Skip to main content
SpringerLink
Log in

Magneto-thermoelastic Response in a Functionally Graded Isotropic Unbounded Medium Under a Periodically Varying Heat Source

  • Published:
International Journal of Thermophysics Aims and scope Submit manuscript

Abstract

This paper deals with the problem of magneto-thermoelastic interactions in a functionally graded isotropic unbounded medium due to the presence of periodically varying heat sources in the context of linear theory of generalized thermoelasticity with energy dissipation (TEWED) and without energy dissipation (TEWOED) having a finite conductivity. The governing equations of generalized thermoelasticity (GN model) for a functionally graded material (FGM) under the influence of a magnetic field are established. The Laplace–Fourier double transform technique has been used to get the solution. The inversion of the Fourier transform has been done by using residual calculus, where poles of the integrand are obtained numerically in a complex domain by using Leguerre’s method and the inversion of the Laplace transformation is done numerically using a method based on a Fourier series expansion technique. Numerical estimates of the displacement, temperature, stress, and strain are obtained for a hypothetical material. The solution to the analogous problem for homogeneous isotropic materials is obtained by taking a suitable non-homogeneous parameter. Finally, the results obtained are presented graphically to show the effect of a non-homogeneous, magnetic field and damping coefficient on displacement, temperature, stress, and strain.

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

Abbreviations

u :

Displacement vector

λ, μ :

Lamé constants

ρ :

Constant mass density of the medium

γ :

Thermal module

α t :

Coefficient of linear thermal expansion

T 0 :

Uniform reference temperature

T :

Small temperature increase above the reference temperature T 0

J :

Electric current density vector

B :

Magnetic induction vector

c v :

Specific heat of the medium at constant strain

K*:

A material constant characteristic for the G–N theory

H :

Total magnetic field vector at any time

E :

Electric field vector

μ e :

Magnetic permeability of the medium

σ :

Electric conductivity of the medium

c T :

Non-dimensional finite thermal wave speed of G–N theory of thermoelasticity II

\({\epsilon_{\it T}}\) :

Thermoelastic coupling constant

K :

Thermal conductivity

κ :

Thermal diffusivity

References

  1. Lord H.W., Shulman Y.: J. Mech. Phys. Solids 15, 299 (1967)

    Article  MATH  ADS  Google Scholar 

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

    Article  MATH  Google Scholar 

  3. Paria G.: Proc. Camb. Phil. Soc. 58, 527 (1962)

    Article  MathSciNet  Google Scholar 

  4. Nayfeh A., Nemat-Nasser S.: Acta. Mech. 12, 43 (1971)

    Article  Google Scholar 

  5. Nayfeh A., Nemat-Nasser S.: J. Appl. Mech. 39, 108 (1972)

    MATH  MathSciNet  Google Scholar 

  6. Roychoudhuri S.K., Chatterjee(Roy) G.: Int. J. Math. Mech. Sci. 13(3), 567 (1990)

    Article  Google Scholar 

  7. R.K.T. Hsieh, Proc. IUTAM symposium, Stockholm, Sweden, 461 (1990)

  8. Ezzat M.A.: Int. J. Eng. Sci. 35(8), 741 (1997)

    Article  MATH  Google Scholar 

  9. Ezzat M.A., Othman M.I., El-Karamany A.S.: J. Therm. Stress. 24, 411 (2001)

    Article  Google Scholar 

  10. Sherief H.H., Yoset H.M.: J. Therm. Stress. 27, 537 (2004)

    Article  Google Scholar 

  11. Baksi A., Bera R.K.: Math. Comput. Model. 42, 533 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  12. Green A.E., Naghdi P.M.: Proc. R. Soc. Lond. Ser. 432, 171 (1991)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  13. Green A.E., Naghdi P.M.: J. Elast. 31, 189 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  14. Roychoudhuri S.K.: J. Tech. Phys. 47(2), 63 (2006)

    Google Scholar 

  15. Green A.E., Naghdi P.M.: J. Therm. Stress. 15, 252 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  16. Chandrasekhariah D.S.: J. Elast. 43, 279 (1996)

    Article  Google Scholar 

  17. Chandrasekhariah D.S.: J. Therm. Stress. 19, 267 (1996)

    Article  Google Scholar 

  18. Chandrasekhariah D.S.: J. Therm. Stress. 19, 695 (1996)

    Article  Google Scholar 

  19. Chandrasekhariah D.S., Srinath K.S.: J. Elast. 50, 97 (1998)

    Article  Google Scholar 

  20. Mallik S.H., Kanoria M.: Far East J. Appl. Math. 23(2), 147 (2006)

    MATH  MathSciNet  Google Scholar 

  21. Mallik S.H., Kanoria M.: Indian J. Math. 49, 47 (2007)

    MATH  MathSciNet  Google Scholar 

  22. Kar A., Kanoria M.: Eur. J. Mech. A Solids 26, 269 (2007)

    Article  MathSciNet  Google Scholar 

  23. Kar A., Kanoria M.: Int. J. Solids Struct. 44, 2961 (2007)

    Article  MATH  Google Scholar 

  24. Taheri H., Fariborz S.J., Eslami M.R.: J. Therm. Stress. 28, 911 (2005)

    Article  Google Scholar 

  25. Roychoudhuri S.K., Dutta P.S.: Int. J. Solids Struct. 42, 4192 (2005)

    Article  MATH  Google Scholar 

  26. Bandyopadhyay N., Roychoudhuri S.K.: Bull. Cal. Math. Soc. 97(6), 489 (2005)

    MATH  MathSciNet  Google Scholar 

  27. Whetherhold R.C., Wang S.S.: J. Compos. Sci. Technol. 56, 1099 (1996)

    Article  Google Scholar 

  28. Sankar B.V., Tzeng J.T.: J. AIAA 40, 1228 (2002)

    Article  ADS  Google Scholar 

  29. Vel S.S., Batra R.C.: J. AIAA 40, 1421 (2002)

    Article  ADS  Google Scholar 

  30. Qian L.F., Batra R.C.: J. Therm. Stress. 27, 705 (2004)

    Article  Google Scholar 

  31. Lutz M.P., Zimmerman R.W.: J. Therm. Stress. 19, 39 (1996)

    Article  MathSciNet  Google Scholar 

  32. Lutz M.P., Zimmerman R.W.: J. Therm. Stress. 22, 177 (1999)

    Article  Google Scholar 

  33. Ye G.R., Chen W.Q., Cai J.B.: J. Mech. Res. Commun. 28, 535 (2001)

    Article  MATH  Google Scholar 

  34. El-Naggar A.M., Abd-Alla A.M., Fahmy M.A., Ahmed S.M.: J. Heat Mass Transf. 39, 41 (2002)

    Article  ADS  Google Scholar 

  35. Wang B.L., Mai Y.W.: Int. J. Mech. Sci. 47, 303 (2005)

    Article  Google Scholar 

  36. Ootao Y., Tanigawa Y.: J. Therm. Stress. 29, 1031 (2006)

    Article  Google Scholar 

  37. Shao Z.S., Wang T.J., Ang K.K.: J. Therm. Stress. 30, 81 (2007)

    Article  Google Scholar 

  38. Hosseini Kordkheili S.A., Naghbadi R.: J. Therm. Stress. 31, 1 (2008)

    Article  Google Scholar 

  39. Ootao Y., Tanigawa Y.: J. Therm. Stress. 30, 441 (2007)

    Article  Google Scholar 

  40. Bagri A., Eslami M.R.: J. Therm. Stress. 30, 911 (2007)

    Article  Google Scholar 

  41. Bagri A., Eslami M.R.: J. Therm. Stress. 30, 1175 (2007)

    Article  Google Scholar 

  42. Nayfeh A., Nemat-Nasser S.: J. Appl. Mech. 39, 108 (1972)

    MATH  MathSciNet  Google Scholar 

  43. Rakshit M., Mukhopadhyay B.: Int. J. Eng. Sci. 43, 925 (2005)

    Article  MathSciNet  Google Scholar 

  44. Tianhu H., Shirong L.: J. Therm. Stress. 29, 683 (2006)

    Article  Google Scholar 

  45. Baksi A., Bera R.K., Debnath L.: Int. J. Eng. Sci. 43, 1419 (2005)

    Article  MathSciNet  Google Scholar 

  46. Roychoudhuri S.K., Chattopadhyay M.: Int. J. Thermophys. 28(4), 1401 (2007)

    Article  Google Scholar 

  47. Banik S., Mallik S.H., Kanoria M.: Int. J. Pure Appl. Math. 34, 231 (2007)

    MATH  MathSciNet  Google Scholar 

  48. Mallik S.H., Kanoria M.: Int. J. Solids Struct. 44, 7633 (2007)

    Article  MATH  Google Scholar 

  49. Honig G., Hireds U.: J. Comput. Appl. Math 10, 113 (1984)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Netaji Subhash Engineering College, Technocity, Police Para, Panchpota, Garia, Kolkata, 700152, India

    Payel Das

  2. Department of Applied Mathematics, University of Calcutta, 92 A.P.C Road, Kolkata, 700 009, West Bengal, India

    M. Kanoria

Authors
  1. Payel Das
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Kanoria
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Kanoria.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Das, P., Kanoria, M. Magneto-thermoelastic Response in a Functionally Graded Isotropic Unbounded Medium Under a Periodically Varying Heat Source. Int J Thermophys 30, 2098–2121 (2009). https://doi.org/10.1007/s10765-009-0679-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10765-009-0679-y

Keywords

Search

Navigation