Heating a slab of finite thickness with a pulsed laser in view of the theory of linear systems

Abstract

The problem of heating a slab of finite thickness induced by surface absorption of a pulsed laser is solved using the two-dimensional Laplace integral transform technique. In the solution procedure the cases of constant and temperature-dependent absorption coefficient of the front surface considering different cooling conditions at the front and rear surfaces are taken into account. Mathematical expressions for the temperature distribution within the slab, and the temperature of its front and rear surfaces as a function of the time are obtained for all cases considered. The time required to initiate melting is found only for the case of temperature-dependent surface absorption and negligible cooling at both surfaces. The linear system theoretical treatment showed that the slab behaves like a linear system only for the case of temperature-independent absorption coefficient, where it is found to be invariant and its transfer function is defined. To illustrate the physical validity of the results obtained, computations are carried out on Al and Au slabs during and after irradiation with a measured time-dependent laser pulse profile.