Modeling of Temperature-Dependent Absorptivity of Laser-Treated Surface

Abstract

In this work, we have considered the effect of the various properties on the thermal field, the absorptivity plays a special role, because it controls directly the heat input to the sample, while being itself a function of surface temperature. In order to take this dependence into account, the one-dimensional heat conduction equation was solved for a semi-infinite geometry using variable absorptivity and assuming constant thermal conductivity and thermal diffusivity. It is shown that the surface temperature satisfies an Abel integral equation with an approximate analytical solution that gives a temperature rise at the surface linear with t. Comparison is made between analytical approximate expressions, numerical solutions, previous models and experimental results.