(10)Memory-dependent magneto–thermoelasticity for perfectly conducting two-dimensional elastic solids with thermal shock

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Sarhan Y. Atwa ^a,∗, Nantu Sarkar ^b

^a Department of Engineering Mathematics and Physics, Higher Institute of Engineering, El Shorouk Academy, Egypt 

^b Department of Applied Mathematics, University of Calcutta, Kolkata 700009, India 

Received 10 April 2019; received in revised form 4 May 2019; accepted 15 May 2019 

Available online 21 May 2019 

Abstract 

    Recently, Yu et al. (2014) proposed a new model in generalized thermoelasticity based on heat conduction with the memory-dependent derivative.  The magneto–thermoelastic responses in a perfectly conducting thermoelastic solid half-space is investigated in the context of the above new theory. Normal mode analysis together with an eigenvalue expansion technique is used to solve the resulting non-dimensional coupled governing equations. The obtained solutions are then applied to a specific problem for thermoelastic half-space whose boundary is subjected to a time-dependent thermal shock and zero stress. The effects of the kernel function, time-delay parameter, magnetic field and thermoelastic coupling parameter on the variations of different field quantities inside the half-space are analyzed graphically. The results show that these parameters has significant influence on the variations of the considered variables. 

© 2019 Published by Elsevier B.V. on behalf of Shanghai Jiaotong University. 

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

Keywords: Magneto–thermoelasticity; Memory-dependent derivative; Time-delay; Normal mode analysis.