Magneto-thermo-elastic disturbances with thermal relaxation in a solid due to heat sources

AbstractA study is made of the propagation of magneto-thermo-elastic disturbances with thermal relaxation in a perfectly conducting unbounded solid, due to heat sources distributed over a plane parallel to the applied magnetic field. The governing partial differential equations are solved in the Laplace transform domain by the state space approach of the modern control theory. The small-time solutions of the problem are obtained with physical significance. The solutions are found to consist of thermal wave (T-wave) and acoustic wave (A-wave). The speeds of these waves are increased due to the presence of the external magnetic field. The displacement field, the thermal field and the magnetic field experience discontinuities at each of the wave fronts. The effect of the magnetic field is to shift the position of discontinuities and to reduce their decay with distance from the source. The significant effect of the thermal relaxation is to exhibit the occurrence of some new discontinuities not encountered in the conventional theory. In the absence of the thermal relaxation and or the magnetic field, several limiting results follow as special cases of this analysis