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Geomechanics and Engineering Volume 23, Number 4, November25 2020 , pages 393-403 DOI: https://doi.org/10.12989/gae.2020.23.4.393 |
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Modeling of GN type III with MDD for a thermoelectric solid subjected to a moving heat source |
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Magdy A. Ezzat
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| Abstract | ||
| We design the Green-Naghdi model type III (GN-III) with widespread thermoelasticity for a thermoelectric half space using a memory-dependent derivative rule (MDD). Laplace transformations and state-space techniques are used in order to find the general solution for any set of limit conditions. A basic question of heat shock charging half space and a traction-free surface was added to the formulation in the present situation of a traveling heat source with consistent heating speed and ramp-type heating. The Laplace reverse transformations are numerically recorded. There are called the impacts of several calculations of the figure of the value, heat source spead, MDD parameters, magnetic number and the parameters of the ramping period. | ||
| Key Words | ||
| thermoelectric materials; Green-Naghdi of type III; memory-dependent derivative; ramp-type heating; moving heat source; state-space approach; Laplace transforms; numerical result | ||
| Address | ||
| Magdy A. Ezzat: 1.) Department of Mathematics, College of Science and Arts,Qassim University, Al Bukairyah, Saudi Arabia 2.) Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt | ||