The effect of modified Ohm’s and Fourier’s laws in generalized magneto-thermo viscoelastic spherical region

Alaa. K. Khamis; Allal Bakali; A. A. El-Bary; Haitham. M. Atef; Alaa. K. Khamis; Allal Bakali; A. A. El-Bary; Haitham. M. Atef

doi:10.3934/matersci.2020.4.381

AIMS Materials Science

2020, Volume 7, Issue 4: 381-398. doi: 10.3934/matersci.2020.4.381

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Research article

The effect of modified Ohm’s and Fourier’s laws in generalized magneto-thermo viscoelastic spherical region

1.
Mathematics Department-Faculty of Science-Northern Border University, Arar, Saudi Arabia.
2.
Basic and Applied Science Institute, Arab Academy for Science, Technology and Maritime Transport, P. O. Box 1029, Alexandria, Egypt
3.
Department of Mathematics, Faculty of science, Damanhur University, Damanhur, Egypt

Received: 11 April 2020 Accepted: 09 June 2020 Published: 23 June 2020

This paper is dealing the modified Ohm’s law, including the temperature gradient and charge thickness impacts, and the generalized Fourier’s law, including the current density impact, the conditions of generalized thermo-viscoelasticity for a thermally, isotropic and electrically leading unbounded body with a spherical cavity is given. The detailing is applied to the generalized thermo elasticity dependent on Green–Naghdi (G-N II) and (G-N III) theory, where there is an underlying magnetic field corresponding to the plane limit, because of the utilization of the magnetic field, it results an incited magnetic and electric fields in the medium. The state space investigation is applied to acquire the temperature, displacement, stresses, induced electric field, instigated magnetic field and current density. Application is utilized to our concern to get the arrangement in the total structure. The considered variables are introduced graphically and discussions are made.
- generalized thermoelasticity,
- viscosity,
- magnetic field,
- spherical cavity,
- modified Ohm’s and Fourier’s laws
Citation: Alaa. K. Khamis, Allal Bakali, A. A. El-Bary, Haitham. M. Atef. The effect of modified Ohm’s and Fourier’s laws in generalized magneto-thermo viscoelastic spherical region[J]. AIMS Materials Science, 2020, 7(4): 381-398. doi: 10.3934/matersci.2020.4.381

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Abstract

This paper is dealing the modified Ohm’s law, including the temperature gradient and charge thickness impacts, and the generalized Fourier’s law, including the current density impact, the conditions of generalized thermo-viscoelasticity for a thermally, isotropic and electrically leading unbounded body with a spherical cavity is given. The detailing is applied to the generalized thermo elasticity dependent on Green–Naghdi (G-N II) and (G-N III) theory, where there is an underlying magnetic field corresponding to the plane limit, because of the utilization of the magnetic field, it results an incited magnetic and electric fields in the medium. The state space investigation is applied to acquire the temperature, displacement, stresses, induced electric field, instigated magnetic field and current density. Application is utilized to our concern to get the arrangement in the total structure. The considered variables are introduced graphically and discussions are made.

References

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