International Journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN: 2313-626X

Frequency: 12
line decor
  
line decor

 Volume 8, Issue 6 (June 2021), Pages: 40-47

----------------------------------------------

 Original Research Paper

 Title: Effect of modified Ohm's and Fourier's laws on magneto thermoviscoelastic waves with Green-Naghdi theory in a homogeneous isotropic hollow cylinder

 Author(s): A. K. Khamis 1, *, Amir Mohamed Abdel Allah Nasr 2, A. A. El-Bary 3, 4, Haitham M. Atef 5

 Affiliation(s):

 1Department of Mathematics, Faculty of Science, Northern Border University, Arar, Saudi Arabia
 2Department of Statistics and Quantitative Methods, College of Business Administration, Northern Border University, Arar, Saudi Arabia
 3Basic and Applied Science Institute, Arab Academy for Science and Technology, Alexandria, Egypt
 4National Committee for Mathematics, Academy of Scientific Research and Technology, Egypt
 5Department of Mathematics, Faculty of Science, Damanhur University, Damanhur, Egypt

  Full Text - PDF          XML

 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0002-8846-0487

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2021.06.005

 Abstract:

This paper deals with the modified Ohm's law, including the temperature gradient and charge density effects, and the generalized Fourier's law, including the present current density impact, the problem of conveyance of thermal stresses and temperature in a generalized Magneto–Thermo-Viscoelastic Solid Cylinder of radius L. The formulation is applied to the generalized thermoelasticity dependent on the Green-Naghdi (G-N II) hypothesis. The Laplace change system is utilized to solve the problem. At last, the outcomes got are introduced graphically to show the impact of Magnetic Field and time and on the field variables. 

 © 2021 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: Thermal stress, Generalized magneto–thermoviscoelastic, Solid cylinder, Thermal shock, Laplace transform technique, Modified Ohm's and Fourier's laws

 Article History: Received 11 April 2020, Received in revised form 1 July 2020, Accepted 21 February 2021

 Acknowledgment 

The authors wish to acknowledge the approval and the support of this research study by Project NO. SCI-2018-3-9–F from the Deanship of Scientific Research in Northern Border University, Arar, KSA.

 Compliance with ethical standards

 Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

 Citation:

  Khamis AK, Nasr AMAA, and El-Bary AA et al. (2021). Effect of modified Ohm's and Fourier's laws on magneto thermoviscoelastic waves with Green-Naghdi theory in a homogeneous isotropic hollow cylinder. International Journal of Advanced and Applied Sciences, 8(6): 40-47

 Permanent Link to this page

 Figures

 Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6 Fig. 7 Fig. 8

 Tables

 No Table 

----------------------------------------------

 References (39)

  1. Abd-Alla AM and Abo-Dahab SM (2009). Time-harmonic sources in a generalized magneto-thermo-viscoelastic continuum with and without energy dissipation. Applied Mathematical Modelling, 33(5): 2388-2402. https://doi.org/10.1016/j.apm.2008.07.008   [Google Scholar]
  2. Abd-Alla AM, Abo-Dahab SM, and Bayones FS (2011). Effect of the rotation on an infinite generalized magneto-thermoelastic diffusion body with a spherical cavity. International Review of Physics, 5(4): 171-181.   [Google Scholar]
  3. Abd-Alla AM, Hammad HAH, and Abo-Dahab SM (2004). Magneto-thermo-viscoelastic interactions in an unbounded body with a spherical cavity subjected to a periodic loading. Applied Mathematics and Computation, 155(1): 235-248. https://doi.org/10.1016/S0096-3003(03)00773-2   [Google Scholar]
  4. Acharya DP and Roy I (1978). Magneto-thermo-elastic surface waves in initially stressed conducting media. Acta Geophysica Polonica, 26: 299-311.   [Google Scholar]
  5. Amin M, El-Bary A, and Atef H (2018a). Effect of viscous fractional parameter on generalized magneto thermo-viscoelastic thin slim strip exposed to moving heat source. Materials Focus, 7(6): 814-823. https://doi.org/10.1166/mat.2018.1591   [Google Scholar]
  6. Amin MM, El-Bary AA, and Atef HM (2018b). Modification of kelvin-voigt model in fractional order for thermoviscoelastic isotropic material. Materials Focus, 7(6): 824-832. https://doi.org/10.1166/mat.2018.1592   [Google Scholar]
  7. Banerjee S and Roychoudhuri SK (1995). Spherically symmetric thermo-visco-elastic waves in a visco-elastic medium with a spherical cavity. Computers and Mathematics with Applications, 30(1): 91-98. https://doi.org/10.1016/0898-1221(95)00070-F   [Google Scholar]
  8. Bayones FS (2012). The influence of diffusion on generalized magneto-thermo-viscoelastic problem of a homogenous isotropic material. Advances in Theoretical and Applied Mechanics, 5(2): 69-92.   [Google Scholar]
  9. Belbachir N, Bourada M, Draiche K, Tounsi A, Bourada F, Bousahla AA, and Mahmoud SR (2020). Thermal flexural analysis of anti-symmetric cross-ply laminated plates using a four variable refined theory. Smart Structures and Systems, 25(4): 409-422.   [Google Scholar]
  10. Biot MA (1955). Variational principles in irreversible thermodynamics with application to viscoelasticity. Physical Review, 97(6): 1463-1469. https://doi.org/10.1103/PhysRev.97.1463   [Google Scholar]
  11. Biot MA (1956). Thermoelasticity and irreversible thermodynamics. Journal of Applied Physics, 27(3): 240-253. https://doi.org/10.1063/1.1722351   [Google Scholar]
  12. Chandrasekharaiah DS (1986). Thermoelasticity with second sound: A review. Applied Mechanics Reviews, 39(3): 355-376. https://doi.org/10.1115/1.3143705   [Google Scholar]
  13. Chandrasekharaiah DS and Krivoshapko SN (1998). Hyperbolic thermoelasticity: A review of recent literature. Applied Mechanics Reviews, 51(12): 705-729. https://doi.org/10.1115/1.3098984   [Google Scholar]
  14. Chaudhary S, Kauhsik VP, and Tomar SK (2006). Plane SH-wave response from elastic slab interposed between two different self-reinforced elastic solids. Applied Mechanics and Engineering, 11(4): 787-801.   [Google Scholar]
  15. Chaudhary S, Kaushik VP, and Tomar SK (2004). Reflection/transmission of plane SH wave through a self-reinforced elastic layer between two half-spaces. Acta Geophysica Polonica, 52(2): 219-236.   [Google Scholar]
  16. De SN and Sengupta PR (1971). Surface waves in magneto-elastic initially stressed conducting media. Pure and Applied Geophysics, 88(1): 44-52. https://doi.org/10.1007/BF00877891   [Google Scholar]
  17. El-Bary AA and Atef H (2016a). On effect of viscous fractional parameter on infinite thermo viscoelastic medium with a spherical cavity. Journal of Computational and Theoretical Nanoscience, 13(1): 1027-1036. https://doi.org/10.1166/jctn.2016.4332   [Google Scholar]
  18. El-Bary AA and Atef M (2016b). Modified approach for stress strain equation in the linear Kelvin–Voigt solid based on fractional order. Journal of Computational and Theoretical Nanoscience, 13(1): 579-583. https://doi.org/10.1166/jctn.2016.4843   [Google Scholar]
  19. Ezzat MA and El-Bary AA (2009). On three models of magneto-hydrodynamic free-convection flow. Canadian Journal of Physics, 87(12): 1213-1226. https://doi.org/10.1139/P09-071   [Google Scholar]
  20. Ezzat MA, El-Karamany AS, and El-Bary AA (2015). On thermo-viscoelasticity with variable thermal conductivity and fractional-order heat transfer. International Journal of Thermophysics, 36(7): 1684-1697. https://doi.org/10.1007/s10765-015-1873-8   [Google Scholar]
  21. Ezzat MA, El-Karamany AS, and El-Bary AA (2017). Thermoelectric viscoelastic materials with memory-dependent derivative. Smart Structures and Systems, 19: 539-551. https://doi.org/10.12989/sss.2017.19.5.539   [Google Scholar]
  22. Green AE and Lindsay KA (1972). Thermoelasticity. Journal of Elasticity, 2(1): 1-7. https://doi.org/10.1007/BF00045689   [Google Scholar]
  23. Green AE and Naghdi PM (1991). A re-examination of the basic postulates of thermomechanics. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 432(1885): 171-194. https://doi.org/10.1098/rspa.1991.0012   [Google Scholar]
  24. Gross B (1968). Mathematical structure of the theories of viscoelasticity. Hermann Publisher, Paris, France.   [Google Scholar]
  25. Gurtin ME and Sternberg E (1962). On the linear theory of viscoelasticity. Archive for Rational Mechanics and Analysis, 11: 291-356. https://doi.org/10.1007/BF00253942   [Google Scholar]
  26. Hetnarski RB and Ignaczak J (1996). Soliton-like waves in a low temperature nonlinear thermoelastic solid. International Journal of Engineering Science, 34(15): 1767-1787. https://doi.org/10.1016/S0020-7225(96)00046-8   [Google Scholar]
  27. Hetnarski RB and Ignaczak J (1999). Generalized thermoelasticity. Journal of Thermal Stresses, 22(4-5): 451-476. https://doi.org/10.1080/014957399280832   [Google Scholar]
  28. Kosiński W (1989). Elasic waves in the presence of a new temperature scale. North-Holland Series in Applied Mathematics and Mechanics, 35: 629-634. https://doi.org/10.1016/B978-0-444-87272-2.50099-3   [Google Scholar]
  29. Liioushin AA and Pobedria BE (1970). Mathematical theory of thermal viscoelasticity. Nauka, Moscow, Russia.   [Google Scholar]
  30. Othman MIA and Song Y (2006). The effect of rotation on the reflection of magneto-thermoelastic waves under thermoelasticity without energy dissipation. Acta Mechanica, 184(1-4): 189-204. https://doi.org/10.1007/s00707-006-0337-4   [Google Scholar]
  31. Roychoudhuri SK and Banerjee S (1998). Magneto-thermo-elastic interactions in an infinite viscoelastic cylinder of temperature-rate dependent material subjected to a periodic loading. International Journal of Engineering Science, 36(5-6): 635-643. https://doi.org/10.1016/S0020-7225(97)00096-7   [Google Scholar]
  32. Song YQ, Zhang YC, Xu HY, and Lu BH (2006). Magneto-thermoviscoelastic wave propagation at the interface between two micropolar viscoelastic media. Applied Mathematics and Computation, 176(2): 785-802. https://doi.org/10.1016/j.amc.2005.10.027   [Google Scholar]
  33. Staverman AJ, Schwarzl F, and Stuart HA (1956). Die physic der Hochpolymeren. Volume 4, Springer, Berlin, Germany.   [Google Scholar]
  34. Tanner RI (1988). Engineering rheology. Oxford University Press, Oxford, UK.   [Google Scholar]
  35. Tianhu H, Yapeng S, and Xiaogeng T (2004). A two-dimensional generalized thermal shock problem for a half-space in electromagneto-thermoelasticity. International Journal of Engineering Science, 42(8-9): 809-823. https://doi.org/10.1016/j.ijengsci.2003.09.006   [Google Scholar]
  36. Tzou D (1995). A unified field approach for heat conduction from macro-to micro-scales. Journal of Heat Transfer, 117(1): 8-16. https://doi.org/10.1115/1.2822329   [Google Scholar]
  37. Verma PDS, Rana OH, and Verma MEENU (1988). Magnetoelastic transverse surface waves in self-reinforced elastic bodies. Indian Journal of Pure and Applied Mathematics, 19(7): 713-716.   [Google Scholar]
  38. Youssef HM, El-Bary AA, and Elsibai KA (2014). Vibration of gold nano beam in context of two-temperature generalized thermoelasticity subjected to laser pulse. Latin American Journal of Solids and Structures, 11(13): 2460-2482. https://doi.org/10.1590/S1679-78252014001300008   [Google Scholar]
  39. Youssef HM, Elsibai KA, and El-Bary AA (2017). Effect of the speed, the rotation and the magnetic field on the Q-factor of an axially clamped gold micro-beam. Meccanica, 52(7): 1685-1694. https://doi.org/10.1007/s11012-016-0498-8   [Google Scholar]