Frequency-domain analytic method for efficient thermal simulation under curved trajectories laser heating

In the context of Computer Simulation, the problem of heat transfer analysis of thin plate laser heating is relevant for downstream simulations of machining processes. Alternatives to address the problem include (i) numerical methods, which require unaffordable time and storage computing resources even for very small domains, (ii) analytical methods, which are less expensive but are limited to simple geometries, straight trajectories and do not account for material non-linearities or convective cooling. This manuscript presents a parallel efficient analytic method to determine, in a thin plate under convective cooling, the transient temperature field resulting from application of a laser spot following a curved trajectory. Convergence of both FEA (Finite Element Analysis) and the analytic approaches for a small planar plate is presented, estimating a maximum relative error for the analytic approach below 3.5% at the laser spot. Measured computing times evidence superior efficiency of the analytic approach w.r.t. FEA. A study case, with the analytic solution, for a large spatial and time domain (1m×1m and 12s history, respectively) is presented. This case is not tractable with FEA, where domains larger than 0.05m×0.05m and 2s require high amounts of computing time and storage.