Advances in materials Research

  • 제7권3호
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  • Pages.203-220
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  • 2018
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  • 2234-0912(pISSN)
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  • 2234-179X(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Effect of hall current in Transversely Isotropic magneto thermoelastic rotating medium with fractional order heat transfer due to normal force

  • Lata, Parveen (Department of Basic and Applied Sciences, Punjabi University) ;
  • Kaur, Iqbal (Department of Basic and Applied Sciences, Punjabi University)
  • 투고 : 2019.04.30
  • 심사 : 2019.05.15
  • 발행 : 2018.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

This investigation is focused on the study of effect of hall current in transversely isotropic magneto thermoelastic homogeneous medium with fractional order heat transfer and rotation. As an application the bounding surface is subjected to normal force. The research becomes more interesting due to interaction of Hall current with the effect of rotation as it has found various applications. Laplace and Fourier transform is used for solving field equations. The analytical expressions of temperature, displacement components, stress components and current density components are computed in the transformed domain. The effects of hall current and fractional order parameter at different values are represented graphically.

키워드

참고문헌

  1. Abbas, I. (2018), "A study on fractional order theory in thermoelastic half-space under thermal loading", Physical Mesomech., 21(2), 150-156. https://doi.org/10.1134/S102995991802008X
  2. Bachher, M. and Sarkar, N. (2016), "Fractional order magneto-thermoelasticity in a rotating media with one relaxation time", Math. Model. Eng., 2(1), 56-68.
  3. Chen, P.J. and Gurtin, E.M. (1968), "On a theory of heat conduction involving two temperatures", Zeitschrift fur Angewandte Mathematik und Physik, 19(4), 614-627. https://doi.org/10.1007/BF01594969
  4. Chen, P.J., Gurtin, M.E. and Williams, W.O. (1968), "A note on non-simple heat conduction", Zeitschrift fur Angewandte Mathematik und Physik ZAMP, 19(4), 969-970. https://doi.org/10.1007/BF01602278
  5. Chen, P.J., Gurtin, E.M. and Williams, O.W. (1969), "On the thermodynamics of non-simple elastic materials with two temperatures", Zeitschrift fur angewandte Mathematik und Physik, 20(1), 107-112. https://doi.org/10.1007/BF01591120
  6. Chauthale, S. and Khobragade, N.W. (2017), "Thermoelastic Response of a Thick Circular Plate due to Heat Generation and its Thermal Stresses", Global J. Pure Appl. Math., 13(10), 7505-7527.
  7. Dhaliwal, R.S. and Sherief, H.H. (1980), "Generalized thermoelasticity for anisotropic media", Quarterly Appl. Math., 38(1), 1-8. https://doi.org/10.1090/qam/575828
  8. Ezzat, M. and AI-Bary, A. (2016), "Magneto-thermoelectric viscoelastic materials with memory dependent derivatives involving two temperature", Int. J. Appl. Electromagnet. Mech., 50(4), 549-567. https://doi.org/10.3233/JAE-150131
  9. Ezzat, M. and AI-Bary, A. (2017), "Fractional magneto-thermoelastic materials with phase lag Green-Naghdi theories", Steel Compos. Struct., Int. J., 24(3), 297-307.
  10. Ezzat, M.A., Karamany, A.S. and Fayik, M.A. (2011), "Fractional order theory in thermoelastic solid with three-phase lag heat transfer", Arch. Appl. Mech., 82, 557-572.
  11. Ezzat, M.A., El-Karamany, A.S. and Ezzat, S.M. (2012), "Two-temperature theory in magnetothermoelasticity with fractional order dual-phase-lag heat transfer", Nuclear Eng. Des., 252, 267- 277. https://doi.org/10.1016/j.nucengdes.2012.06.012
  12. Ezzat, M., El-Karamany, A. and El-Bary, A. (2015), "Thermo-viscoelastic materials with fractional relaxation operators", Appl. Math. Model., 39(23), 7499-7512. https://doi.org/10.1016/j.apm.2015.03.018
  13. Ezzat, M., El-Karamany, A. and El-Bary, A. (2016), "Generalized thermoelasticity with memory-dependent derivatives involving two temperatures", Mech. Adv. Mater. Struct., 23(5), 545-553. https://doi.org/10.1080/15376494.2015.1007189
  14. Ezzat, M.A., El-Karamany, A.S. and El-Bary, A.A. (2017), "Two-temperature theory in Green-Naghdi thermoelasticity with fractional phase-lag heat transfer", Microsyst. Technol., 24(2), 951-961.
  15. Green, A. and Nagdhi, P. (1991), "A re-examination of the basic postulates of thermomechanics", Proceedings of Royal Society of London, pp. 171-194.
  16. Green, A. and Naghdi, P. (1992), "On undamped heat waves in an elastic solid", J. Thermal Stress., 15(2), 253-264. https://doi.org/10.1080/01495739208946136
  17. Green, A., & Naghdi, P. (1993). "Thermoelasticity without energy dissipation". Journal of Elasticity: The Physical and Mathematical Science of Solids, 31(3), 189-208. https://doi.org/10.1007/BF00044969
  18. Honig, G. and Hirdes, U. (1984), "A method for the numerical inversion of Laplace transform", J. Computat. Appl. Math., 10, 113-132. https://doi.org/10.1016/0377-0427(84)90075-X
  19. Kumar, R., Sharma, N. and Lata, P. (2016), "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. Math. Model., 40(13-14), 6560-6575. https://doi.org/10.1016/j.apm.2016.01.061
  20. Kumar, R., Sharma, N. and Lata, P. (2017a), "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
  21. Kumar, R., Sharma, N., Lata, P. and Abo-Dahab, S.M. (2017b), "Rayleigh waves in anisotropic magnetothermoelastic medium", Coupl. Syst. Mech., Int. J., 6(3), 317-333.
  22. Kumar, R., Kaushal, P. and Sharma, R. (2018), "Transversely Isotropic Magneto-Visco Thermoelastic Medium with Vacuum and without Energy Dissipation", J. Solid Mech., 10(2), 416-434.
  23. 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.
  24. Lata, P. and Kaur, I. (2019b), "Study of Transversely Isotropic Thick circular Plate due to Ring Load with Two Temperature & Green Nagdhi Theory of Type-I, II and III", Proceedings of International Conference on Sustainable Computing in Science, Technology & Management (SUSCOM-2019), Amity University Rajasthan, Jaipur, India, pp. 1753-1767.
  25. Lata, P. and Kaur, I. (2019c), "Thermomechanical Interactions in transversely isotropic thick circular plate with axisymmetric heat supply", Struct. Eng. Mech., Int. J., 69(6), 607-614.
  26. Lata, P. and Kaur, I. (2019d), "Transversely isotropic magneto thermoelastic solid with two temperature and without energy dissipation in generalized thermoelasticity due to inclined load", SN Appl. Sci., 1(5), p. 426. DOI: https://doi.org/10.1007/s42452-019-0438-z
  27. Lata, P. and Kaur, I. (2019e), "Effect of rotation and inclined load on transversely isotropic magneto thermoelastic solid", Struct. Eng. Mech., Int. J., 70(2), 245-255.
  28. Lata, P., Kumar, R. and Sharma, N. (2016), "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. Math. Model.E, 40(13-14), 6560-6575. https://doi.org/10.1016/j.apm.2016.01.061
  29. Marin, M. (1996), "Generalized solutions in elasticity of micropolar bodies with voids", Revista de la Academia Canaria de Ciencias, 8(1), 101-106.
  30. Marin, M. (1997a), "Cesaro means in thermoelasticity of dipolar bodies", Acta Mechanica, 122(1-4), 155-168. https://doi.org/10.1007/BF01181996
  31. Marin, M. (1997b), "On weak solutions in elasticity of dipolar bodies with voids", J. Computat. Appl. Math., 82(1-2), 291-297. https://doi.org/10.1016/S0377-0427(97)00047-2
  32. Marin, M. (1998), "Contributions on uniqueness in thermoelastodynamics on bodies with voids", Revista Ciencias Matematicas(Havana), 16(2), 101-109.
  33. Marin, M. (2008), "Weak solutions in elasticity of dipolar porous materials", Math. Problems Eng., 1-8.
  34. Marin, M. (2009), "On the minimum principle for dipolar materials with stretch", Nonlinear Anal. Real World Appl., 10(3), 1572-1578. https://doi.org/10.1016/j.nonrwa.2008.02.001
  35. Marin, M. (2010), "A partition of energy in thermoelasticity of microstretch bodies", Nonlinear Anal.: Real World Appl., 11(4), 2436-2447. https://doi.org/10.1016/j.nonrwa.2009.07.014
  36. Marin, M. and Baleanu, D. (2016), "On vibrations in thermoelasticity without energy dissipation for micropolar bodies", Boundary Value Problems, 111.
  37. Marin, M. and Nicaise, S. (2016), "Existence and stability results for thermoelastic dipolar bodies with double porosity", Continuum Mech. Thermodyn., 28(6), 1645-1657. https://doi.org/10.1007/s00161-016-0503-4
  38. Marin, M. and O chsner, A. (2017), "The effect of a dipolar structure on the Holder stability in Green-Naghdi thermoelasticity", Continuum Mech. Thermodyn., 29, 1365-1374. https://doi.org/10.1007/s00161-017-0585-7
  39. Marin, M. and Stan, G. (2013), "Weak solutions in Elasticity of dipolar bodies with stretch", Carpathian J. Math., 29(1), 33-40.
  40. Marin, M., Ellahi, R. and Chirila, A. (2017), "On solutions of Saint-Venant's problem for elastic dipolar bodies with voids", Carpathian J. Math., 33(2), 219-232.
  41. Moreno-Navarro, P., Ibrahimbegovic, A. and Perez-Aparicio, J.L. (2018), "Linear elastic mechanical system interacting with coupled thermo-electro-magnetic fields", Coupl. Syst. Mech., Int. J., 7(1), 5-25.
  42. Othman, M.I. 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
  43. Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (1986), FORTRAN numerical recipes, Cambridge University Press Cambridge.
  44. Salama, M.M., Kozae, A., Elsafty, M.A. and Abelaziz, S. (2015), "A half-space problem in the theory of fractional order thermoelasticity with diffusion", Int. J. Sci. Eng. Res., 6(1), 358-371.
  45. Schoenberg, M. and Censor, D. (1973), "Elastic Waves In Rotating Media", Quarterly Appl. Math., 31, 115-125. https://doi.org/10.1090/qam/99708
  46. Sheoran, S.S. and Kundu, P. (2016), "Fractional order generalized thermoelasticity theories: A review", Int. J. Adv. Appl. Math. Mech., 3(4), 76-81.
  47. Slaughter, W.S. (2002), "The Linearized Theory of Elasticity, Birkhauser.
  48. Tripathi, J.J., Deshmukh, K. and Verma, J. (2017), "Fractional order generalized thermoelastic problem in a thick circular plate with periodically varying heat source", Int. J. Thermodyn., 20(3), 132-138. https://doi.org/10.5541/eoguijt.336651
  49. Youssef, H.M. and Abbas, I. (2014), "Fractional order generalized thermoelasticity with variable thermal conductivity", J. Vibroeng., 16(8), 4077-4087.
  50. Zakaria, M. (2012), "Effects of Hall current and rotation on magneto-micropolar generalized thermoelasticity due to ramp-type heating", Int. J. Electromagnet. Appl., 2(3), 24-32. https://doi.org/10.5923/j.ijea.20120203.02

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