Mathematical modeling of laser induced heating and melting in solids

An analytical method for treating the problem of laser heating and melting is developed in this paper. The analytical method has been applied to aluminum, titanium, copper, silver and fused quartz and the time needed to melt and vaporize and the effects of laser power density on the melt depth for four metals are also obtained. In addition, the depth profile and time evolution of the temperature of aluminum before melting and after melting are given, in which a discontinuity in the temperature gradient is obviously observed due to the latent heat of fusion and the increment in thermal conductivity in solid phase. Additionally, the calculated melt depth evolution of fused quartz induced by 10.6 μm laser irradiation is in good agreement with the experimental results.