# 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

## 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

*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

- λ
_{ij} 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

- Φ
_{v} change in the volume fraction field

- Ω
angular velocity

## Chinese Library Classification

O357.5## 2010 Mathematics Subject Classification

76F02## Preview

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