State space approach of two-temperature magneto-thermoelasticity with thermal relaxation in a medium of perfect conductivity

A one-dimensional model of the two-temperature generalized magneto-thermoelasticity theory with one relaxation time in a perfect conducting medium is established. The state space approach developed in I M. Ezzat, Can. J. Phys. 72 (1994) 311: M. Ezzat, Int. J. Eng. Sci. 35 (1997) 7411 is adopted for the solution of one-dimensional problems for any set of boundary conditions. The resulting formulation together with the Laplace transform techniques are applied to a specific problem of a half-space subjected to thermal shock and traction-free surface. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results are given and illustrated graphically for the problem. Some comparisons have been shown in figures to estimate the effects of the two-temperature parameter and the applied magnetic field. (c) 2009 Elsevier Ltd. All rights reserved.