HEAT WAVE SIMULATION IN MICRO-BARS WITH THE FINITE ELEMENT METHOD

In this study we perform a finite element solution of the 1D ‘telegraph’ equation, which describes the formation of heat waves in a solid bar. Such waves are not predicted by the classical parabolic heat equation which implies that heat is dissipated with infinite speed. In order to overcome this paradox, several investigators have proposed a modified Fourier law, known as the Maxwell-Vernotte-Cattaneo law. The use of this modified law returns a hyperbolic equation. In our analysis we have considered a rectangular bar of small thickness with adiabatic ends. A laser pulse of small duration acts on a certain point of the bar, producing a localized heat flux q0. This thermal loading generates thermal waves, traveling through the bar with finite speed. Thermal losses due to convection from the free surface are taken into account, so actually the bar acts like a thermal fin eqn. (1).