Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Temperature-dependent multi-phase-lags theory on a magneto-thermoelastic medium with microtemperatures

  • Samia M. Said (Department of Mathematics, Faculty of Science, Zagazig University)
  • Received : 2021.02.06
  • Accepted : 2023.10.05
  • Published : 2024.03.10
⟨ Previous Next ⟩

Abstract

A temperature-dependent generalized thermoelasticity is constructed in the context of a new consideration of the multi-phase-lags model. The theory is then adopted to study wave propagation in anisotropic homogenous generalized magneto-thermoelastic medium under the influence of gravity whose boundary is subjected to thermal and mechanical loading. The basic equations of the problem are solved by using normal mode analysis. The numerical quantities of physical interest are obtained and depicted graphically. Some comparisons of the results are shown in figures to study the effects of the magnetic field, temperature discrepancy, and the gravity field.

Keywords

References

  1. Akbas, S.D. (2020), "Dynamic responses of laminated beams under a moving load in thermal environment", Steel Comp. Struct., 35(6), 729-737. http://dx.doi.org/10.12989/scs.2020.35.6.729.
  2. Alharbi, A.M., Othman, M.I.A. and Abd-Elaziz, E.M. (2021), "2-D Analysis of generalized thermoelastic porous medium under the effect of laser pulse and microtemperature", Int. J. Struct. Stab. Dyn., 21(9), 2150126. https://doi.org/10.1142/S0219455421501261.
  3. Bazarra, N., Fernandez, J.R. and Quintanilla, R. (2020), "Lord-shulman thermoelasticity with microtemperatures", Appl. Math. Optim., https://doi.org/10.1007/s00245-020-09691-2.
  4. Casas, P. and Quintanilla, R. (2005), "Exponential stability in thermoelasticity with microtemperatures", Int. J. Eng. Sci., 43 (1-2), 33-47. https://doi.org/10.1016/j.ijengsci.2004.09.004.
  5. Cosserat, E. and Cosserat, F. (1909), "Theorie des Corps Deformables", Nature, 81, 67. https://doi.org/10.1038/081067a0.
  6. Ellahi, R. (2013), "The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nanofluid in a pipe: analytical solutions", Appl. Math. Model. , 37(3), 1451-1467. https://doi.org/10.1016/j.apm.2012.04.004.
  7. Ezzat, M.A. and El-Bary, A.A. (2017), "Fractional magneto-Thermoelastic materials with phase-lag Green-Naghdi theories", Steel Comp. Struct., 24 (3), 297-307. http://dx.doi.org/10.12989/scs.2017.24.3.297.
  8. Grot, R.A. (1969), "Thermodynamics of a continuum with microstructure", Int. J. Eng. Sci., 7(8), 801-814. https://doi.org/10.1016/0020-7225(69)90062-7.
  9. Iesan, D. (2007), "Thermoelasticity of bodies with microstructure and microtemperatures", Int. J. Sol. Struct., 44(25-26), 8648-8662. https://doi.org/10.1016/j.ijsolstr.2007.06.027.
  10. Kumar, R., Kaur, M. and Rajvanshi, S.C. (2013), "Wave propagation at an interface of elastic and microstretch thermoelastic solids with microtemperatures", J. Sol. Mech., 5(3), 226-244.
  11. Kutbi, M.A. and Zenkour, A.M. (2022a), "Refined dual-phase-lag Green-Naghdi models for thermoelastic diffusion in an infinite medium", Wav. Rand. Compl. Media, 32 (2), 947-967. https://doi.org/10.1080/17455030.2020.1807073.
  12. Lata, P. and Singh, S. (2021), "Stoneley wave propagation in nonlocal isotropic magnetothermoelastic solid with multi-dual-phase lag heat transfer", Steel Comp. Struct., 38(2), 141-150. https:// doi:10.12989/scs.2021.38.2.141.
  13. Marin, M., Baleanu, D. and Vlase, S. (2017), "Effect of microtemperatures for micropolar thermoelastic bodies", Struct. Eng. Mech., 61 (3), 381-387. https://doi:10.12989/sem.2017.61.3.381.
  14. Noda, N. (1986), Thermal Stresses in Materials with Temperature-Dependent Properties", Thermal stresses I, North-Holland, Amsterdam. https://doi.org/10.1007/978-94-015-8200-1_2.
  15. Othman, M.I.A. and Kumar, R. (2009), "Reflection of magneto-thermoelasticity waves with temperature dependent properties in generalized thermoelasticity", Int. Commun. Heat Mass Transfer, 36(5), 513-520. https://doi.org/10.1016/j.icheatmasstransfer.2009.02.002.
  16. Othman, M.I.A., Zidan, M.E.M. and Mohamed, I.E.A. (2021), "Dual-phase-lag model on thermo-microstretch elastic solid under the effect of initial stress and temperature-dependent", Steel Comp. Struct., 38(4), 355-363. https://doi.org/10.12989/scs.2021.38.4.355.
  17. Quintanilla, R. (2011), "On growth and continous dependence in thermoelasticity with microtemperatures", J. Thermal Stress., 34(9), 911-922. https://doi.org/10.1080/01495739.2011.586278.
  18. Riha, P. (1976), "On the microcontinuum model of heat conduction in materials with inner structure", Int. J. Eng. Sci., 14 (6), 529-535. https://doi.org/10.1016/0020-7225(76)90017-3.
  19. Said, S.M. (2016), "Influence of gravity on generalized magneto-thermoelastic medium for three-phase-lag model", J. Com. Appl. Math., 291, 142-157. https://doi.org/10.1016/j.cam.2014.12.016.
  20. Steeb, H., Singh, J. and Tomar, S.K. (2013), "Time harmonic waves in thermoelastic material with microtemperatures", Mech. Res. Commun., 48, 8-18. https://doi.org/10.1016/j.mechrescom.2012.11.006.
  21. Sobhy, M. and Zenkour, A.M. (2020 a), "Modified three-phase-lag Green-Naghdi models for thermomechanical waves in an axisymmetric annular disk", J. Therm Stress., 43(8), 1017-1029. https://doi.org/10.1080/01495739.2020.1766390.
  22. Suhara, T. (1918), "Elasticity of steel strained by unequal heating", Japan Soc. Mech. Eng., 21(50), 25-63.
  23. Tzou, D.Y. (1995), "A unified filed approach for heat conduction from macro to macroscales", ASME J. Heat Transfer, 117(1), 8-16. https://doi.org/10.1115/1.2822329.
  24. Zenkour, A.M. and Abouelregal, A.E. (2015), "Thermoelastic interaction in functionally graded nanobeams subjected to time-dependent heat flux", Steel Comp. Struct., 18(4), 909-924. http://dx.doi.org/10.12989/scs.2015.18.4.909.
  25. Zenkour, A.M. (2018), "Refined microtemperatures multi-phaselags theory for plane wave propagation in thermoelastic medium", Res. Phys., 11, 929-937. https://doi.org/10.1016/j.rinp.2018.10.030.
  26. Zenkour, A.M. (2020b), "Thermo-diffusion of solid cylinders based upon refined dual-phase-lag models", Multidiscip Model Mater Struct., 16(6), 1417-1434. https://doi.org/10.1108/MMMS-12-2019-0213
  27. Zenkour, A.M. (2020c), "Thermoelastic diffusion problem for a half-space due to a refined dual-phase-lag Green-Naghdi model", J Ocean Eng Sci., 5(3), 214-222. https://doi.org/10.1016/j.joes.2019.12.001.
  28. Zenkour A.M. (2020d), "Thermal-shock problem for a hollow cylinder via a multi-dual-phase-lag theory", J. Therm. Stresses, 43(6), 687-706. https://doi.org/10.1080/01495739.2020.1736966.
  29. Zenkour A.M. (2020e), "Magneto-thermal shock for a fiber-reinforced anisotropic half-space studied with a refined multidual phase-lag model", J. Phys. Chemist. Solids, 137, 109213. https://doi.org/10.1016/j.jpcs.2019.109213
  30. Zenkour, A.M. (2020f), "Wave propagation of a gravitated piezo-thermoelastic half-space via a refined multi-phase-lags theory", Mech. Adv. Mater. Struct., 27(22), 1923-1934.
  31. Zenkour, A.M. and El-Mekawy, H.F. (2020), "On a multi-phase-lag model of coupled thermoelasticity", Int. Commun. Heat Mass Transfer, 116, 104722. https://doi.org/10.1016/j.icheatmasstransfer.2020.104722.
  32. Zenkour, A.M. (2022b), "Thermal diffusion of an unbounded solid with a spherical cavity via refined three-phase-lag Green-Naghdi models", Ind. J. Phys, 96(3), 1087-1104. https://doi.org/10.1007/s12648-021-02042-z.