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Analytical solution of the dual phase lag equation describing the laser heating of thin metal film

Ciesielski M.

Journal of Applied Mathematics and Computational Mechanics

2017

Vol. 16, nr 1

33--40

Heat transfer processes occurring in the micro-domains can be described using the dual-phase lag equation (DPLE). This equation can be applied as a model of heating of the thin metal film subjected to the femtosecond laser pulse. In the paper, the 1D dual phase lag equation containing the additional internal heat source resulting from the laser pulse irradiation and supplemented by the appropriate boundary and initial conditions is considered. Appearing in this equation two lag times τq the phase lag of the heat flux) and τT (the phase lag of the temperature gradient) are taken into account. An analytical solution of this equation under the assumption that τT > τq is presented. The separation of the variables technique and the Green’s function method are used in order to find this solution. In the final part of the paper, the example of computations is presented.