International journal of

ADVANCED AND APPLIED SCIENCES

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

Frequency: 12

line decor
  
line decor

 Volume 7, Issue 1 (January 2020), Pages: 117-124

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

 Original Research Paper

 Title: Effect of magnetic field on thermos: Viscoelastic cylinder subjected to a constant thermal shock

 Author(s): Shadia Fathi Mohamed El Sherif 1, *, Mahmoud A. Ismail 1, A. A. El-Bary 2, Haitham M. Atef 3

 Affiliation(s):

 1Department of Mathematics, Faculty of Science, Northern Border University, Arar, Saudi Arabia
 2Basic and Applied Science Institute, Arab Academy for Science, Technology and Maritime Transport, Alexandria, Egypt
 3Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, 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.2020.01.012

 Abstract:

In this paper, we will discuss the problem of distribution of thermal stresses and temperature in a generalized Magneto–Thermo-Viscoelastic Solid Cylinder of radius L. The surface of the cylinder is assumed to be free traction and subjected to a constant thermal shock. The Laplace transform technique is used to solve the problem. A solution to the problem in the physical domain is obtained by using a numerical method of MATLAB Programmer and the expression for the temperature, strain, and stress are obtained. Numerical computations are carried out for a particular material for illustrating the results. Finally, the results obtained are presented graphically to show the effect of time on the field variables. And to show a comparison between Lord- Shulman and Coupled theory. 

 © 2019 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, Numerical computations

 Article History: Received 10 May 2019, Received in revised form 5 August 2019, Accepted 12 November 2019

 Acknowledgment:

The authors wish to acknowledge the approval and the support of this research study by Project NO. 7503–SCI–2017–1–8–F from the Deanship of Scientific Research in Northern Border University, Arar, KSA.

 Compliance with ethical standards

 Conflict of interest:  The authors declare that they have no conflict of interest.

 Citation:

 El Sherif SFM, Ismail MA, and El-Bary AA et al. (2020). Effect of magnetic field on thermos: Viscoelastic cylinder subjected to a constant thermal shock. International Journal of Advanced and Applied Sciences, 7(1): 117-124

 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 (54) 

  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 Sengupta PR (1978). Magneto-thermo-elastic surface waves in initially stressed conducting media. Acta Geophysica Polonica. 26(4): 299-311.   [Google Scholar]
  5. 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]
  6. 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]
  7. 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]
  8. Biot MA (1956). Thermoelasticity and irreversible thermodynamics. Journal of Applied Physics, 27(3): 240-253. https://doi.org/10.1063/1.1722351   [Google Scholar]
  9. 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]
  10. Chandrasekharaiah DS (1998). Hyperbolic thermoelasticity: A review of recent literature. Applied Mechanics Reviews, 51(12): 705-729. https://doi.org/10.1115/1.3098984   [Google Scholar]
  11. 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]
  12. 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]
  13. De SN and Sengupta PR (1972). Magneto-elastic waves and disturbances in initially stressed conducting media. Pure and Applied Geophysics, 93(1): 41-54. https://doi.org/10.1007/BF00875220   [Google Scholar]
  14. El-Karamany AS, Ezzat MA, and El-Bary AA (2018). Thermodiffusion with two time delays and Kernel functions. Mathematics and Mechanics of Solids, 23(2): 195-208. https://doi.org/10.1177/1081286516676870   [Google Scholar]
  15. 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]
  16. Ezzat MA and El-Bary AA (2012). Mhd free convection flow with fractional heat conduction law. Magnetohydrodynamics, 48(4): 587-606. https://doi.org/10.22364/mhd.48.4.1   [Google Scholar]
  17. Ezzat MA and El-Bary AA (2014). Two-temperature theory of magneto-thermo-viscoelasticity with fractional derivative and integral orders heat transfer. Journal of Electromagnetic Waves and Applications, 28(16): 1985-2004. https://doi.org/10.1080/09205071.2014.953639   [Google Scholar]
  18. Ezzat MA and El-Bary AA (2015a). State space approach to two-dimensional magneto-thermoelasticity with fractional order heat transfer in a medium of perfect conductivity. International Journal of Applied Electromagnetics and Mechanics, 49(4): 607-625. https://doi.org/10.3233/JAE-150095   [Google Scholar]
  19. Ezzat MA and El-Bary AA (2015b). Memory-dependent derivatives theory of thermo-viscoelasticity involving two-temperature. Journal of Mechanical Science and Technology, 29(10): 4273-4279. https://doi.org/10.1007/s12206-015-0924-1   [Google Scholar]
  20. Ezzat MA and El-Bary AA (2016a). Effects of variable thermal conductivity on Stokes' flow of a thermoelectric fluid with fractional order of heat transfer. International Journal of Thermal Sciences, 100: 305-315. https://doi.org/10.1016/j.ijthermalsci.2015.10.008   [Google Scholar]
  21. Ezzat MA and El-Bary AA (2016b). Modeling of fractional magneto-thermoelasticity for a perfect conducting materials. Smart Structures and Systems, 18(4): 707-731. https://doi.org/10.12989/sss.2016.18.4.707   [Google Scholar]
  22. Ezzat MA and El-Bary AA (2017a). Fractional magneto-thermoelastic materials with phase-lag Green-Naghdi theories. Steel and Composite Structures, 24(3): 297-307. https://doi.org/10.1007/s00542-017-3425-6   [Google Scholar]
  23. Ezzat MA and El-Bary AA (2017b). On thermo-viscoelastic infinitely long hollow cylinder with variable thermal conductivity. Microsystem Technologies, 23(8): 3263-3270. https://doi.org/10.1007/s00542-016-3101-2   [Google Scholar]
  24. Ezzat MA and El-Bary AA (2017c). A functionally graded magneto-thermoelastic half space with memory-dependent derivatives heat transfer. Steel and Composite Structures, 25(2): 177-186.   [Google Scholar]
  25. Ezzat MA and El-Bary AA (2017d). Electro-magneto interaction in fractional Green-Naghdi thermoelastic solid with a cylindrical cavity. Waves in Random and Complex Media, 28(1): 150-168. https://doi.org/10.1080/17455030.2017.1332798   [Google Scholar]
  26. Ezzat MA and El-Bary AA (2018). Thermoelectric spherical shell with fractional order heat transfer. Microsystem Technologies, 24(2): 891-899. https://doi.org/10.1007/s00542-017-3400-2   [Google Scholar]
  27. Ezzat MA, El Bary AA, and El Karamany AS (2009). Two-temperature theory in generalized magneto-thermo-viscoelasticity. Canadian Journal of Physics, 87(4): 329-336. https://doi.org/10.1139/P08-143   [Google Scholar]
  28. Ezzat MA, El-Karamany AS, and El-Bary AA (2015a). 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]
  29. Ezzat MA, El-Karamany AS, and El-Bary AA (2015b). Thermo-viscoelastic materials with fractional relaxation operators. Applied Mathematical Modelling, 39(23-24): 7499-7512. https://doi.org/10.1016/j.apm.2015.03.018   [Google Scholar]
  30. Ezzat MA, El-Karamany AS, and El-Bary AA (2017). Thermoelectric viscoelastic materials with memory-dependent derivative. Smart Structures and Systems, 19(5): 539-551. https://doi.org/10.12989/sss.2017.19.5.539   [Google Scholar]
  31. Ezzat MA, El-Karamany AS, and Samaan AA (2001). State-space formulation to generalized thermo viscoelasticity with thermal relaxation. Journal of Thermal Stresses, 24(9): 823-846. https://doi.org/10.1080/014957301750379612   [Google Scholar]
  32. Ezzat MA, Zakaria M, and El‐Bary AA (2010). Thermo‐electric‐visco‐elastic material. Journal of Applied Polymer Science, 117(4): 1934-1944. https://doi.org/10.1002/app.32170   [Google Scholar]
  33. Green AE and Lindsay KA (1972). Thermoelasticity. Journal of Elasticity, 2(1): 1-7. https://doi.org/10.1007/BF00045689   [Google Scholar]
  34. 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]
  35. Gross B (1968). Mathematical structure of the theories of viscoelasticity. Hermann, Paris, French.   [Google Scholar]
  36. Gurtin ME and Sternberg E (1962). On the linear theory of viscoelasticity. Archive for Rational Mechanics and Analysis, 11(1): 291-356. https://doi.org/10.1007/BF00253942   [Google Scholar]
  37. 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]
  38. 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]
  39. Ilioushin AA and Pobedria BE (1970). Fundamentals of the mathematical theory of thermal viscoelasticity. Nauka, Moscow, Russia.   [Google Scholar]
  40. Ismail MAH, Khamis AK, El-Bary AA, and Youssef HM (2017). Effect of the rotation of generalized thermoelastic layer subjected to harmonic heat: State-space approach. Microsystem Technologies, 23(8): 3381-3388. https://doi.org/10.1007/s00542-016-3137-3   [Google Scholar]
  41. Khamis AK, Ismail MAH, Youssef HM, and El-Bary AA (2017). Thermal shock problem of two-temperature generalized thermoelasticity without energy dissipation with rotation. Microsystem Technologies, 23(10): 4831-4839. https://doi.org/10.1007/s00542-017-3279-y   [Google Scholar]
  42. 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]
  43. Mukhopadhyay S (2000). Effects of thermal relaxations on thermoviscoelastic interactions in an unbounded body with a spherical cavity subjected to a periodic loading on the boundary. Journal of Thermal Stresses, 23(7): 675-684. https://doi.org/10.1080/01495730050130057   [Google Scholar]
  44. 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]
  45. 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]
  46. 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]
  47. Tanner RI (1988). Engineering rheology. Oxford University Press, Oxford, UK.   [Google Scholar]
  48. Tianhu H, Yapeng S, and Xiaogeng (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]
  49. Tzou DY (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]
  50. 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]
  51. Youssef HM and El-Bary AA (2014). Thermoelastic material response due to laser pulse heating in context of four theorems of thermoelasticity. Journal of Thermal Stresses, 37(12): 1379-1389. https://doi.org/10.1080/01495739.2014.937233   [Google Scholar]
  52. Youssef HM and El-Bary AA (2018). The reference temperature dependence of Young's modulus of two-temperature thermoelastic damping of gold nano-beam. Mechanics of Time-Dependent Materials, 22(4): 435-445. https://doi.org/10.1007/s11043-017-9365-9   [Google Scholar]
  53. 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]
  54. 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]