Investigations on the thermal behavior and associated thermal stresses for short pulse laser heating

The fractional type Cattaneo heat conduction equation and the associated thermal stress equation are established for studying the thermal and related stress behavior of the short pulse laser heating. With the Laplace transform method, the analytical solution of the temperature distribution and thermal stress field are derived. Compared to the classical Fourier heat transfer model and the standard C-V one, the results of the present model show the thermal diffusion feature as well as the thermal wave behaviour, which is more realistic. Furthermore, the influences of the fractional order parameter on the thermal and related stress behavior are discussed. The thermal velocity, thermal variation rate and the peak value of the temperature and the thermal stress depend on the fractional order parameter. The fractional type Cattaneo heat model and associated thermal stress exhibit the non-local nature. (paper)