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Analysis of thermal processes occurring in heated multilayered metal films using the dual-phase lag model

100%

Majchrzak E. , Kałuża G.

tom Vol. 69, nr 4-5

275--287

A multilayered thin metal film subjected to an ultra-short laser pulse is considered. A mathematical description of the discussed process is based on the system of the dual-phase lag equations supplemented by appropriate boundary and initial conditions. Special attention is devoted to the ideal contact conditions at the interfaces between the layers, which in the case of the dual-phase lag model must be formulated in a different way than in the macroscopic Fourier model. To solve the problem the explicit scheme of the finite difference method is developed. In the final part of the paper the example of computations is shown.

Implicit scheme of the finite difference method for 1D dual-phase lag equation

63%

Majchrzak E. , Mochnacki B.

tom Vol. 16, nr 3

37--46

The 1D dual-phase lag equation (DPLE) is solved using the implicit FDM scheme. The dual phase lag equation is the hyperbolic PDE and contains a second order time derivative and higher order mixed derivative in both time and space. The DPLE results from the generalization of the well known Fourier law in which the delay times are taken into account. So, in the equation discussed, two positive parameters appear. They correspond to the relaxation time τq and the thermalization time τ T. The DPLE finds, among others, the application as the mathematical description of the thermal processes proceeding in the micro-scale. In the paper, the numerical solution of DPLE based on the implicit scheme of the FDM is presented. The authors show that a such an approach in the case of DPLE leads to the unconditionally stable differential scheme.