Meccanica

, Volume 45, Issue 4, pp 451–462 | Cite as

Magneto-thermoelastic problem in rotating non-homogeneous orthotropic hollow cylinder under the hyperbolic heat conduction model

Article

Abstract

In this paper, we proposed a model of generalized magneto-thermoelastic for orthotropic hollow cylinder whose surfaces are subjected to a thermal relaxation under the effect of rotation with one relaxation time. The system of fundamental equations is solved by using an implicit finite-difference scheme. A numerical method is used to calculate the temperature, displacement and the components of stresses with time and through the radial of the cylinder. Numerical results are given and illustrated graphically for each case considered. The results indicate that the effect of rotation, inhomogeneity and magnetic field are very pronounced. Comparison made with the results predicted by the theory of generalized magneto-thermoelasticity with one relaxation time in the absence of rotation.

Magneto-thermoelasticity Thermal relaxation Hyperbolic problems Orthotropic cylinder Rotating Implicit finite difference method 

Nomenclature

ui

are the components of the displacement tensor

T0

is a reference temperature

k1

is the thermal diffusivity

k2

is the thermal conductivity

Q

is the intensity

αi

are the thermal expansion coefficients

H0

is the constant magnetic field

τ

is the thermal relaxation time

\(\,\hat{}\)

is dimensionless variables

ν

is the Poisson’s ratio

ρ

is the mass density

Ω

is the uniform angular velocity

cij

are the elastic constants

eij

are the strain

σij

are the stress components

μ

is the magnetic permeability

τrr

is the Maxwell’s stress

t

is the time

E

is the Young’s modulus

T

is the temperature

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Mathematics Department, Faculty of ScienceTaif UniversityTa’ifSaudi Arabia
  2. 2.Mathematics Department, J.T.C.King Abdul Aziz UniversityJeddahSaudi Arabia

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