Skip to main content
SpringerLink
Log in

The Effect of Diffusion and Microconcentration on Plane Waves in a Generalized Thermoelastic Material

  • MISCELLANEA
  • Published:
Journal of Engineering Physics and Thermophysics Aims and scope

The governing equations for a linear, isotropic, homogeneous, thermoelastic material with diffusion and microconcentration in a plane have been stated in accordance with the Lord and Shulman theory of generalized thermoelasticity. The plane harmonic solutions of these equations have been obtained. It has been shown that there exist four dispersive coupled longitudinal waves and two uncoupled transverse waves. A half-space with thermally insulated surface has been taken for exploring the reflection of these plane waves. For an incident plane wave, the coefficients of reflection and energy shares of the reflected waves have been presented graphically. The numerical results have made possible to observe the effects of the diffusion and microconcentration parameters on the speeds, reflection coefficients, and the energy ratios.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. A. Biot, Thermoelasticity and irreversible thermodynamics, J. Appl. Phys., 27, No. 3, 240–253 (1956).

    Article  MathSciNet  MATH  Google Scholar 

  2. H. W. Lord and Y. Shulman, A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids, 15, Issue 5, 299–309 (1967).

    Article  MATH  Google Scholar 

  3. A. E. Green and K. A. Lindsay, Thermoelasticity, J. Elast., 2, No. 1, 1–7 (1972).

    Article  MATH  Google Scholar 

  4. A. E. Green and P. M. Naghdi, Thermoelasticity without energy dissipation, J. Elast., 31, 189–208 (1993).

    Article  MathSciNet  MATH  Google Scholar 

  5. P. Puri, Plane waves in generalized thermoelasticity, Int. J. Eng. Sci., 11, 735–744 (1973).

    Article  MATH  Google Scholar 

  6. A. N. Sinha and S. B. Sinha, Reflection of thermoelastic waves at a solid half-space with thermal relaxation, J. Phys. Earth, 22, Issue 2, 237–244 (1974).

    Article  Google Scholar 

  7. V. K. Agarwal, On plane waves in generalized thermoelasticity, Acta Mech., 31, Nos. 3–4, 185–198 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  8. S. B. Sinha and K. A. Elsibai, Reflection of thermoelastic waves at a solid half-space with two relaxation times, J. Therm. Stresses, 19, 749–762 (1996).

    Article  Google Scholar 

  9. J. N. Sharma, V. Kumar, and D. Chand, Reflection of generalized thermoelastic waves from the boundary of a halfspace, J. Therm. Stresses, 26, 925–942 (2003).

    Article  Google Scholar 

  10. B. Singh, Reflection of plane waves at the free surface of a monoclinic thermoelastic solid half-space, Eur. J. Mech. A Solids, 29, 911–916 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  11. B. Singh, Reflection of plane waves from surface of a thermoelastic saturated porous solid half-space with impedance boundary conditions, J. Porous Media, 22, 1333–1349 (2019).

    Article  Google Scholar 

  12. N. Sarkar, S. De, and N. Sarkar, Memory response in plane wave reflection in generalized magneto-thermoelasticity, J. Electromagn. Waves, 33, 1354–1374 (2019).

    Article  Google Scholar 

  13. M. Gupta and S. Mukhopadhyay, Analysis of harmonic plane wave propagation predicted by strain and temperaturerate-dependent thermoelastic model, Waves Random Complex Media, 31, No. 6, 2481–2498 (2021).

    Article  MathSciNet  MATH  Google Scholar 

  14. W. Nowacki, Dynamic problems of thermodiffusion in elastic solids. Part I, Bull. Pol. Acad. Sci. Tech. Sci., 22, 55–64 (1974).

  15. W. Nowacki, Dynamical problems of thermodiffusion in solids. Part II, Bull. Pol. Acad. Sci. Tech. Sci., 22, 129–135 (1974).

  16. W. Nowacki, Dynamical problems of thermodiffusion in solids. Part III, Bull. Pol. Acad. Sci. Tech. Sci., 22, 257–266 (1974).

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

    Article  MathSciNet  MATH  Google Scholar 

  18. M. Aouadi, The coupled theory of micropolar thermoelastic diffusion, Acta Mech., 208, Nos. 3–4, 181–203 (2009).

    Article  MATH  Google Scholar 

  19. M. A. Ezzat and M. A. Fayik, Fractional order theory of thermoelastic diffusion, J. Therm. Stresses, 34, 851–872 (2011).

    Article  Google Scholar 

  20. M. Aouadi, Classic and generalized thermoelastic diffusion theories, in: Encyclopedia of Thermal Stresses, Springer (2013), pp. 567–575.

  21. A. S. El-Karamany and M. A. Ezzat, Thermoelastic diffusion with memory-dependent derivative, J. Therm. Stresses, 39, 1035–1050 (2016).

    Article  Google Scholar 

  22. B. Singh, Reflection of SV waves from the free surface of an elastic solid in generalized thermoelastic diffusion, J. Sound Vib., 291, 764–778 (2006).

    Article  MATH  Google Scholar 

  23. J. N. Sharma, Generalized thermoelastic diffusive waves in heat conducting materials, J. Sound Vib., 301, 979–993 (2007).

    Article  Google Scholar 

  24. B. Singh, On theory of generalized thermoelastic solids with voids and diffusion, Eur. J. Mech. A Solids, 30, 976–982 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  25. R. Bijarnia and B. Singh, Propagation of plane waves in an anisotropic generalized thermoelastic solid with diffusion, J. Eng. Phys. Thermophys., 85, No. 2, 478–486 (2012).

    Article  MATH  Google Scholar 

  26. R. Kumar and V. Gupta, Plane wave propagation in an anisotropic dual-phase-lag thermoelastic diffusion medium, Multidiscip. Model. Mater. Struct., 10, 562–594 (2014).

    Article  Google Scholar 

  27. B. Singh and H. Singla, Effects of rotation, voids and diffusion on characteristics of plane waves in a thermoelastic material, Multidiscip. Model. Mater. Struct., 16, No. 1, 73–92 (2020).

    Article  Google Scholar 

  28. R. A. Grot, Thermodynamics of a continuum with microstructure, Int. J. Eng. Sci., 7, 801–814 (1969).

    Article  MATH  Google Scholar 

  29. P. Říha, On the microcontinuum model of heat conduction in materials with inner structure, Int. J. Eng. Sci., 14, 529–535 (1976).

    Article  Google Scholar 

  30. A. C. Eringen, Microcontinuum Field Theories: I. Foundations and Solids, Springer (2012).

    MATH  Google Scholar 

  31. D. Iesan, On a theory of micromorphic elastic solids with microtemperatures, J. Therm. Stresses, 24, 737–752 (2001).

    Article  MathSciNet  Google Scholar 

  32. D. Ieşan and L. Nappa, On the theory of heat for micromorphic bodies, Int. J. Eng. Sci., 43, Nos. 1–2, 17–32 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  33. D. Ieşan, Thermoelasticity of bodies with microstructure and microtemperatures, Int. J. Solids Struct., 44, 8648–8662 (2007).

    Article  MATH  Google Scholar 

  34. D. Ieşan and R. Quintanilla, On thermoelastic bodies with inner structure and microtemperatures, J. Math. Anal. Appl., 354, Issue 1, 12–23 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  35. D. Ieşan, On a theory of thermoelasticity without energy dissipation for solids with microtemperatures, Z. Angew. Math. Mech., 98, 870–885 (2018).

    Article  MathSciNet  Google Scholar 

  36. M. Ciarletta, F. Passarella, and V. Tibullo, Plane harmonic waves in strongly elliptic thermoelastic materials with microtemperatures, J. Math. Anal. Appl., 424, 1186–1197 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  37. A. M. Zenkour, Refined microtemperatures multi-phase-lags theory for plane wave propagation in thermoelastic medium, Results Phys., 11, 929–937 (2018).

    Article  Google Scholar 

  38. M. Aouadi, M. Ciarletta, and V. Tibullo, A thermoelastic diffusion theory with microtemperatures and microconcentrations, J. Therm. Stresses, 40, 486–501 (2017).

    Article  Google Scholar 

  39. N. Bazarra, M. Campo, and J. R. Fernández, A thermoelastic problem with diffusion, microtemperatures, and microconcentrations, Acta Mech., 230, No. 2, 31–48 (2019).

    Article  MathSciNet  MATH  Google Scholar 

  40. S. Deswal, A. Gunghas, and K. K. Kalkal, Reflection of plane waves in a thermoelastic diffusive medium under the effect of microtemperatures, J. Therm. Stresses, 42, 1316–1329 (2019).

    Article  Google Scholar 

  41. A. Gunghas, D. Sheoran, S. Kumar, and K. K. Kalkal, Waves in a magneto-thermoelastic diffusive half-space with microconcentrations, Waves Random Complex Media, 32, No. 2, 708–727 (2022).

    Article  MathSciNet  MATH  Google Scholar 

  42. J. D. Achenbach, Wave Propagation in Elastic Solids, Elsevier, North Holland (1973).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Panjab University, Chandigarh, 160014, India

    H. Singla

  2. Department of Mathematics, Post Graduate Government College, Sector 11, Chandigarh, 160011, India

    B. Singh

Authors
  1. H. Singla
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. Singh.

Additional information

Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 96, No. 3, pp. 834–847, May–June, 2023.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Singla, H., Singh, B. The Effect of Diffusion and Microconcentration on Plane Waves in a Generalized Thermoelastic Material. J Eng Phys Thermophy 96, 834–847 (2023). https://doi.org/10.1007/s10891-023-02745-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10891-023-02745-6

Keywords

Search

Navigation