Analytical solutions for laser heating and burnthrough of opaque solid slabs

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Abstract
The thermal response of an opaque solid slab exposed to intense laser radiation is described using the heat‐balance integral method. Approximate analytical solutions are obtained for the one‐dimensional temperature distribution T (x,t), for the velocity ?s(t) of the moving vapor‐phase boundary, and for various characteristic quantities such as the front‐surface vaporization time tv, the time tl required for heat to diffuse through the sample to the back surface, and the slab burnthrough time tBT. Account is taken of the influence on tl and tBT of partial vaporization of the target material. The thermophysical properties of the target are assumed to be constant independent of temperature, but the theory accommodates a time‐varying laser intensity and a temperature‐dependent surface absorptivity. Illustrative calculations are presented which compare the results of this theory to those derived from heat‐transfer computer programs. These include a treatment of laser heating of an aluminum slab with temperature‐dependent absorptivity and calculations of the time required to burn through aluminum, stainless‐steel, and carbon‐phenolic targets, covering a wide range of values of target thickness and laser intensity.

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