Magneto-thermoelastic Response in a Functionally Graded Isotropic Unbounded Medium Under a Periodically Varying Heat Source

Abstract

This paper deals with the problem of magneto-thermoelastic interactions in a functionally graded isotropic unbounded medium due to the presence of periodically varying heat sources in the context of linear theory of generalized thermoelasticity with energy dissipation (TEWED) and without energy dissipation (TEWOED) having a finite conductivity. The governing equations of generalized thermoelasticity (GN model) for a functionally graded material (FGM) 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 the Fourier transform has been done by using residual calculus, where poles of the integrand are obtained numerically in a complex domain by using Leguerre's method and the inversion of the Laplace transformation is done numerically using a method based on a Fourier series expansion technique. Numerical estimates of the displacement, temperature, stress, and strain are obtained for a hypothetical material. The solution to the analogous problem for homogeneous isotropic materials is obtained by taking a suitable non-homogeneous parameter. Finally, the results obtained are presented graphically to show the effect of a non-homogeneous, magnetic field and damping coefficient on displacement, temperature, stress, and strain.

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

“…In order to avoid such type of failures, FGMs are very useful as discussed by Weterhold and Wang [27]. Among several works done, we may mention a few: Das and Kanoria [28], Fahmy [29], Banik and Kanoria [30], Khosravifard et al [31], Mallik and Kanoria [32], Ghosh and Kanoria [33], and Arani et al [34].…”

Thermodynamical interactions in a rotating functionally graded semiconductor material with gravity

“…Generalised TE interactions in functionally graded solid with a periodically varying heat source were investigated by Das and Kanoria (2009). Kumar and Devi (2017) used the Laplace transform technique to study the effect of ramp type heating on a modified coupled stressed non-homogeneous medium.…”

Generalized thermoelastic interaction in functional graded material with fractional order three-phase lag heat transfer

“…These novel nonhomogeneous materials have excellent thermomechanical properties to withstand high temperature and have extensive applications to important structures, such as pressure vessels, chemicals plants, aerospace, pipes and nuclear reactors. MALLIK and KANORIA [17], DAS and KANORIA [18] studied a periodically varying heat source in generalized thermoelastic functionally graded solid. Applying the above theories of generalized thermoelasticity, several problems have been solved by finite element method and analytical method [19−35].…”