A brief outline of several approaches taken to model the thermal behavior of laser materials interaction is presented. Starting with simple one-dimensional analytic solutions for heat conduction in opaque solids; it then transcends through numerical simulation in two dimensions by finite difference techniques; and finally discusses more complex finite element analysis. This rationale is based upon findings that gentler forms of heat treatment by an extended laser source may be modeled quite accurately by one-dimensional analytic expressions in closed form, while harsher situations such as those encountered in laser welding by a concentrated source generally require the use of numerical simulation methods. Illustrative examples are used to highlight thermal modeling approaches, graduating from simpler to more complex laser material interaction situations.
"Thermal Modeling Of Laser Materials Interaction", Proc. SPIE 0668, Laser Processing: Fundamentals, Applications, and Systems Engineering, (12 November 1986); doi: 10.1117/12.938891; https://doi.org/10.1117/12.938891