Laser Melting of a Plastic

A high-intensity laser beam that deposits energy over a millisecond time scale into a mostly transparent plastic is an ideal candidate for analysis using the equations of thermal explosions.  
In this case, the equation to use is for the line-source of energy:
 

The energy deposition per unit length can be estimated from the power attenuation of the laser beam between entrance and exit from the plastic.  With known melting temperature and material properties of the plastic, it is possible to determine the location of a melting front as a function of time by simply re-arranging equation [1]:

 (This analysis assumes that the latent heat of melting of the plastic is negligible, that melting does not significantly alter the thermal and optical properties, and that the plastic melts and re-solidfies at a single fixed temperature.)
This figure shows the temperature distribution in the plastic at several different times.

This figure shows the position of the melting/solidification front as a function of time.