International Journal of

ADVANCED AND APPLIED SCIENCES

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

Frequency: 12
line decor
  
line decor

 Volume 9, Issue 7 (July 2022), Pages: 33-41

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

 Original Research Paper

Magneto-thermoelasticity Green–Naghdi theory with memory-dependent derivative in the presence of a moving heat source

 Author(s): Sayed I. El-Attar 1, Mohamed H. Hendy 1, 2, *, Magdy A. Ezzat 3

 Affiliation(s):

 1Department of Mathematics, Faculty of Science, Northern Border University, Arar, Saudi Arabia
 2Department of Mathematics, Faculty of Science, Al Arish University, Al Arish, Egypt
 3Department of Mathematics, College of Science and Arts, Qassim University, Al Bukairyah, Saudi Arabia

  Full Text - PDF          XML

 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0003-1919-1647

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2022.07.005

 Abstract:

In the present work, a mathematical model of the Green-Naghdi thermoelasticity theory of type III (GN-III) with memory-dependent derivative (MDD) heat transfer for a perfectly conducting isotropic media has been constructed. The state-space and Laplace transform techniques are adopted for the solution of a half-space problem in the presence of a moving heat source with constant velocity. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results for all fields are given and illustrated graphically. Comparison is made with the results predicted by coupled thermoelasticity (DCT). The influences of MDD parameters and heat source speed on all fields are examined.

 © 2022 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: Thermoelectric materials, Memory-dependent derivative, Green-Naghdi theory of type III (GN-III), Moving heat source, Laplace transforms, Numerical result

 Article History: Received 21 January 2022, Received in revised form 15 April 2022, Accepted 17 April 2022

 Acknowledgment 

The authors gratefully acknowledge the approval and the support of this research study by Grant No. SCI-2018-3-9-F-7605 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:

 El-Attar SI, Hendy MH, and Ezzat MA (2022). Magneto-thermoelasticity Green–Naghdi theory with memory-dependent derivative in the presence of a moving heat source. International Journal of Advanced and Applied Sciences, 9(7): 33-41

 Permanent Link to this page

 Figures

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

 Tables

 Table 1

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

 References (24)

  1. Biot MA (1956). Thermoelasticity and irreversible thermodynamics. Journal of Applied Physics, 27(3): 240-253. https://doi.org/10.1063/1.1722351   [Google Scholar]
  2. Chandrasekharaiah DS (1996). A uniqueness theorem in the theory of thermoelasticity without energy dissipation. Journal of Thermal Stresses, 19(3): 267-272. https://doi.org/10.1080/01495739608946173   [Google Scholar]
  3. El Sherif SFM, Ismail MA, El-Bary AA, and Atef HM (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. https://doi.org/10.21833/ijaas.2020.01.012   [Google Scholar]
  4. El-Karamany AS and Ezzat MA (2013). On the three-phase-lag linear micropolar thermoelasticity theory. European Journal of Mechanics-A/Solids, 40: 198-208. https://doi.org/10.1016/j.euromechsol.2013.01.011   [Google Scholar]
  5. El-Karamany AS and Ezzat MA (2015). Two-temperature Green–Naghdi theory of type III in linear thermoviscoelastic anisotropic solid. Applied Mathematical Modelling, 39(8): 2155-2171. https://doi.org/10.1016/j.apm.2014.10.031   [Google Scholar]
  6. El-Karamany AS and Ezzat MA (2016). On the phase-lag Green–Naghdi thermoelasticity theories. Applied Mathematical Modelling, 40(9-10): 5643-5659. https://doi.org/10.1016/j.apm.2016.01.010   [Google Scholar]
  7. Ezzat MA (1997). State space approach to generalized magneto-thermoelasticity with two relaxation times in a medium of perfect conductivity. International Journal of Engineering Science, 35(8): 741-752. https://doi.org/10.1016/S0020-7225(96)00112-7   [Google Scholar]
  8. Ezzat MA (2008). State space approach to solids and fluids. Canadian Journal of Physics, 86(11): 1241-1250. https://doi.org/10.1139/p08-069   [Google Scholar]
  9. Ezzat MA (2011). Magneto-thermoelasticity with thermoelectric properties and fractional derivative heat transfer. Physica B: Condensed Matter, 406(1): 30-35. https://doi.org/10.1016/j.physb.2010.10.005   [Google Scholar]
  10. Ezzat MA and Youssef HM (2010). Stokes’ first problem for an electro-conducting micropolar fluid with thermoelectric properties. Canadian Journal of Physics, 88(1): 35-48. https://doi.org/10.1139/P09-100   [Google Scholar]
  11. Ezzat MA, El-Karamany AS, and El-Bary AA (2014). Generalized thermo-viscoelasticity with memory-dependent derivatives. International Journal of Mechanical Sciences, 89: 470-475. https://doi.org/10.1016/j.ijmecsci.2014.10.006   [Google Scholar]
  12. Ezzat MA, El-Karamany AS, and El-Bary AA (2015). 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]
  13. Ezzat MA, El-Karamany AS, and El-Bary AA (2016). Modeling of memory-dependent derivative in generalized thermoelasticity. The European Physical Journal Plus, 131: 372. https://doi.org/10.1140/epjp/i2016-16372-3   [Google Scholar]
  14. Green AE and Naghdi P (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]
  15. Green AE and Naghdi P (1993). Thermoelasticity without energy dissipation. Journal of Elasticity, 31(3): 189-208. https://doi.org/10.1007/BF00044969   [Google Scholar]
  16. Hendy MH, Amin MM, and Ezzat MA (2019). Two-dimensional problem for thermoviscoelastic materials with fractional order heat transfer. Journal of Thermal Stresses, 42(10): 1298-1315. https://doi.org/10.1080/01495739.2019.1623734   [Google Scholar]
  17. Hoing G and Hirdes U (1984). A method for the numerical inversion of the Laplace transform. Journal of Computational and Applied Mathematics, 10(1): 113-132. https://doi.org/10.1016/0377-0427(84)90075-X   [Google Scholar]
  18. Khamis AK, El-Bary AA, Youssef HM, and Bakali A (2020). Generalized thermoelasticity with fractional order strain of infinite medium with a cylindrical cavity. International Journal of Advanced and Applied Sciences, 7(7): 102-108. https://doi.org/10.21833/ijaas.2020.07.013   [Google Scholar]
  19. Khamis AK, Nasr AMAA, El-Bary AA, and Atef HM (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. https://doi.org/10.21833/ijaas.2021.06.005   [Google Scholar]
  20. Load H and Shulman Y (1967). A generalized dynamical theory of thermoelasticty. Journal of the Mechanics and Physics of Solids, 15: 299-309. https://doi.org/10.1016/0022-5096(67)90024-5   [Google Scholar]
  21. Povstenko YZ (2009). Thermoelasticity that uses fractional heat conduction equation. Journal of Mathematical Sciences, 162(2): 296-305. https://doi.org/10.1007/s10958-009-9636-3   [Google Scholar]
  22. Sherief HH, El-Sayed AMA, and Abd El-Latief AM (2010). Fractional order theory of thermoelasticity. International Journal of Solids and Structures, 47(2): 269-275. https://doi.org/10.1016/j.ijsolstr.2009.09.034   [Google Scholar]
  23. Yu YJ, Hu W, and Tian XG (2014). A novel generalized thermoelasticity model based on memory-dependent derivative. International Journal of Engineering Science, 81: 123-134. https://doi.org/10.1016/j.ijengsci.2014.04.014   [Google Scholar]
  24. Yu YJ, Tian XG, and Lu TJ (2013). Fractional order generalized electro-magneto-thermo-elasticity. European Journal of Mechanics-A/Solids, 42: 188-202. https://doi.org/10.1016/j.euromechsol.2013.05.006   [Google Scholar]