Analytical Solution of Cattaneo and Thermal Stress Equations

Abstract

Laser short pulse heating of metallic surfaces initiates non-equilibrium energy transport in the irradiated region. In this case, thermal separation of electron and lattice sub-systems takes place. The thermal communication of these sub-systems occurs through the collisional process and the electrons transfer some of their excess energy during this process. Although electron temperature attains significantly high values due to the energy gain from the irradiated field through absorption, lattice site temperature remains low. Since the heated region is limited within a small volume, temperature gradients remain high across the irradiated region despite the attainment of low temperature field. Consequently, high temperature gradients cause the development of high thermal stress field in the small region. This limits the practical applications of the laser treatment process at microscopic scales. In this chapter, heat transfer at micro-scale is formulated and temperature field is presented analytically. The closed for solutions for the temperature and stress fields are obtained for various heating situations.