Analysis of Magneto-Thermoelastic Response in a Transversely Isotropic Hollow Cylinder Under Thermal Shock with Three-Phase-Lag Effect

Abstract

This article deals with a problem of magneto-thermoelastic interactions in a transversely isotropic hollow cylinder due to thermal shock in the context of three-phase-lag theory of generalized thermoelasticity. The governing equations of generalized thermoelasticity of the above model under the influence of a magnetic field are established. The Laplace transform method has been used to transform the equation into the space domain, where the Galerkin finite element technique has been employed to solve the resulting equations in the transformed domain. The inversion of the Laplace transformation is done by applying a method of Bellman et al. The stresses and temperature distributions have been computed numerically and presented graphically in a numbers of figures. A comparison of the results for different theories (GN-III and 3P models) are presented and the effect of magnetic field is discussed. The results for an isotropic material (Cu) have been deduced numerically and presented graphically to compare with those of transversely isotropic material (Mg).

Keywords:

• Galerkin finite element technique
• Generalized magneto-thermoelasticity
• Laplace transformation
• Three-phase-lag model

Acknowledgments

We are grateful to Professor S. C. Bose of the Department of Applied Mathematics, University of Calcutta, for his kind help and guidance in preparation of the article. We also express our sincere thanks to the reviewer to his valuable suggestions for the improvement of the article.