Skip to main content
SpringerLink
Log in

Wave propagation at interface of heat conducting micropolar solid and fluid media

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

The present investigation is concerned with the wave propagation at an interface of a micropolar generalized thermoelastic solid half space and a heat conducting micropolar fluid half space. Reflection and transmission phenomena of plane waves are investigated, which impinge obliquely at the plane interface between a micropolar generalized thermoelastic solid half space and a heat conducting micropolar fluid half space. The incident wave is assumed to be striking at the interface after propagating through the micropolar generalized thermoelastic solid. The amplitude ratios of various reflected and transmitted waves are obtained in a closed form. It is found that they are a function of the angle of incidence and frequency and are affected by the elastic properties of the media. Micropolarity and thermal relaxation effects are shown on the amplitude ratios for a specific model. The results of some earlier literatures are also deduced from the present investigation.

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. Eringen, A. C. Simple microfluids. International Journal of Engineering Science, 2, 205–217 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  2. Eringen, A. C. Theory of microfluids. Journal of Applied Mathematics and Mechanics, 16, 1–18 (1966)

    MathSciNet  Google Scholar 

  3. Ariman, T., Sylvester, N. D., and Turk, M. A. Microcontinuum fluid mechanics — a review. International Journal of Engineering Science, 11, 905–930 (1973)

    Article  MATH  Google Scholar 

  4. Ariman, T., Sylvester, N. D., and Turk, M. A. Review article applications of microcontinuum fluid mechanics. International Journal of Engineering Science, 12, 273–293 (1974)

    Article  MATH  Google Scholar 

  5. Riha, P. On the theory of heat-conducting micropolar fluid with microtemperature. Acta Mechanica, 23, 1–8 (1975)

    Article  MATH  Google Scholar 

  6. Eringen, A. C. and Kafadar, C. B. Polar field theories. Continuum Physics (ed. Eringen, A. C.), Vol. IV, Academic Press, New York (1976)

    Google Scholar 

  7. Brulin, O. Linear micropolar media. Mechanics of Micropolar Media (eds. Brulin, O. and Hstiehr, K. T.), World Scientific, Singapore (1982)

    Google Scholar 

  8. Aggarwal, R. S. and Dhanapal, C. Flow and heat transfer in a micropolar fluid past a flate plate with suction and heat sources. International Journal of Engineering Science, 26, 1257–1266 (1988)

    Article  Google Scholar 

  9. Payne, L. E. and Straughan, B. Critical Rayleigh numbers for oscillatory and nonlinear convection in an isotropic thermomicropolar fluid. International Journal of Engineering Science, 27, 827–836 (1989)

    Article  MATH  Google Scholar 

  10. Gorla, R. S. R. Combined forced and free convection in the boundary layer flow of a micropolar fluid on a continuous moving vertical cylinder. International Journal of Engineering Science, 27, 77–86 (1989)

    Article  MATH  Google Scholar 

  11. Eringen, A. C. Theory of microstretch and bubbly liquids. International Journal of Engineering Science, 28, 133–143 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  12. Aydemir, N. U. and Venart, J. E. S. Flow of a thermomicropolar fluid with stretch. International Journal of Engineering Science, 28, 1211–1222 (1990)

    Article  Google Scholar 

  13. Yerofeyev, V. I. and Soldatov, I. N. A shear surface wave at the interface of an elastic body and a micropolar liquid. Journal of Applied Mathematics and Mechanics, 63(2), 277–281 (1999)

    Article  MathSciNet  Google Scholar 

  14. Yeremeyev, V. A. and Zubov, L. M. The theory of elastic and viscoelastic micropolar liquids. Journal of Applied Mathematics and Mechanics, 63(5), 755–767 (1999)

    Article  MathSciNet  Google Scholar 

  15. Hsia, S. Y. and Cheng, J. W. Longitudinal plane waves propagation in elastic micropolar porous media. Japanese Journal of Applied Physics, 45, 1743–1748 (2006)

    Article  Google Scholar 

  16. Hsia, S. Y., Chiu, S. M., Su, C. C., and Chen, T. H. Propagation of transverse waves in elastic micropolar porous semispaces. Japanese Journal of Applied Physics, 46, 7399–7405 (2007)

    Article  Google Scholar 

  17. Eringen, A. C. Linear theory of micropolar elasticity. Journal of Applied Mathematics and Mechanics, 15, 909–923 (1966)

    MATH  MathSciNet  Google Scholar 

  18. Biot, M. Thermoelasticity and irreversible thermodynamics. Journal of Applied Physics, 27, 240–253 (1956)

    Article  MATH  MathSciNet  Google Scholar 

  19. Lord, H. and Shulman, Y. A generalized dynamical theory of thermoelasticity. Journal of the Mechanics and Physics of Solids, 15, 299–309 (1967)

    Article  MATH  Google Scholar 

  20. Muller, I. M. The coldness, a universal function in thermoelastic bodies. Archive for Rational Mechanics and Analysis, 41, 319–332 (1971)

    Article  MathSciNet  Google Scholar 

  21. Green, A. E. and Laws, N. On the entropy production inequality. Archive for Rational Mechanics and Analysis, 45, 47–53 (1972)

    Article  MathSciNet  Google Scholar 

  22. Green, A. E. and Lindsay, K. A. Thermoelasticity. Journal of Elasticity, 2, 1–7 (1972)

    Article  MATH  Google Scholar 

  23. Suhubi, E. S. Thermoelastic solids. Continuum Physics (ed. Eringen, A. C.), Vol. 2, Academic Press, New York (1975)

    Google Scholar 

  24. Tomar, S. K. and Gogna, M. L. Reflection and refraction of a longitudinal microrotational wave at an interface between two micropolar elastic solids in welded contact. International Journal of Engineering Science, 30(11), 1637–1646 (1992)

    Article  MATH  Google Scholar 

  25. Tomar, S. K. and Gogna, M. L. Reflection and refraction of a longitudinal displacement wave at an interface between two micropolar elastic solids in welded contact. Journal of the Acoustical Society of America, 97, 827–830 (1995)

    Article  Google Scholar 

  26. Tomar, S. K. and Gogna, M. L. Reflection and refraction of coupled transverse and microrotational waves at an interface between two different micropolar elastic solids in welded contact. International Journal of Engineering Science, 33(4), 485–496 (1995)

    Article  MATH  Google Scholar 

  27. Kumar, R., Sharma, N., and Ram, P. Reflection and transmission of micropolar elastic waves at an imperfect boundary. Multidiscipline Modelling in Materials and Structures, 4, 15–36 (2008)

    Article  Google Scholar 

  28. Kumar, R., Sharma, N. and Ram, P. Interfacial imperfection on reflection and transmission of plane waves in anisotropic micropolar media. Theoretical and Applied Fracture Mechanics, 49, 305–312 (2008)

    Article  Google Scholar 

  29. Singh, D. and Tomar, S. K. Longitudinal waves at a micropolar fluid/solid interface. International Journal of Solids and Structures, 45(1), 225–244 (2008)

    MATH  Google Scholar 

  30. Ciarletta, M. Spatial decay estimates for heat conducting micropolar fluids. International Journal of Engineering Science, 39(6), 655–668 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  31. Singh, B. and Kumar, R. Reflection of plane waves from the flat boundary of a micropolar generalized thermoelastic half-space. International Journal of Engineering Science, 36(7–8), 865–890 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  32. Schoenberg, M. Transmission and reflection of plane wave at an elastic-viscoelastic interface. Geophysics Journal of Royal Astronomical Society, 25, 35–47 (1971)

    MATH  Google Scholar 

  33. Parfit, V. R. and Eringen, A. C. Reflection of plane waves from the flat boundary of a micropolar elastic half space. Journal of the Acoustical Society of America, 45, 1258–1272 (1969)

    Article  Google Scholar 

  34. Dhaliwal, R. S. and Singh, A. Dynamic Coupled Thermoelasticity, Hindustan Publication Corporation, New Delhi (1980)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Kurukshetra University, Kurukshetra, 136119, India

    R. Kumar

  2. Department of Applied Sciences, Guru Nanak Dev Engineering College, Ludhiana, Punjab, 141008, India

    M. Kaur

  3. Department of Applied Sciences, Gurukul Vidyapeeth, Institute of Engineering and Technology, Banur, Punjab, 140601, India

    S. C. Rajvanshi

Authors
  1. R. Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Kaur
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. C. Rajvanshi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Kumar.

Additional information

Communicated by Yi-ming FU

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kumar, R., Kaur, M. & Rajvanshi, S.C. Wave propagation at interface of heat conducting micropolar solid and fluid media. Appl. Math. Mech.-Engl. Ed. 32, 881–902 (2011). https://doi.org/10.1007/s10483-011-1467-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-011-1467-6

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation