Analytical Solution for a Transient Three-Dimensional Temperature Distribution in Laser Assisted Machining Processes

Laser assisted machining is a recent technique for machining brittle ceramic materials by first softening them by heating the material with a laser beam, without reaching the melting point and, in this way, minimizing the damage of the workpiece and tool. The use of a laser source is a common procedure in numerous electronic and optical material processes. This research presents a new analytical solution to determine transient temperature distributions in a finite solid when it is heated by a moving heat source. The analytical solution is obtained by solving the transient three-dimensional heat conduction equation in a finite domain by the method of separation of variables. Previous studies focus on analytical solutions for semi-infinite domains. In this study, for a moving heat source, the temperature field is obtained in a finite domain. The purpose of this study is to obtain an analytical solution to predict transient temperature distribution in a finite solid due to a moving heat source.