Experimental and Mathematical Modeling of Thermal Diffusion in Steel Alloys via Finite Fourier Transform With In‐Situ Analysis of Single and Double Pulses in Laser‐Induced Breakdown Spectroscopy

ABSTRACT This study unveils the power of laser‐induced breakdown spectroscopy (LIBS) in unlocking the full potential of spatially resolved single‐pulse (SP) and double‐pulse (DP) configurations for high‐precision elemental analysis of duplex steel alloy. Using a Q‐switched Nd:YAG laser (1064 nm) in an air medium, examining plasma dynamics by local thermodynamic equilibrium conditions through emission spectral lines. Furthermore, a computational model based on laser‐target interaction, thermodynamics, and heat transport to better characterize energy deposition within a steel alloy. The governing partial differential equation (PDE) of heat diffusion has been given in its dimensionless form with the appropriate initial and boundary conditions and then solved analytically with the finite Fourier cosine transform (FFCT), proving that DP‐LIBS is superior in the limit of detection.