Finite Thermal Wave Propagation in a Half-Space Due to Variable Thermal Loading

The thermoelastic interaction for the dual-phase-lag (DP) heat conduction in a thermoelastic half space is studied in the light of two-temperature generalized thermoelasticity theory (2TT). The medium is assumed to be initially quiescent. Using Laplace transform, the fundamental equations are expressed in the form of a vector-matrix differential equation which is then solved by state-space approach. The obtained general solution is then applied to the mechanical loading and various types of thermal loading (the thermal shock and the ramp-type heating). The numerical inversion of the Laplace transforms are carried out by the method of Fourier series expansion technique. The numerical results are computed for copper like material. Significant dissimilarities between two models (the two-temperature Lord-Shulman (2TLS) and the two-temperature Dual-phase-lag model (2TDP)) are shown graphically. Because of the short duration of the second sound effect, the small-time solutions are analyzed and the discontinuities that occur at the wave fronts are also discussed. The effects of two-temperature and ramping parameters are studied.