Once the fluid configuration and the associated velocity field are obtained in a given time step using the VOF method which tracks the free surface, the energy equation is solved as an advection-diffusion equation using the control volume finite difference method. The energy equation rigorously models the phase-change both ways and tracks down the phase front as well. This paper discusses the verification of the phase-change model in cylindrical coordinates with the available results in the literature for a two-region freezing problem and its subsequent incorporation into the laser drilling model making the phase-change submodel robust in many respects. Numerical material removal rates are compared with experimental ones and found to be in good agreement. Contour plots of solid, fluid, pressure and temperature are provided at different times during the drilling process.