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A two-temperature generalized magneto-thermoelastic formulation for a rotating medium with thermal shock under hydrostatic initial stress

  • S. M. Abo-DahabEmail author
Original Article
  • 12 Downloads

Abstract

The interaction between magnetic field and thermal field in an elastic half-space, homogeneous and isotropic under two temperature and initial stress are investigated using a normal mode method in the framework of the Lord–Şhulman theory, with thermal shock and rotation. The medium rotates with a uniform angular velocity, and it is considered to be permeated by a uniform magnetic field and hydrostatic initial stress. The general solution we obtain is finally applied to a specific problem. The variations in temperature, the dynamical temperature, the stress and the strain distributions through the horizontal distance are calculated by an appropriate numerical example and graphically illustrated.

Keywords

Generalized thermoelasticity Thermal shock Two-temperature problem Lord–Şhulman theory 

List of symbols

\(\delta _{{ij}}\)

Kronecker delta function

\(\alpha _{t}\)

Coefficient of linear thermal expansion

T

Absolute temperature

\(T_0\)

Reference temperature chosen so that \(\left| {\frac{T-T_0 }{T_0 }} \right| <1\)

\(\phi =\phi _0 -{T}\)

Conductive temperature

\(\eta \)

Hydrostatic initial stress

\(\lambda , \mu \)

Lame’s constants

\(\mu _0\)

Magnetic permeability

\(\theta ={T}-{T}_0\)

Thermodynamical temperature

\(\rho \)

Density of the medium

\(\sigma _{{ij}}\)

Components of the stress tensor

\(\tau _0\)

Thermal relaxation time

a

Two-temperature parameter

\({C}_{{E}}\)

Specific heat at constant strain

e

Cubical dilatation

\({e}_{{ij}}\)

Components of the strain tensor

\({F}_{i}\)

Lorentz force

K

Thermal conductivity

P

Initial pressure

\({u}_{i}\)

Components of the displacement vector

\(F_{i}\)

Lorentz body force

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Notes

References

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Authors and Affiliations

  1. 1.Mathematics Department, Faculty of ScienceTaif UniversityTaifSaudi Arabia
  2. 2.Mathematics Department, Faculty of ScienceSouth Valley UniversityQenaEgypt

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