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# Numerical Solution of a Problem of Thermal Stresses of a Magnetothermoelastic Cylinder with Rotation by Finite-Difference Method

F. S. Bayones1, A. M. Abd-Alla2, A. M. Farhan3,4,*

1 Department of Mathematics and Statistics, College of Science, Taif University, Taif, 21944, Saudi Arabia
2 Department of Mathematics, Faculty of Science, Sohag University, Egypt
3 Physics Department, Faculty of Science, Jazan University, Jazan, Saudi Arabia
4 Physics Department, Faculty of Science, Zagazig University, Zagazig, Egypt

* Corresponding Author: A. M. Farhan. Email:

Computers, Materials & Continua 2021, 68(3), 3339-3352. https://doi.org/10.32604/cmc.2021.016021

## Abstract

The present article deals with the investigation thermal stress of a magnetothermoelastic cylinder subjected to rotation, open or closed circuit, thermal and mechanical boundary conditions. The outer and inner surfaces of the cylinder are subjected to both mechanical and thermal boundary conditions. A The transient coupled thermoelasticity in an infinite cylinder with its base abruptly exposed to a heat flux of a decaying exponential function of time is devised solve by the finite-difference method. The fundamental equations’ system is solved by utilizing an implicit finite-difference method. This current method is a second-order accurate in time and space; it is also unconditionally stable. To illustrate the present model’s efficiency, we consider a suitable material and acquire the numerical solution of temperature, displacement components, and the components of stresses with time t and through the radial of an infinite cylinder. The results indicate that the effect of coupled thermoelasticity, magnetic field, and rotation on the temperature, stresses, and displacement is quite pronounced. In order to illustrate and verify the analytical developments, the numerical solution of partial differential equations, stress components, displacement components and temperature is carried out and computer simulated results are presented graphically. This study is helpful in the development of piezoelectric devices.

## Keywords

APA Style
Bayones, F.S., Abd-Alla, A.M., Farhan, A.M. (2021). Numerical solution of a problem of thermal stresses of a magnetothermoelastic cylinder with rotation by finite-difference method. Computers, Materials & Continua, 68(3), 3339-3352. https://doi.org/10.32604/cmc.2021.016021
Vancouver Style
Bayones FS, Abd-Alla AM, Farhan AM. Numerical solution of a problem of thermal stresses of a magnetothermoelastic cylinder with rotation by finite-difference method. Comput Mater Contin. 2021;68(3):3339-3352 https://doi.org/10.32604/cmc.2021.016021
IEEE Style
F.S. Bayones, A.M. Abd-Alla, and A.M. Farhan "Numerical Solution of a Problem of Thermal Stresses of a Magnetothermoelastic Cylinder with Rotation by Finite-Difference Method," Comput. Mater. Contin., vol. 68, no. 3, pp. 3339-3352. 2021. https://doi.org/10.32604/cmc.2021.016021

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