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

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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.

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  • 03 November 2020

    Unfortunately, the original version of the article contained error in the below equation terms.

Abbreviations

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

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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Authors and Affiliations

  1. Mathematics Department, Faculty of Science, Taif University, Taif, 888, Saudi Arabia

    S. M. Abo-Dahab

  2. Mathematics Department, Faculty of Science, South Valley University, Qena, 83523, Egypt

    S. M. Abo-Dahab

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Abo-Dahab, S.M. A two-temperature generalized magneto-thermoelastic formulation for a rotating medium with thermal shock under hydrostatic initial stress. Continuum Mech. Thermodyn. 32, 883–900 (2020). https://doi.org/10.1007/s00161-019-00765-3

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