Skip to main content

Eigenvalue approach for generalized thermoelastic porous medium under the effect of thermal loading due to a laser pulse in DPL model

Abstract

The aim of the present study is concerned with the thermal loading due to laser pulse on thermoelastic porous medium under dual-phase-lag model DPL. The material is a homogeneous isotropic elastic half-space and heated by a non-Gaussian laser beam with the pulse duration of 8 ps. Eigenvalue approach is proposed to analyze the problem and obtain the analytical solutions of the displacement components, stresses, temperature distribution and change in the volume fraction field. The results of the physical quantities have been illustrated graphically by the comparison between the coupled theory, DPL model and Lord–Shulman theory of the certain value of time and distance. The results presented in this article should prove useful for researchers in material science (porous media), designers of new materials, physicists as well as for those working on the development of heat laser pulse practical situations as in geophysics, optics, acoustics and geomagnetic.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

References

  1. [1]

    M A Biot J. Appl. Phys.27 240 (1956).

  2. [2]

    H W Lord and Y A Shulman J. Mech. Phys. Solids15 299 (1967).

    ADS  Article  Google Scholar 

  3. [3]

    A E Green and K A Lindsay J. Elast.2 1 (1972).

    Article  Google Scholar 

  4. [4]

    D Y Tzou Macro- to Micro Scale Heat Transfer: The Lagging Behavior, 1st edn (Washington: Taylor & Francis) (1996)

  5. [5]

    I A Abbas and A M Zenkour J. Comput. and Theor. Nanosci.11 642 (2014)

    Article  Google Scholar 

  6. [6]

    M I A Othman, W M Hasona and E M Abd-Elaziz Can. J. Phys.92 148 (2014)

    ADS  Google Scholar 

  7. [7]

    H M Al-Qahtani and S K Datta J. Therm. Stress.31 569 (2008)

    Article  Google Scholar 

  8. [8]

    A M Abd-Alla, M I.A. Othman and S M Abo-Dahab Comput. Mater. Control51 63 (2016)

  9. [9]

    M I A Othman and M Marin Results Phys.7 3863 (2017)

    ADS  Article  Google Scholar 

  10. [10]

    M A Goodmann and S C Cowin Arch. Ration. Mech. Anal.44 249 (1972).

    Article  Google Scholar 

  11. [11]

    J W Nunziato and S C Cowin Arch. Ration. Mech. Anal.72 175 (1979).

    Article  Google Scholar 

  12. [12]

    S C Cowin and J W Nunziato J. Elast.13 125 (1983).

    Article  Google Scholar 

  13. [13]

    D Iesan Acta Mech60 67 (1986).

  14. [14]

    I A Abbas and R Kumar J. Comput. and Theor. Nanosci.11 1472 (2004)

    Article  Google Scholar 

  15. [15]

    M I A Othman and E E M Eraki, Multi. Model. Mater. Struct.14 457 (2018)

    Article  Google Scholar 

  16. [16]

    M I A Othman and E R M Edeeb J. Comput. Theor. Nanosci.13 294 (2016).

    Article  Google Scholar 

  17. [17]

    M I A Othman and E M Abd-Elaziz J. Therm. Stress.38 1068 (2015).

    Article  Google Scholar 

  18. [18]

    M Marin and A Oechsner, Contin. Mech. Thermodyn.29 1365 (2017).

    ADS  MathSciNet  Article  Google Scholar 

  19. [19]

    M Marin Meccanica51 1127 (2016).

  20. [20]

    M Marin Acta Mechanica122 155 (1997).

  21. [21]

    M Hassan, M Marin, A Alsharif and R Ellahi Phys. Lett. A382 2749 (2018).

    ADS  Article  Google Scholar 

  22. [22]

    C Fetecau, R Ellahi, M Khan and N A Shah J. Porous Media21 589 (2018)

    Article  Google Scholar 

  23. [23]

    R Ellahi, M Raza and N S Akbar J. Porous Media20 461 (2017).

    Article  Google Scholar 

  24. [24]

    M M Bhatti, A Zeeshan, R Ellahi and G C Shit Adv. Powder Technol.29 1189 (2018).

    Article  Google Scholar 

  25. [25]

    K M Shirvan, M Mamourian, S Mirzakhanlari, R Ellahi and K Vafai Int. J. Heat Mass Transf.105 811 (2017).

    Article  Google Scholar 

  26. [26]

    S Z Alamri, R Ellahi, N Shehzad and A Zeeshan J. Mol. Liq., 273 292 (2019).

  27. [27]

    M Sheikholeslami Comput. Methods Appl. Mech. Eng.344 306 (2019).

  28. [28]

    M Sheikholeslami, S A Shehzad, Z Li and A Shafee Int. J. Heat Mass Transf.127 614 (2018).

    Article  Google Scholar 

  29. [29]

    M Sheikholeslami, J. Mol. Liq.265 347 (2018).

    Article  Google Scholar 

  30. [30]

    M Sheikholeslami, S A Shehzad, F M Abbasi and Z Li, Comput. Methods Appl. Mech. Eng.338 491 (2018).

    ADS  Article  Google Scholar 

  31. [31]

    I A Abbas Comput. Math. Appl.68 2036 (2014).

  32. [32]

    I A Abbas J. Mech. Sci. Tech. 28 4193 (2014).

  33. [33]

    M I A Othman and IA Abbas J. Comput. and Theor. Nanosci.12 2399 (2015).

  34. [34]

    I A Abbas J. Magn. and Magn. Mater.377 452 (2015).

  35. [35]

    R S Dhaliwal and A Singh Dynamic Coupled Thermoelasticity (New Delhi: Hindustan Publ. Corp.) (1980)

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Mohamed I. A. Othman.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Othman, M.I.A., Abbas, I.A. Eigenvalue approach for generalized thermoelastic porous medium under the effect of thermal loading due to a laser pulse in DPL model. Indian J Phys 93, 1567–1578 (2019). https://doi.org/10.1007/s12648-019-01431-9

Download citation

Keywords

  • Generalized thermoelastic
  • Laser pulse
  • Porous medium
  • DPL model
  • Eigenvalue approach

PACS Nos.

  • 44.05.+e
  • 81.40.Jj
  • 62.20. fq
  • 62.20.Dc
  • 62.40.+i