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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

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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.

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Abbreviations

a :

wave number

a c, b c :

magnitudes of thermoelastic diffusion

B :

magnetic induction vector

C :

strength of diffusion

C E :

specialized heat per unit mass

d :

thermoelastic diffusion constant

e ij :

component of the strain tensor

E :

electric intensity vector

F i :

Lorentz’s body force vector

g :

gravity field

g*:

intrinsic equilibrated body force

h :

perturbed magnetic field vector

H 0 :

primary constant magnetic field vector

H :

magnetic field vector

J :

electric current density vector

K :

thermal conductivity

m :

thermo-void coefficient

P :

initial stress

q i :

heat flux vector

t :

time of wave

T 0 :

reference temperature

χ :

equilibrated inertia

S i :

component of the equilibrated stress vector

T :

temperature

α, b, ω 0, ζ :

void material parameters

α t :

coefficient of linear thermal extension

α c :

coefficient of linear diffusion extension

δ ij :

Kronecker delta

ε 0 :

electric permeability

η :

entropy per unit mass

λ, μ :

Lame’s constants

μ r :

magnetic permeability

ρ :

density

σ ij :

component of the stress tensor

λij :

Maxwell’s stress tensor

τ 1 :

phase-lag of the heat flux

τ Θ :

phase-lag of the temperature gradient

ω :

complex frequency

τ 2, τ η :

diffusion relaxation time

Φv :

change in the volume fraction field

Ω:

angular velocity

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Authors and Affiliations

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

    S. M. Abo-Dahab

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

    S. M. Abo-Dahab

  3. Department of Mathematics, Faculty of Science, Sohag University, Sohag, 82524, Egypt

    A. M. Abd-Alla & A. A. Kilany

Authors
  1. S. M. Abo-Dahab
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  2. A. M. Abd-Alla
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  3. A. A. Kilany
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Correspondence to A. A. Kilany.

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Citation: ABO-DAHAB, S. M., ABD-ALLA, A. M., and KILANY, A. A. 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. Applied Mathematics and Mechanics (English Edition) 40(8), 1135–1154 (2019) https://doi.org/10.1007/s10483-019-2504-6

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Abo-Dahab, S.M., Abd-Alla, A.M. & Kilany, A.A. 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. Appl. Math. Mech.-Engl. Ed. 40, 1135–1154 (2019). https://doi.org/10.1007/s10483-019-2504-6

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  • DOI: https://doi.org/10.1007/s10483-019-2504-6

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