Sensitivity analysis of transient temperature field in micro-domains with respect to the dual phase lag model parameters

The classical Fourier law constitutes quite good approximation of real heat conduction proceeding in the macro domain. The differences between the macroscopic heat conduction models and the models describing the microscale heat transfer appear, first of all, because of extremely short duration, extreme temperature gradients and the very small geometrical dimensions of domain considered. For example, the heat transfer through thin metal film subjected to an ultrafast laser pulse can be mentioned. From the mathematical point of view, nowadays there exist different models describing the mechanism of process discussed. In this paper the dual phase lag model (DPLM) is considered. This model results, among others, from the microscopic two-step parabolic model. This model involves two energy equations determining the thermal processes in the electron gas and the metal lattice. It is also possible to transform this model to the DPL equation containing a second order time derivative and higher order mixed derivative in both time and space. Two positive constants t q, tT appear in this equation. 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. The paper presented concerns the problems of sensitivity analysis application in order to estimate the changes of transient temperature field resulting from the perturbations of parameters appearing in the DPL equation (volumetric specific heat, thermal conductivity, relaxation and thermalization times). In particular, the axially symmetrical object subjected to the laser pulse is considered. To formulate the sensitivity model the direct approach is used. Numerical computations are realized using the explicit FDM scheme. In the final part of the paper the examples of computations are shown.