Scientific Research of the Institute of Mathematics and Computer Science ’ONE-SHOT’ IDENTIFICATION OF LASER INTENSITY IN A PROCESS OF THIN METAL FILM HEATING Ewa Majchrzak 1, 2 , Bohdan Mochnacki 2 , Jolanta Poteralska 1 1 Silesian University of Technology, Gliwice, Poland 2 Czestochowa University of Technology, Czestochowa, Poland ewa.majchrzak@polsl.pl, moch@imi.pcz.pl Abstract. Thermal interactions between thin metal film and external laser pulse are consi- dered. In particular on a basis of the knowledge of surface temperature distribution the laser intensity is estimated. The problem is described by dual-phase-lag model in which two relaxa- tion parameters (relaxation time and thermalization time) are introduced in order to take into account the microscopic thermal interactions. The laser action is taken into account by addi- tional term (source function) supplemented the basic energy equation. In the paper the mathe- matical model of the thin film heating process is discussed, the inverse problem is formulated and also the example of computations is presented. 1. Formulation of the problem We will consider a thin film of thickness L and an initial temperature distribution T (x, 0) = T 0 . The constant thermal properties, this means the thermal conductivity λ [W/(mK)] and the volumetric specific heat c [J/(m 3 K)] are assumed. A front sur- face x = 0 is irradiated by high-intensity and ultra-short duration laser beam as shown in Figure 1. A heat transfer in direction perpendicular to the layer is taken into ac- count (this assumption is entirely acceptable) and then the temperature distribution is described by the following equation [1, 2] 2 2 2 2 3 2 ( ,) ( ,) ( ,) ( ,) (,) ( ,) q q T Tx t Tx t Tx t c t t x Tx t Qxt Qx t t x t   ∂ ∂ ∂ + =λ + τ   ∂ ∂ ∂   ∂ ∂ λτ + + τ ∂ ∂ ∂ (1) where τ q [s], τ T [s] are the relaxation time and thermalization time, respectively, Q (x, t) [W/m 3 ] is the capacity of internal heat sources. Function Q (x, t) results from laser action and it can be expressed as follows [3] 2 2 ( 2 ) β 1 ( ,) exp β π δ δ p p p t t R x Qx t I t t   - - = - -       (2) Please cite this article as: Ewa Majchrzak, Bohdan Mochnacki, Jolanta Poteralska, 'One-shot' identification of laser intensity in a process of thin metal film heating, Scientific Research of the Institute of Mathematics and Computer Science, 2009, Volume 8, Issue 1, pages 131-136. The website: http://www.amcm.pcz.pl/