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Magnetothermoelastic Waves in a Rotating Orthotropic Medium with Diffusion

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In this paper, the governing partial differential equations for a rotating orthotropic magnetothermoelastic medium with diffusion are proposed on the basis of the Lord–Shulman theory of generalized thermoelasticity and the velocity equation is obtained. The plane wave solution of this equation is indicative of the existence of four quasi-plane waves, namely, quasi-longitudinal displacement (qLD), quasi-thermal (qT), quasi-mass diffusion (qMD), and quasitransverse displacement (qTD) waves. The real values of the wave speeds are calculated for a particular material, and the effects of anisotropy, as well as of the diffusion, magnetic, and rotation parameters and the angle of incidence on the speeds are shown graphically.

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References

  1. M. A. Biot, Thermoelasticity and irreversible thermodynamics, J. Appl. Phys., 27, 240–253 (1956).

    Article  MathSciNet  Google Scholar 

  2. H. W. Lord and Y. Shulman, A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids, 15, 299–309 (1967).

    Article  Google Scholar 

  3. A. E. Green and K. A. Lindsay, Thermoelasticity, J. Elast., 2, 1–7 (1972).

    Article  Google Scholar 

  4. R. B. Hetnarski and J. Ignaczak, Generalized thermoelasticity, J. Therm. Stresses, 22, 451–476 (1999).

    Article  MathSciNet  Google Scholar 

  5. J. Ignaczak and M. Ostoja-Starzewski, Thermoelasticity with Finite Wave Speeds, Oxford University Press, Oxford (2009).

    Book  Google Scholar 

  6. R. S. Dhaliwal and H. H. Sherief, Generalized thermoelasticity for anisotropic media, Quart. Appl. Math., 38, 1–8 (1980).

    Article  MathSciNet  Google Scholar 

  7. H. Jeffreys, The thermodynamics of an elastic solid, Proc. Camb. Phil. Soc., 26, 101–106 (1930).

    Article  Google Scholar 

  8. R. Gutenberg, Energy relation of reflected and refracted seismic waves, Bull. Seismol. Soc. Am., 34, 85–102 (1944).

    Article  Google Scholar 

  9. A. N. Sinha and S. B. Sinha, Reflection of thermoelastic waves at a solid half-space with thermal relaxation, J. Phys. Earth, 22, 237–244 (1974).

    Article  Google Scholar 

  10. M. Schoenberg and D. Censor, Elastic waves in rotating media, Quart. Appl. Math., 31,115–125 (1973).

    Article  Google Scholar 

  11. B. Singh and A. K. Yadav, Plane waves in a transversely isotropic rotating magnetothermoelastic medium, J. Eng. Phys. Thermophys., 85, 1226–1232 (2012).

    Article  Google Scholar 

  12. B. Singh and A. K. Yadav, Reflection of plane waves in a rotating transversly isotropic magneto-thermoelastic solid half-space, J. Theor. Appl. Mech., Sofia, 42, 33–60 (2012).

    Article  Google Scholar 

  13. D. S. Chandrasekharaiah and K. R. Srikantiah, Thermoelastic plane waves in a rotating solid, Acta Mech., 50, 211–219 (1984).

    Article  Google Scholar 

  14. L. Knopoff, The interaction between elastic wave motion and a magnetic field in electrical conductors, J. Geophys. Res., 60, 441–456 (1955).

    Article  Google Scholar 

  15. M. I. A. Othman and N. T. Mansour, 2-D problem of magneto-thermoelastic medium under the effect of different fields with two-temperature and 3PHL model, Am. J. Nano Res. Appl., 4, 33–42 (2016).

    Google Scholar 

  16. D. Chand, J. N. Sharma, and S. P. Sud, Transient generalized magneto-thermoelastic waves in a rotating half-space, Int. J. Eng. Sci., 28, 547–556 (1990).

    Article  Google Scholar 

  17. B. Singh and A. K. Yadav, Plane waves in a rotating monoclinic magnetothermoelastic medium, J. Eng. Phys. Thermophys., 89, 428–440 (2016).

    Article  Google Scholar 

  18. S. M. Abo-Dahab and S. Biswas, Effect of rotation on Rayleigh waves in magneto-thermoelastic transversely isotropic medium with thermal relaxation times, J. Electromagn. Waves Appl., 31, 1485–1507 (2017).

    Article  Google Scholar 

  19. S. Shaw and M. I. A. Othman, Characteristics of Rayleigh wave propagation in orthotropic magneto-thermoelastic half-space: An eigenfunction expansion method, Appl. Math. Model., 67, 605–620 (2019).

    Article  MathSciNet  Google Scholar 

  20. S. Biswas and B. Mukhopadhyay, Eigenfunction expansion method to analyze thermal shock behaviour in magnetothermoelastic orthotropic medium under three theories, J. Therm. Stresses, 41, 366–382 (2018).

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  22. W. Nowacki, Dynamical problems of thermodiffusion in solids. Part I, Bull. Pol. Acad. Sci., Ser. Sci. Technol., 22, 55–64 (1974).

  23. W. Dudziak and S. J. Kowalski, Theory of thermodiffusion for solids, Int. J. Heat Mass Transf., 32, 2005–2013 (1989).

    Article  Google Scholar 

  24. B. Singh, Reflection of P and SV waves from free surface of an elastic solid with generalized thermodiffusion, J. Earth Syst. Sci., 114, 159–168 (2005).

    Article  Google Scholar 

  25. M. Aouadi, Theory of generalized micropolar thermoelastic diffusion under Lord–Shulman model, J. Therm. Stresses, 32, 923–942 (2009).

    Article  Google Scholar 

  26. K. Lotfy, S. M. Abo-Dahab, and R. Tantawy, Thermomechanical response model on a reflection photothermal diffusion waves (RPTD) for semiconductor medium, Silicon, 12, 199–209 (2020).

    Article  Google Scholar 

  27. N. Mabrouk, Moh′d Yasein, K. Lotfy, and A. A. El-Bary, Effect of magneto-rotator-diffusive waves on the photothermal excitation medium of a dual-phase-lag model and variable thermal conductivity, J. Electromagn. Waves Appl., 34, 330–348 (2020).

  28. Anand Kumar Yadav, Reflection of plane waves from the free surface of a rotating orthotropic magneto-thermoelastic solid half-space with diffusion, J. Therm. Stresses, 44, 86–106 (2021).

    Article  Google Scholar 

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Correspondence to A. K. Yadav.

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Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 94, No. 6, pp. 1663–1672, November–December, 2021.

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Yadav, A.K. Magnetothermoelastic Waves in a Rotating Orthotropic Medium with Diffusion. J Eng Phys Thermophy 94, 1628–1637 (2021). https://doi.org/10.1007/s10891-021-02444-0

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  • DOI: https://doi.org/10.1007/s10891-021-02444-0

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