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Effects of rotation and gravity on an electro-magneto-thermoelastic medium with diffusion and voids by using the Lord-Shulman and dual-phase-lag models

  • S. M. Abo-Dahab
  • A. M. Abd-Alla
  • A. A. KilanyEmail author
Article

Abstract

The effects of rotation and gravity on an electro-magneto-thermoelastic medium with diffusion and voids in a generalized thermoplastic half-space are studied by using the Lord-Shulman (L-S) model and the dual-phase-lag (DPL) model. The analytical solutions for the displacements, stresses, temperature, diffusion concentration, and volume fraction field with different values of the magnetic field, the rotation, the gravity, and the initial stress are obtained and portrayed graphically. The results indicate that the effects of gravity, rotation, voids, diffusion, initial stress, and electromagnetic field are very pronounced on the physical properties of the material.

Key words

electromagnetic field gravity field rotation initial stress voids diffusion normal mode analysis Lord-Shulman (L-S) model dual-phase-lag (DPL) model 

Nomenclature

a

wave number

ac, bc

magnitudes of thermoelastic diffusion

B

magnetic induction vector

C

strength of diffusion

CE

specialized heat per unit mass

d

thermoelastic diffusion constant

eij

component of the strain tensor

E

electric intensity vector

Fi

Lorentz’s body force vector

g

gravity field

g*

intrinsic equilibrated body force

h

perturbed magnetic field vector

H0

primary constant magnetic field vector

H

magnetic field vector

J

electric current density vector

K

thermal conductivity

m

thermo-void coefficient

P

initial stress

qi

heat flux vector

t

time of wave

T0

reference temperature

χ

equilibrated inertia

Si

component of the equilibrated stress vector

T

temperature

α, b, ω0, ζ

void material parameters

αt

coefficient of linear thermal extension

αc

coefficient of linear diffusion extension

δij

Kronecker delta

ε0

electric permeability

η

entropy per unit mass

λ, μ

Lame’s constants

μr

magnetic permeability

ρ

density

σij

component of the stress tensor

λij

Maxwell’s stress tensor

τ1

phase-lag of the heat flux

τΘ

phase-lag of the temperature gradient

ω

complex frequency

τ2, τη

diffusion relaxation time

Φv

change in the volume fraction field

Ω

angular velocity

Chinese Library Classification

O357.5 

2010 Mathematics Subject Classification

76F02 

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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • S. M. Abo-Dahab
    • 1
    • 2
  • A. M. Abd-Alla
    • 3
  • A. A. Kilany
    • 3
    Email author
  1. 1.Department of Mathematics, Faculty of SciencesTaif UniversityTaifSaudi Arabia
  2. 2.Department of Mathematics, Faculty of ScienceSouth Valley UniversityQenaEgypt
  3. 3.Department of Mathematics, Faculty of ScienceSohag UniversitySohagEgypt

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