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Effects of phase lags on wave propagation in an infinite solid due to a continuous line heat source

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Abstract

The present work is concerned with the wave propagation in a homogeneous, isotropic and unbounded solid due to a continuous line heat source under the theory of thermoelasticity with three phase-lags (Roychoudhari in J Therm Stress 30:231–238, 2007). For the solution of the problem, we employ a potential function approach together with Laplace and Hankel transform method. Analytical expressions for the distributions of different fields like temperature, displacement and stresses inside the medium are derived by inverting Laplace transforms in an approximate manner for small values of time. The problem is illustrated by computing numerical values of the field variables for a particular material. The theoretical as well as numerical results are compared with the corresponding results for other theories of thermoelasticity reported earlier.

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References

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  4. Green A.E., Naghdi P.M.: A re-examination of the basic postulates of thermomechanics. Proc. R. Soc. Lond. A 432, 171–194 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  5. Green A.E., Naghdi P.M.: On undamped heat waves in an elastic solid. J. Therm. Stress. 15, 253–264 (1992)

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  7. Chandrasekharaiah D.S.: Hyperbolic thermoelasticity: A review of recent literature. Appl. Mech. Rev. 51, 705–729 (1998)

    Article  Google Scholar 

  8. Tzou D.Y.: A unified field approach for heat conduction from micro to macroscales. ASME J. Heat Trans. 117, 8–16 (1995)

    Article  Google Scholar 

  9. Roychoudhari S.K.: On a thermoelastic three-phase-lag model. J. Therm. Stress. 30, 231–238 (2007)

    Article  Google Scholar 

  10. Quintanilla R.: Spatial behavior of solutions of the three-phase-lag heat equation. Appl. Math. Comput. 213, 153–162 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  11. Mukhopadhyay, S., Kothari, S., Kumar, R.: On the representation of solutions for the theory of generalized thermoelasticity with three phase lags. Acta Mech. (2010) Online(doi:10.1007/s00707-010-0291-z)

  12. Kar A., Kanoria M.: Generalized thermo-visco-elastic problem of a spherical shell three-phase-lag effect. Appl. Math. Model. 33, 3287–3298 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  13. Mukhopadhyay S., Kumar R.: Effect of three phase lag on generalized thermoelasticity for an infinite medium with a cylindrical cavity. J. Therm. Stress. 32, 1149–1165 (2009)

    Article  Google Scholar 

  14. Mukhopadhyay S., Kumar R.: Analysis of phase-lag effects on wave propagation in a thick plate under axisymmetric temperature distribution. Acta. Mech. 210, 331–344 (2010)

    Article  MATH  Google Scholar 

  15. Sherief H.H., Anwar M.N.: Problem in generalized thermoelasticity. J. Therm. Stress. 9, 165–181 (1986)

    Article  Google Scholar 

  16. Ezzat M.A.: Fundamental solution in thermoelasticity with two relaxation times for cylindrical regions. Int. J. Eng. Sci. 14, 2011–2020 (1995)

    Article  Google Scholar 

  17. Chandrasekharaiah D.S., Murthy H.N.: Temperature-rate-dependent thermoelastic interactions due to a line heat source. Acta Mech. 89, 1–12 (1991)

    Article  MATH  Google Scholar 

  18. Dhaliwal R.S., Majumdar S.R., Wang J.: Thermoelastic in an infinite solid caused by a line heat source. Int. J. Math. Sci. 20, 323–334 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  19. Chandrasekharaiah D.S., Srinath K.S.: Thermoelastic interactions without energy dissipation due to a line heat source. Acta Mech. 128, 243–251 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  20. Oberhettinger F., Badii L.: Tables of Laplace Transforms. Springer Verlag, New York (1973)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics Institute of Technology, Banaras Hindu University, Varanasi, 221005, India

    Rajesh Prasad, Roushan Kumar & Santwana Mukhopadhyay

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  1. Rajesh Prasad
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  2. Roushan Kumar
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  3. Santwana Mukhopadhyay
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Correspondence to Rajesh Prasad.

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Prasad, R., Kumar, R. & Mukhopadhyay, S. Effects of phase lags on wave propagation in an infinite solid due to a continuous line heat source. Acta Mech 217, 243–256 (2011). https://doi.org/10.1007/s00707-010-0389-3

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  • DOI: https://doi.org/10.1007/s00707-010-0389-3

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