International Journal of

ADVANCED AND APPLIED SCIENCES

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

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

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 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

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 * 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

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