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Fractional magneto-thermoelastic materials with phase-lag Green-Naghdi theories

  • Ezzat, M.A. (Department of Mathematics, Faculty of Education, Alexandria University) ;
  • El-Bary, A.A. (Arab Academy for Science and Technology)
  • 투고 : 2016.12.10
  • 심사 : 2017.03.30
  • 발행 : 2017.06.30

초록

A unified mathematical model of phase-lag Green-Naghdi magneto-thermoelasticty theories based on fractional derivative heat transfer for perfectly conducting media in the presence of a constant magnetic field is given. The GN theories as well as the theories of coupled and of generalized magneto-thermoelasticity with thermal relaxation follow as limit cases. The resulting nondimensional coupled equations together with the Laplace transforms techniques are applied to a half space, which is assumed to be traction free and subjected to a thermal shock that is a function of time. The inverse transforms are obtained by using a numerical method based on Fourier expansion techniques. The predictions of the theory are discussed and compared with those for the generalized theory of magneto-thermoelasticity with one relaxation time. The effects of Alfven velocity and the fractional order parameter on copper-like material are discussed in different types of GN theories.

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참고문헌

  1. Abbas, I.A. and Kumar, R. (2016), "2D deformation in initially stressed thermoelastic half-space with voids", Steel Compos. Struct., Int. J., 20(5), 1103-1117 https://doi.org/10.12989/scs.2016.20.5.1103
  2. Alzahrani, F.S. and Abbas, I.A. (2016), "The effect of magnetic field on a thermoelastic fiber-reinforced material under GN-III theory", Steel Compos. Struct., Int. J., 22(2), 369-386. https://doi.org/10.12989/scs.2016.22.2.369
  3. Biot, M. (1956), "Thermoelasticity and irreversible thermodynamics", J. Appl. Phys., 27(3), 240-253. https://doi.org/10.1063/1.1722351
  4. Chandrasekharaiah, D.S. (1998), "Hyperbolic thermoelasticity: A review of recent literature", Appl. Mech. Rev., 51, 705-730. https://doi.org/10.1115/1.3098984
  5. Chirita, S. and Ciarletta, M. (2010), "Reciprocal and variational principles in linear thermoelasticity without energy dissipation", Mech. Res. Commu., 37(3), 271-275. https://doi.org/10.1016/j.mechrescom.2010.03.001
  6. Ciarletta, M. (2009), "A theory of micropolar thermoelasticity without energy dissipation", J. Therm. Stress., 22(6), 581-594. https://doi.org/10.1080/014957399280760
  7. El-Karamany, A.S. and Ezzat, M.A. (2016), "On the phase- lag Green-Naghdi thermoelasticity theories", Appl. Math. Model., 40(9), 5643-5659. https://doi.org/10.1016/j.apm.2016.01.010
  8. El-Karamany, A.S. and Ezzat, M.A. (2011), "On fractional thermoelasticity", Math. Mech. Solids, 16(3), 334-346. https://doi.org/10.1177/1081286510397228
  9. El-Karamany, A.S. and Ezzat, M.A. (2014), "On the dual-phaselag thermoelasticity theory", Meccanica, 49(1), 79-89. https://doi.org/10.1007/s11012-013-9774-z
  10. Ezzat, M.A. (2001), "Free convection effects on perfectly conducting fluid", Int. J. Eng. Sci., 39(7), 799-819. https://doi.org/10.1016/S0020-7225(00)00059-8
  11. Ezzat, M.A. (2006), "The relaxation effects of the volume properties of electrically conducting viscoelastic material", Mater. Sci. Eng. B: Solid-State Mater. Adv. Technol., 130(1-3), 11-23. https://doi.org/10.1016/j.mseb.2006.01.020
  12. Ezzat, M.A. (2011), "Thermoelectric MHD with modified Fourier's law", Int. J. Therm. Sci., 50(4), 449-455. https://doi.org/10.1016/j.ijthermalsci.2010.11.005
  13. Ezzat, M.A. (2012), "State space approach to thermoelectric fluid with fractional order heat transfer", Heat Mass Trans., 48(1), 71-82. https://doi.org/10.1007/s00231-011-0830-8
  14. Ezzat, M.A. and Abd-Elaal, M.Z. (1997a), "Free convection effects on a viscoelastic boundary layer flow with one relaxation time through a porous medium", J. Frank. Inst., 334(4), 685-706. https://doi.org/10.1016/S0016-0032(96)00095-6
  15. Ezzat, M.A. and Abd-Elaal, M.Z. (1997b), "State space approach to viscoelastic fluid flow of hydromagnetic fluctuating boundary-layer through a porous medium", ZAMM, 77(3), 197-209. https://doi.org/10.1002/zamm.19970770307
  16. Ezzat, M.A. and El-Bary, A.A. (2016), "Modeling of fractional magneto-thermoelasticity for a perfect conducting materials", Smart Struct. Syst., Int. J., 18(4), 707-731. https://doi.org/10.12989/sss.2016.18.4.707
  17. Ezzat, M.A. and El-Karamany, A.S. (2011a), "Fractional order heat conduction law in magneto- thermoelasticity involving two temperatures", ZAMP, 62(5), 937- 952. https://doi.org/10.1007/s00033-011-0126-3
  18. Ezzat, M.A. and El-Karamany, A.S. (2011b), "Theory of fractional order in electro-thermoelasticity", Eur. J. Mech. A/Solids, 30(4), 491-500. https://doi.org/10.1016/j.euromechsol.2011.02.004
  19. Ezzat, M.A., El-Karamany, A.S. and Fayik, M.A. (2012), "Fractional order theory in thermoelastic solid with three-phase lag heat transfer", Arch. Appli. Mech., 82(4), 557-572. https://doi.org/10.1007/s00419-011-0572-6
  20. Gorenflo, R. and Mainardi, F. (1997), "Fractional Calculus: Integral and Differential Equations of Fractional Orders, Fractals and Fractional Calculus in Continuum Mechanics", Springer, Wien, Austria.
  21. Green, A.E. and Naghdi, P.M. (1991), "A re-examination of the basic postulates of thermomechanics", Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 432(1885), 171-194.
  22. Green, A.E. and Naghdi, P.M. (1992), "On undamped heat waves in an elastic solid", J. Therm. Stress., 15(2), 253-264. https://doi.org/10.1080/01495739208946136
  23. Green, A.E. and Naghdi, P.M. (1993), "Thermoelasticity without energy dissipation", J. Elas., 31(3), 189-208. https://doi.org/10.1007/BF00044969
  24. Honig, G. and Hirdes, U. (1984), "A method for the numerical inversion of Laplace transforms", J. Comput. Appl. Math., 10(1), 113-132. https://doi.org/10.1016/0377-0427(84)90075-X
  25. Horgan, C.O. and Quintanilla, R. (2005), "Spatial behaviour of solutions of the dual-phase-lag heat equation", Math. Meth. Appl. Sci., 28(1), 43-57. https://doi.org/10.1002/mma.548
  26. Jou, D. and Criado-Sancho, M. (1998), "Thermodynamic stability and temperature overshooting in dual-phase-lag heat transfer", Phys. Lett. A, 248(2), 172-178. https://doi.org/10.1016/S0375-9601(98)00573-8
  27. Kumar, R. and Ailawalia, P. (2007), "Mechanical/thermal sources in a micropolar thermoelastic medium possessing cubic symmetry without energy dissipation", Int. J. Thermophys., 28(1), 342-367. https://doi.org/10.1007/s10765-007-0156-4
  28. Kumar, R. and Ranil, L. (2008), "Thermoelastic interactions without energy dissipation due to inclined load", Tamk. J. Sci. Eng., 11(2), 109-118.
  29. Kumar, R., Sharma, K.D. and Garg, S.K. (2014), "Effect of two temperatures on reflection coefficient in micropolar thermoelastic with and without energy dissipation media", Adv. Acoust. Vib., 846721.
  30. Lata, P., Kumar, R. and Sharma, N. (2016), "Plane waves in an anisotropic thermoelastic", Steel Compos. Struct., Int. J., 22(3), 567-587. https://doi.org/10.12989/scs.2016.22.3.567
  31. Lord, H. and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solids, 15(5), 299-309. https://doi.org/10.1016/0022-5096(67)90024-5
  32. Mehditabar, A., Akbari Alashti, R. and Pashaei, M.H. (2014), "Magneto-thermo-elastic analysis of a functionally graded conical shell", Steel Compos. Struct., Int. J., 16(1), 79-98.
  33. Othman, M.I., Ezzat, M.A., Zaki, S.A. and El-Karamany, A.S. (2002), "Generalized thermo-viscoelastic plane waves with two relaxation times", Int. J. Eng. Sci., 40(12), 1329-1347. https://doi.org/10.1016/S0020-7225(02)00023-X
  34. Parkus, H. (1970), Variational Principles in Thermo-and Magneto-Elasticity, International Centre for Mechanical Sciences, Springer, Vienna, Austria, pp. 1-47.
  35. Roy Choudhuri, S.K. (2007), "On a thermoelastic three-phase-lag model", J. Therm. Stress., 30(3), 231-238. https://doi.org/10.1080/01495730601130919
  36. Sharma, S. and Sharma, K. (2014), "Influence of heat sources and relaxation time on temperature distribution in tissues", Int. J. Appl. Mech. Eng., 19(2), 427-433. https://doi.org/10.2478/ijame-2014-0029
  37. Sharma, K., Sharma, S. and Bhargava, R. (2013a), "Propagation of waves in micropolar thermoelastic solid with two temperatures bordered with layers of half-space of inviscid liquid", Mater. Phys. Mech., 16, 66-81.
  38. Sharma, S., Sharma, K. and Bhargava, R. (2013b), "Effect of viscosity on wave propagation in anistropic thermoelastic with Green-Naghdi theory type-II and type-III", Mater. Phys. Mech., 16(2), 144-158.
  39. Sharma, S., Sharma, K. and Bhargava, R. (2014), "Plane waves and fundamental solution in an electro-microstretch elastic solids", Afrika Matematika, 25(2), 483-497. https://doi.org/10.1007/s13370-013-0161-7
  40. Sharma, N., Kumar, R. and Lata, P. (2015), "Disturbance due to inclined load in transversely isotropic thermoelastic medium with two temperatures and without energy dissipation", Mater. Phys. Mech., 22, 107-117.
  41. Tzou, D.Y. (1995), "A unified filed approach for heat conduction from macro- to macro-scales", ASME J. Heat Trans., 117(1), 8-16. https://doi.org/10.1115/1.2822329
  42. Zenkour, A.M. (2014), "Torsional analysis of heterogeneous magnetic circular cylinder", Steel Compos. Struct., Int. J., 17(4), 535-548. https://doi.org/10.12989/scs.2014.17.4.535

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