  During the laser drilling process the recoil pressure drives melt flow and
affects the heat transfer and material removal rate. To get a more realistic
picture of the melt flow, a series of differential equations are formulated
here that govern the process from pre-heating to melting and evaporation. In
particular, the Navier-Stokes equation governing the melt flow is solved with
the use of the boundary layer theory and integral methods. Heat conduction in
solid is investigated by using the classical method with the corrections that
reflect the change in boundary condition from the constant heat flux to Stefan
condition. The dependence of saturation temperature on the vapor pressure is
taken into account by using the Clausius-Clapeyron equation. Both constantly
rising radial velocity profiles and rising-fall velocity profiles are
considered. The proposed approach is compared with existing ones. In spite of
the assumed varying velocity profiles, the proposed model predicts that the
drilling hole profiles are very close to each other in a specific super alloy
for given laser beam intensity and pulse duration. The numerical results show
that the effect of melt flow on material removal can be ignored in some cases.
The findings obtained from the current work provide a better understanding of
the effects of melt flow and vaporization on the laser drilling profile
evolution, and could improve the solid material removal efficiency.
