Application of interval arithmetic in numerical modeling of microscale heat transfer

摘要

Thermal processes in the domain of a thin metal film which are subjected to a laser pulse are considered. The mathematical model based on the dual phase lag equation (DPLE) results from the generalized form of the Fourier law. The governing equation is supplemented by appropriate boundary and initial conditions. The numerical model of metal heating is constructed using the explicit scheme of the finite difference method for hyperbolic equations. The thermophysical parameters of the material (gold) are treated as interval numbers and at the stage of the FDM algorithm construction the rules of interval arithmetic are applied. In this way the numerical solution is obtained in the fuzzy form. Such an approach gives interesting practical information about the course of the process because the values of thermophysical parameters collected in the literature often differ significantly. In the final part of the paper an example for a numerical solution is presented.