Analysis of the heating of solids by laser radiation allowing for the temperature dependence of the absorptivity

An analysis is made of the heating of a half-space by a local surface source of heat with a normal distribution. Allowance is made for the temperature dependence of the absorptivity. It is assumed that the absorptivity is a linear function of the temperature. The solution is found by the method of successive approximations. The results are compared with the solution obtained in the one-dimensional formulation.