A steady-state melt layer model with absorption, conduction, and surface vaporization

An analytic solution is presented for the steady-state moving boundary melt layer problem with volumetric energy absorption. Energy balances across the melt layer and the liquid-solid interface show the relative contributions of absorption, conduction, and phase change energy transfer and allow the melt layer thickness to be determined. Due to the vaporization (ablation) of material from the melt layer surface, the temperature profiles exhibit a maximum value within the melt layer. The temperature profiles and melt layer thickness are shown to be functions of the spectral absorptivity, the thermal diffusivity, and the surface recession rate. These variables occur together in a dimensionless group.