Eigenfunction expansion method for the solution of magneto-thermoelastic problems with thermal relaxation and heat source in two dimensions

In this paper, the linear theory of magneto-thermoelasticity with thermal relaxation is employed to study the disturbances in an infinite elastic solid containing instantaneous heat source and permeated by a primary uniform magnetic field. It is assumed that the elastic field under consideration is a homogeneous, orthotropic, electrically as well as thermally conducting one. The fundamental equations of the general two-dimensional problem of magneto-thermoelasticity have been written in the form of an inhomogeneous vector matrix differential equation and solved in the Laplace-Fourier transform domain by eigenfunction expansion method. Finally, the solution for space-time domain has been made by numerical methods and the graphs for stresses, etc., are drawn.