(7)A magneto – thermo-elastic problem for a half-space without energy dissipation subjected to rotation and gravity field

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A.M. Abd-Alla ^a,∗, S.M. Abo-Dahab ^b,c,  S.M. Ahmed ^d,  M.M. Rashid ^a

^a Faculty of Science, Mathematics Department, Sohag University, Egypt 

^b Faculty of Science, Mathematics Department, South Valley University, Qena 83523, Egypt 

^c Faculty of Science, Mathematics Department, Taif University, 888, Saudi Arabia 

^d Faculty of Science, Mathematics Department, Al-Arish University, Egypt 

Received 24 November 2018; received in revised form 27 December 2018; accepted 29 December 2018 

Available online 3 January 2019 

Abstract 

    The prime objective of the present paper is to analyze the effects of the rotation, magnetic field and gravity in a thermo-elastic half- space containing heat source on the boundary of the half-space.  The medium assumed under consideration is traction free, homogeneous, isotropic, as well as without energy dissipation. The normal mode analysis and eigenvalue approach technique are used to solve the resulting non-dimensional coupled equations. The comparisons for the physical quantities are established numerically and represented graphically in different cases with respect to the used effects. A comparative and remarkable study has been carried out through various graphs to deliberate the consequences of different parameter on the displacement components, stress components and temperature. 

© 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: Green–Naghdi theory; Thermo-elasticity; Energy dissipation; Rotation; Magnetic field; Gravity field.