Heating a slab induced by a time-dependent laser irradiance—An exact solution

The problem of heating a homogeneous slab of material induced by time-dependent laser irradiance is studied. An exact solution for the temperature distribution of the slab is obtained using the Fourier series expansion technique. The temperatures for the front and rear surfaces are also obtained. The case of time-independent laser irradiance is considered. The exact expressions for the thermal penetration depth and the critical time required to initiate melting (i.e., damage) are recovered and compared with the published data for this special case.