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Magneto-thermoelastic response in a functionally graded rotating medium due to a periodically varying heat source

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Abstract

This paper deals with the problem of magneto-thermoelastic interactions in a functionally graded isotropic, unbounded, rotating medium due to a periodically varying heat source in the context of the linear theory of generalized thermoelasticity without energy dissipation and with energy dissipation. The governing equations of generalized thermoelasticity (GN model) for a functionally graded material under the influence of a magnetic field are established. The Laplace–Fourier double transform technique has been used to get the solution. The inversion of Fourier transform is done by using residual calculus, where the poles of the integrand are obtained numerically in the complex domain by using Laguerre’s method, and the inversion of the Laplace transformation is done numerically using a method based on Fourier series expansion technique. The numerical estimates for displacements, temperature and stress are obtained for a hypothetical material. The solution to the analogous problem is obtained by taking a suitable non-homogeneous parameter. Finally, the results obtained are presented graphically to show the effect of rotation, non-homogeneity, damping coefficient and magnetic field on displacements, temperature and stress.

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Abbreviations

u :

Displacement vector

λ, μ :

Lamé constants

ρ :

Constant mass density of the medium

γ :

Thermal modulus

α t :

Coefficient of linear thermal expansion

T 0 :

Uniform reference temperature

T :

Small temperature increase above the reference temperature T 0

J :

Electric current density vector

B :

Magnetic induction vector

c v :

Specific heat of the medium at constant strain

K*:

A material constant characteristic for the GN theory

H :

Total magnetic field vector at any time

h :

Perturbed magnetic field

E :

Electric field vector

F :

Body force

μ e :

Magnetic permeability of the medium

σ :

Electric conductivity of the medium

C T :

Non-dimensional finite thermal wave speed of GN theory

\({\epsilon_{T} }\) :

Thermoelastic coupling constant

K :

Thermal conductivity

κ :

Thermal diffusivity

Ω :

Angular velocity

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Calcutta, 92, A.P.C. Road, Kolkata, 700009, West Bengal, India

    P. Pal & M. Kanoria

  2. Netaji Subhash Engineering College, Technocity, Police Para, Panchpota, Garia, Kolkata, India

    P. Das

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  1. P. Pal
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Correspondence to M. Kanoria.

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Pal, P., Das, P. & Kanoria, M. Magneto-thermoelastic response in a functionally graded rotating medium due to a periodically varying heat source. Acta Mech 226, 2103–2120 (2015). https://doi.org/10.1007/s00707-015-1301-y

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  • DOI: https://doi.org/10.1007/s00707-015-1301-y

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