Estimation of dual phase lag model parameters using the evolutionary algorithms

Generalization of Fourier law, in particular the introduction of two ‘delay times’ (relaxation time τ_q and thermalization time τ_T) leads to the new form of energy equation called the dual-phase-lag model (DPLM). This equation should be applied in a case of microscale heat transfer modeling. In particular, DPLM constitutes a good approximation of thermal processes which are characterized by extremely short duration (e.g. ultrafast laser pulse), extreme temperature gradients and geometrical features of domain considered (e.g. thin metal film). The aim of considerations presented in this paper is the identification of two above mentioned positive constants τ_q, τ_T. They correspond to the relaxation time, which is the mean time for electrons to change their energy states and the thermalization time, which is the mean time required for electrons and lattice to reach equilibrium. In this paper the DPLM equation is applied for analysis of thermal processes proceeding in a thin metal film subjected to a laser beam. At the stage of computations connected with the identification problem solution the evolutionary algorithms are used. To solve the problem the additional information concerning the transient temperature distribution on a metal film surface is assumed to be known.