Depth and velocity of ablation under a constant heat flux

Explicit closed-form expressions for the velocity, depth of ablation front, and penetration of the thermal profile valid up to a Stefan number of 30 (the vast majority of technological materials have a value below 10) and for all times in the problem of ablation under a constant heat flux are derived. The analysis is based on the blending of the asymptotic, transient, and steady-state, regimes of the above-mentioned quantities. Expressions to estimate the characteristic values representative of intermediate behaviors are also proposed. The prediction of depth and velocity of penetration calculated with the expressions proposed resulted in a maximum absolute error below 8% in comparison to the numerical solution. This model assumes a thick substrate and a criterion for minimum thickness is also proposed. Equations to predict the thickness of the heat-affected zone and of the mushy zone in ablation are also derived. The ultimate aim of this work is to provide simple and accurate expressions to predict the progress of the ablation or to select optimal process parameters in case ablation is used in manufacturing.