Advances in materials Research

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Reflection of plane harmonic wave in rotating media with fractional order heat transfer

  • Received : 2020.06.28
  • Accepted : 2020.12.14
  • Published : 2020.12.25
⟨ Previous Next ⟩

Abstract

The aim of the present investigation is to examine the propagation of plane harmonic waves in transversely isotropic homogeneous magneto visco thermoelastic rotating medium with fractional order heat transfer and two temperature. It is found that, for two dimensional assumed model, there exist three types of coupled longitudinal waves (quasi-longitudinal, quasi-transverse and quasi-thermal) in frequency domain. phase velocities, specific loss, penetration depth, attenuation coefficients of various reflected waves are computed and depicted graphically. The effects of viscosity and fractional order parameter by varying different values are represented graphically.

Keywords

References

  1. Abbas, I. and Marin, M. (2017), "Analytical solution of thermoelastic interaction in a half-space by pulsed laser heating", Physica E-Low-Dimens. Syst. Nanostruct., 87, 254-260. https://doi.org/10.1016/j.physe.2016.10.048
  2. Abd-Elaziz, E.M., Marin, M. and Othman, M.I. (2019), "On the effect of Thomson and initial stress in a thermo-porous elastic solid under GN electromagnetic theory", Symmetry Basel, 11(3), 413. https://doi.org/10.3390/sym11030413
  3. Alesemi, M. (2018), "Plane waves in magneto-thermoelastic anisotropic medium based on (L-S) theory under the effect of Coriolis and centrifugal forces", Proceedings of International Conference on Materials Engineering and Applications. https://doi.org/10.1088/1757-899X/348/1/012018
  4. Achenbach, J. (1973), Wave Propagation in Elastic Solids, Elsevier, North-Holland, Amsterdam, The Netherlands.
  5. Bayones, F. and Abd-Alla, A. (2017), "Eigenvalue approach to two dimensional coupled magnetothermoelasticity in a rotating isotropic medium", Results Phys., 7, 2941-2949. https://doi.org/10.1016/j.rinp.2017.07.053
  6. Bhatti, M.M., Ellahi, R., Zeeshan, A., Marin, M. and Ijaz, N. (2019), "Numerical study of heat transfer and Hall current impact on peristaltic propulsion of particle-fluid suspension with compliant wall properties", Modern Phys. Lett. B, 35(35), 1950439. https://doi.org/10.1142/S0217984919504396
  7. Craciun, E.-M. and Soos, E. (2006), "Anti-plane states in an anisotropic elastic body containing an elliptical hole", Mathe. Mech. Solids, 11(5), 459-466. https://doi.org/10.1177/1081286505044138
  8. Craciun, E.M., Sadowski, T. and Rabaea, A. (2014), "Stress concentration in an anisotropic body with three equal collinear cracks in Mode II of fracture. I. Analytical study", J. Appl. Mathe. Mech., 94(9), 721-729. https://doi.org/10.1002/zamm.201200293
  9. Deswal, S. and Kalkal, K.K. (2015), "Three-dimensional half-space problem within the framework of twotemperature thermo-viscoelasticity with three-phase-lag effects", Appl. Mathe. Model., 39, 7093-7112. https://doi.org/10.1016/j.apm.2015.02.045
  10. Dhaliwal, R. and Singh, A. (1980), Dynamic Coupled Thermoelasticity, Hindustan Publication Corporation, New Delhi, India.
  11. Ezzat, M.A. and El-Bary, A.A. (2017), "Fractional magneto-thermoelastic materials with phase-lag GreenNaghdi theories", Steel Compos. Struct., Int. J., 24(3), 297-307. http://doi.org/10.12989/scs.2017.24.3.297
  12. Kaliski, S. (1963), "Absorption of magnetoviscoelastic surface waves in a real conductor in a magnetic field", Proceedings of Vibration Problems, 4, 319-329.
  13. Kaur, I. and Lata, P. (2019a), "Effect of hall current on propagation of plane wave in transversely isotropic thermoelastic medium with two temperature and fractional order heat transfer", SN Appl. Sci., 1(8). https://doi.org/10.1007/s42452-019-0942-1
  14. Kaur, I. and Lata, P. (2019b), "Rayleigh wave propagation in transversely isotropic magneto-thermoelastic medium with three-phase-lag heat transfer and diffusion", Int. J. Mech. Mater. Eng., 14(12), 1-11. https://doi.org/10.1186/s40712-019-0108-3
  15. Kaur, I. and Lata, P. (2020), "Stoneley wave propagation in transversely isotropic thermoelastic medium with two temperature and rotation", Int. J. Geomathe., 11(4). https://doi.org/10.1007/s13137-020-0140-8
  16. Kumar, R. and Chawla, V. (2011), "A study of plane wave propagation in anisotropic thteephase-lag model and two-phae-lag model", Int. Commun. Heat Mass Transfer, 38(9), 1262-1268. https://doi.org/10.1016/j.icheatmasstransfer.2011.07.005
  17. Kumar, R. and Gupta, V. (2015), "Dual-phase-lag model of wave propagation at the interface between elastic and thermoelastic diffusion media", J. Eng. Phys. Thermophys., 88(1), 252-265. https://doi.org/10.1007/s10891-015-1188-4
  18. Kumar, R. and Kansal, T. (2017), "Reflection and refraction of plane harmonic waves at an interface between elastic solid and magneto-thermoelastic diffusion solid with voids", Computat. Methods Sci. Technol., 23(1), 43-56. https://doi.org/10.12921/cmst.2016.0000036
  19. Kumar, R., Sharma, N. and Lata, P. (2016a), "Effects of thermal and diffusion phase-lags in a plate with axisymmetric heat supply", Multidiscipl. Model. Mater. Struct. (Emerald), 12(2), 275-290. https://doi.org/10.1108/MMMS-08-2015-0042
  20. Kumar, R., Sharma, N. and Lata, P. (2016b), "Thermomechanical interactions in transversely isotropic magnetothermoelastic medium with vacuum and with and without energy dissipation with combined effects of rotation, vacuum and two temperatures", Appl. Mathe. Model., 40(13-14), 6560-6575. https://doi.org/10.1016/j.apm.2016.01.061
  21. Kumar, R., Sharma, N. and Lata, P. (2017), "Effects of Hall current and two temperatures intransversely isotropic magnetothermoelastic with and without energy dissipation due to ramp-type heat", Mech. Adv. Mater. Struct., 24(8), 625-635. https://doi.org/10.1080/15376494.2016.1196769
  22. Lata, P. (2018a), "Effect of energy dissipation on plane waves in sandwiched layered thermoelastic medium", Steel Compos. Struct., Int. J., 27(4), 439-451. http://doi.org/10.12989/scs.2018.27.4.439
  23. Lata, P. (2018b), "Reflection and refraction of plane waves in layered nonlocal elastic and anisotropic thermoelastic medium", Struct. Eng. Mech., Int. J., 66(1), 113-124. https://doi.org/10.12989/sem.2018.66.1.113
  24. Lata, P. and Kaur, I. (2018), "Effect of hall current in Transversely Isotropic magnetothermoelastic rotating medium with fractional order heat transfer due to normal force", Adv. Mater. Res., Int. J., 7(3), 203-220. https://doi.org/10.12989/amr.2018.7.3.203
  25. Lata, P. and Kaur, I. (2019a), "Transversely isotropic thick plate with two temperature and GN type-III in frequency domain", Coupl. Syst. Mech., Int. J., 8(1), 55-70. http://doi.org/10.12989/csm.2019.8.1.055
  26. Lata, P. and Kaur, I. (2019b), "Thermomechanical interactions in transversely isotropic thick circular plate with axisymmetric heat supply", Struct. Eng. Mech., Int. J., 69(6), 607-614. http://doi.org/10.12989/sem.2019.69.6.607
  27. Lata, P. and Kaur, I. (2019c), "Plane wave propagation in transversely isotropic magneto-thermoelastic rotating medium with fractional order generalized heat transfer", Struct. Monitor. Maint., Int. J., 6(3), 191-218. https://doi.org/10.12989/smm.2019.6.3.191
  28. Lata, P., Kumar, R. and Sharma, N. (2016a), "Plane waves in an anisotropic thermoelastic", Steel Compos. Struct., Int. J., 22(3), 567-587. http://doi.org/10.12989/scs.2016.22.3.567
  29. Lata, P., Kaur, I. and Singh, K. (2020a), "Propagation of plane wave in transversely isotropic magnetothermoelastic material with multi-dual-phase lag and two temperature", Coupl. Syst. Mech., Int. J., 9(5), 411-432. https://doi.org/10.12989/csm.2020.9.5.411
  30. Lata, P., Kaur, I. and Singh, K. (2020b), "Reflection of plane harmonic wave in transversely isotropic magneto-thermoelastic with Two temperature, rotation and Multi-dual-Phase Lag heat transfer", In: Mobile Radio Communications and 5G Networks, 140, 521-551. https://doi.org/10.1007/978-981-15-7130-5_42
  31. Mahmoud, S. (2012), "Influence of rotation and generalized magneto-thermoelastic on Rayleigh waves in a granular medium under effect of initial stress and gravity field", Meccanica, 47, 1561-1579. https://doi.org/10.1007/s11012-011-9535-9
  32. Mahmoud, S.R., Marin, M. and Al-Basyouni, K.S. (2015), "Effect of the initial stress and rotation on free vibrations in transversely isotropic human long dry bone", Versita, 23(1), 171-184. https://doi.org/10.1515/auom-2015-0011
  33. Maitya, N., Barikb, S. and Chaudhuri, P. (2017), "Propagation of plane waves in a rotating magnetothermoelastic fiber-reinforced medium under G-N theory", Appl. Computat. Mech., 11, 47-58. https://doi.org/10.24132/acm.2017.328
  34. Marin, M. (1994), "The Lagrange identity method in thermoelasticity of bodies with microstructure", Int. J. Eng. Sci., 32(8), 1229-1240. https://doi.org/10.1016/0020-7225(94)90034-5
  35. Marin, M. (1995), "On existence and uniqueness in thermoelasticity of micropolar bodies", Comptes Rendus De L Academie, 321, 475-480.
  36. Marin, M. (2009), "On the minimum principle for dipolar materials with stretch", Nonlinear Anal. Real World Applicat., 10(3), 1572-1578. https://doi.org/10.1016/j.nonrwa.2008.02.001
  37. Marin, M. (2010), "Some estimates on vibrations in thermoelasticity of dipolar bodies", J. Vib. Control: SAGE J., 16(1), 33-47. https://doi.org/10.1177/1077546309103419
  38. Mohamed, R.A., Abbas, I.A. and Abo-Dahab, S. (2009), "Finite element analysis of hydromagnetic flow and heat transfer of a heat generation fluid over a surface embedded in a non-Darcian porous medium in the presence of chemical reaction", Commun. Nonlinear Sci. Numer. Simul., 14(4), 1385-1395. https://doi.org/10.1016/j.cnsns.2008.04.006
  39. Othman, M. and Marin, M. (2017), "Effect of thermal loading due to laser pulse on thermoelastic porous medium under G-N theory", Results Phys., 7, 3863-3872. https://doi.org/10.1016/j.rinp.2017.10.012
  40. Othman, M.I. and Song, Y.Q. (2006), "The effect of rotation on the reflection of magneto-thermoelastic waves under thermoelasticity without energy dissipation", Acta Mech., 184, 89-204. https://doi.org/10.1007/s00707-006-0337-4
  41. Othman, M.I. and Song, Y.Q. (2008), "Reflection of magneto-thermoelastic waves from a rotating elastic halfspace", Int. J. Eng. Sci., 46, 459-474. https://doi.org/10.1016/j.ijengsci.2007.12.004
  42. Othman, M.I., Abo-Dahab, S.M. and Alsebaey, O.N. (2017), "Reflection of plane waves from a rotating magneto-thermoelastic medium with two-temperature and initial stress under three theories", Mech. Mech. Eng., 21(2), 217-232.
  43. Othman, M.I., Khan, A., Jahangir, R. and Jahangir, A. (2019), "Analysis on plane waves through magnetothermoelastic microstretch rotating medium with temperature dependent elastic properties", Appl. Mathe. Model., 65, 535-548. https://doi.org/10.1016/j.apm.2018.08.032
  44. Riaz, A., Ellahi, R., Bhatti, M.M. and Marin, M. (2019), "Study of heat and mass transfer in the Eyring-Powell model of fluid propagating peristaltically through a rectangular compliant channel", Heat Transfer Res., 50(16), 1539-1560. https://doi.org/10.1615/heattransres.2019025622
  45. Said, S.M. (2017), "A fiber-reinforced thermoelastic medium with an internal heat source due to hydrostatic initial stress and gravity for the three-phase-lag model", Multidiscipl. Model. Mater. Struct., 13(1), 83-99. https://doi.org/10.1108/MMMS-08-2016-0040
  46. Schoenberg, M. and Censor, D. (1973), "Elastic waves in rotating media", Quarter. Appl. Mathe., 31, 115-125. https://doi.org/10.1090/qam/99708
  47. Sharma, K. and Marin, M. (2014), "Reflection and transmission of waves from imperfect boundary between two heat conducting micropolar thermoelastic solids", Universitatii" Ovidius" Constanta-Seria Matematica, 22(2), 151-175. https://doi.org/10.2478/auom-2014-0040
  48. Ting, T.C. (2004), "Surface waves in a rotating anisotropic elastic half-space", Wave Motion, 40, 329-346. https://doi.org/10.1016/j.wavemoti.2003.10.005
  49. W.S.S. (2002), The Linearised Theory of Elasticity, Birkhausar.
  50. Youssef, H. (2006), "Two-dimensional generalized thermoelasticity problem for a half space subjected to ramp -type heating", Eur. J. Mech. A/solid, 25, 745-763. https://doi.org/10.1016/j.apm.2007.02.025
  51. Youssef, H. (2010), "Theory of fractional order generalized thermoelasticity", J. Heat Transfer, 132, 1-7. https://doi.org/10.1115/1.4000705
  52. Youssef, H.M. (2013), "State-space approach to two-temperature generalized thermoelasticity without energy dissipation of medium subjected to moving heat source", Appl. Mathe. Mech., 34(1), 63-74. https://doi.org/10.1007/s10483-013-1653-7
  53. Youssef, H.M. (2016), "Theory of generalized thermoelasticity with fractional order strain", J. Vib. Control, 22(18), 3840-3857. https://doi.org/10.1177/1077546314566837

Cited by

  1. A dual-phase-lag theory of thermal wave in a porothermoelastic nanoscale material by FEM vol.79, pp.1, 2020, https://doi.org/10.12989/sem.2021.79.1.001