. M. Biot, “Thermoelasticity and irreversible thermodynamics,” J. Appl. Phys. 27, 240–253 (1956). https://doi.org/10.1063/1.1722351

    Article  ADS  MathSciNet  Google Scholar 

  2. H. W. Lord and Y. Shulman, “A generalized dynamical theory of thermoelasticity,” J. Mech. Phys. Solid 15, 299–309 (1967). https://doi.org/10.1016/0022-5096(67)90024-5

    Article  ADS  Google Scholar 

  3. W. Nowacki, “Dynamical problems of thermoelastic diffusion in solids,” Bull. Polish Ac. Sci. Ser., Sci. Technol. 22, 55–64 (1974).

    Google Scholar 

  4. W. Nowacki, “Dynamical problems of thermoelastic diffusion in elastic solids,” Proc. Vib. Prob. 15, 105–128 (1974).

    MathSciNet  Google Scholar 

  5. W. Nowacki, “Dynamical problems of thermoelastic diffusion in solids II,” Bull. Polish Ac. Sci. Ser., Sci. Technol. 22, 129–135 (1974).

    Google Scholar 

  6. W. Nowacki, “Dynamical problems of thermoelastic diffusion in solids III,” Bull. Polish Ac. Sci. Ser., Sci. Technol. 22, 257–266 (1974).

    Google Scholar 

  7. H. H. Sherief, F. Hamza, and H. A. Saleh, “The theory of generalized thermoelastic diffusion,” Int. J. Eng. Sci. 42, 591–608 (2004).

    Article  MathSciNet  Google Scholar 

  8. Kh. Lotfy, “A novel model of magneto photothermal diffusion (MPD) on polymer nano-composite semiconductor with initial stress,” Waves Random Complex Media. 31 (1), 81-100 (2019). https://doi.org/10.1080/17455030.2019.1566680

    Article  MathSciNet  Google Scholar 

  9. A. Bajpai, P. K. Sharma, and R. Kumar, “Modeling of thermoelastic diffusion plate under two temperature, fractional- order, and temperature-dependent material properties,” ZAMM 101 (10), e202000321 (2021). https://doi.org/10.1002/zamm.202000321

  10. M. I. M. Hilal, “Diffusion, rotation, and lagging behavior of a thermoelastic micropolar medium with voids and temperture gradient under mechanical pressure,” Waves Random Complex Media (2021). https://doi.org/10.1080/17455030.2021.2011987

  11. D. Y. Tzou, “Unified field approach for heat conduction from macro-to micro-scales,” J. Heat Transf. 117, 8–16 (1995).

    Article  Google Scholar 

  12. S. K. Roychoudhuri, “On thermoelastic three phase lag model,” J. Therm. Stress. 30, 231–238 (2007).

    Article  Google Scholar 

  13. R. Quintanilla and R. Racke, “A note on stability in three-phase-lag heat conduction,” Int. J. Heat Mass Trans. 51, 24–29 (2008).

    Article  CAS  Google Scholar 

  14. I. Abbas, F. Alzahrani, and A. Elaiw, “A DPL model of photothermal interaction in a semiconductor material,” Waves Random Complex Media 29 (2), 328–343 (2019).

    Article  Google Scholar 

  15. Kh. Lotfy, “The elastic wave motions for a photothermal medium of a dual-phase-lag model with an internal heat source and gravitational field,” Can. J. Phys. 94, 400–409 (2016). https://doi.org/10.1139/cjp-2015-0782

    Article  ADS  CAS  Google Scholar 

  16. M. Marin, “A domain of influence theorem for microstretch elastic materials,” Nonlinear Anal.: Real World Appl. 11 (5), 3446–3452 (2010). https://doi.org/10.1016/j.nonrwa.2009.12.005

    Article  MathSciNet  Google Scholar 

  17. M. Marin, “A partition of energy in thermoelasticity of microstretch bodies,” Nonlinear Anal.: Real World Appl. 11 (4), 2436–2447 (2010). https://doi.org/10.1016/j.nonrwa.2009.07.014

    Article  MathSciNet  Google Scholar 

  18. Sarhan Y. Atwa, M. K. Ammar, and Eman Ibrahim, “The effect of two- temperature on thermoelastic medium with diffusion due to three phase- lag model,” Appl. Math. Nonlin. Sci. 2 (1), 259–270 (2017). https://doi.org/10.21042/AMNS.2017.1.00022

    Article  Google Scholar 

  19. M. A. Abdou, E. M. Abo- Eldahab, M. K. Ammar, and E. Ibrahim, “New model for discussing the diffusion phenomena effect on a thermoelastic plate associated with three- phase- lag,” Informat. Sci. Lett. 11 (6), 2159–2166 (2022).

    Article  Google Scholar 

  20. A. Hobiny and I. Abbas, “Generalized thermo-diffusion interaction in elastic medium under temperture dependent diffusivity and thermal conductivity,” Mathematics 10 (15), 2773 (2022). https://doi.org/10.3390/math10152773

    Article  Google Scholar 

  21. K.A. Aldwoah, Kh. Lotfy, A. Mhemdi, and A. El-Bary, “A novel magneto-photo-elasto-thermodiffusion electrons- holes model of excited semiconductor,” Case Studies Thermal Eng. 32, 101877 (2022). doi.org/https://doi.org/10.1016/j.csite.2022.101877

  22. M. I. A. Othman, S. Y. Atwa, A. Jahangir, and A. Khan, “The effect of rotation on plane waves in generalized thermo- microstretch elastic solid for a mode- I crack under Green Naghdi theory,” J. Computat. Theor. Nanosci. 12, 1–10 (2015).

    Google Scholar 

  23. M. I. A. Othman and S. Y. Atwa, “2- D problem of anistropic rotating thermoelastic half- space under Green- Naghdi theory,” J. Comutat. Theor. Nanosci. 12, 1363–3270 (2015).

    Google Scholar 

  24. S. Y. Atwa and Eman Ibrahim, “Two temperture effect on a rotational themoelastic medium with diffusion due to three- phase- lag model,” J. Nanotechnol. Adv. Mater. 1, 1–15 (2019).

    Article  Google Scholar 

  25. A. M. H. Yahya, A. E. Abouelregal, K. M. Khalil, and D. Atta, “Thermoelastic response in rotating nanomeams with variable physical properties due to periodic pulse heating,” Case Study Therm. Eng. 28, 101443 (2021). https://doi.org/10.1016/j.csite.2021.101443

  26. I. Kaur, K. Singh, and E-M. Craciun, “A mathematical study of a semiconducting thermoelastic rotating solid cylinder with modified Moore- Gibson- Thompson heat transfer under the hall effect,” Mathematics 10 (14), 2386 (2022). https://doi.org/10.3390/math10142386

    Article  Google Scholar 

  27. M. I. A. Othman, “Effect of thermal loading due to laser pulse on 3-D problem on micropolar thermoelastic solid with energy dissipation,” Mech. Mechanical Eng. 21, 679–701 (2017).

    Google Scholar 

  28. A. Mahdy, Kh. Lotfy, A. El-Bary, and I. Tayel, “Variable thermal conductivity and hyperbolic two-temperature theory during magneto-photothermal theory of semiconductor induced by laser pulses,” Eur. Phys. J. Plus. 136, 651 (2021). doi.org/https://doi.org/10.1140/epjp/s13360-021-01633-3

    Article  CAS  Google Scholar 

  29. A. Mahdy, Kh. Lotfy, A. El-Bary, and H. Sarhan, “Effect of rotation and magnetic field on a numerical-refined heat conduction in a semiconductor medium during photo-excitation processes,” Eur. Phys. J. Plus. 136, 553 (2021). doi.org/https://doi.org/10.1140/epjp/s13360-021-01552-3

    Article  Google Scholar 

  30. A. K. Khamis, A. A. El-Bary, Kh. Lotfy, and Allal Bakali, “Photothermal excitation processes with refined multi dual phase-lags theory for semiconductor elastic medium,” Alexandria Eng. J. 59 (1), 1–9 (2020). doi.org/https://doi.org/10.1016/j.aej.2019.11.016

    Article  Google Scholar 

  31. I. M. Tayel, Kh. Lotfy, Alaa A. Al-Bary, et al., “Microelongated thermo-elastodiffusive waves of excited semiconductor material under laser pulses impact,” Mathematics 11 (7), 1627 (2023). https://doi.org/10.3390/math11071627

    Article  Google Scholar 

  32. W. Alhejaili, M. A. El Nasr, Kh. Lotfy, and A. El- Bary, “Laser short-pulse effect on magneto-photo-elasto-thermodiffusion waves of fractional heat equation for non-local excited semiconductor,” Opt. Quantum Electron. 54, 833 (2022). https://doi.org/10.1007/s11082-022-04247-w

    Article  CAS  Google Scholar 

  33. A. E. Abouelregal, “Generalized mathematical novel model of thermoelastic diffusion with four phase lags and higher- order time derivative,” Eur. Phys. J. Plus 135, 263 (2020). https://doi.org/10.1140/epjp/s13360-020-00282-2

    Article  Google Scholar 

  34. A. E. Abouelregal, “Modified fractional thermoelasticity model with multi-relaxation times of higher order: application to spherical cavity exposed to a harmonic varying heat,” Waves Random Complex Media 31 (5), 812–832 (2021). https://doi.org/10.1080/17455030.2019.1628320

    Article  ADS  MathSciNet  Google Scholar 

  35. M. Marin, “A temporally evolutionary equation in elasticity of micropolar bodies with voids,” UPB Sci. Bull. A: Appl. Math. Phys. 60 (3–4), 3–12 (1998).

  36. I. Abbas, A. Hobiny, and M. Marin, “Photo-thermal interactions in a semi-conductor material with cylindrical cavities and variable thermal conductivity,” J. Taibah Univ. Sci. 14 (1), 1369–1376 (2020). https://doi.org/https://doi.org/10.1080/16583655.2020.1824465

    Article  Google Scholar 

  37. M. Marin, A. Seadawy, S. Vlase, and A. Chirila, “On mixed problem in thermoelasticity of type III for Cosserat media,” J. Taibah Univ. Sci. 16 (1), 1264–1274 (2022). https://doi.org/10.1080/16583655.2022.2160290

    Article  Google Scholar 

  38. S. M. Abo-Dahab, A. E. Abouelregal, and M. Marin, “Generalized thermoelastic functionally graded on a thin slim strip non-Gaussian laser beam,” Symmetry 12 (7), 1094 (2020). https://doi.org/10.3390/sym12071094

    Article  ADS  Google Scholar 

  39. M. Othman, M. Fekry, and M. Marin, “Plane waves in generalized magneto-thermo-viscoelastic medium with voids under the effect of initial stress and laser pulse heating,” Struct. Eng. Mech. 73 (6), 621–629 (2020). https://doi.org/10.12989/sem.2020.73.6.621

    Article  Google Scholar 

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ACKNOWLEDGMENT

The authors extend their appreciation to Princess Nourah bint Abdulrahman University for fund this research under Researchers Supporting Project number (PNURSP2023R154) Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

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No funding was received for conducting this study.

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Correspondence to Eman Ibrahim, Shreen El-Sapa, Riadh Chteoui or Khaled Lotfy.

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Ibrahim, E., El-Sapa, S., Chteoui, R. et al. Four-Phase Lags in a Generalized Thermoelastic Rotational Diffusive Plate with Laser Pulse Emission. Mech. Solids 58, 2412–2423 (2023). https://doi.org/10.3103/S0025654423601787

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