Approximate Solution to the Thermal Conductivity Problem and Estimation of the Maximum Excess Temperature during Absorption of a Nanosecond Laser Pulse in a Conductive Half-Space

Abstract

The article addresses the issue of heating a homogeneous isotropic conductive half-space using a single optical pulse with a temporal and spatial profile in the form of a Gaussian function. An analytical solution to the heat conduction problem for the half-space is obtained in quadratures using the Fourier and Fourier-Bessel transforms in the linear approximation of the independence of the thermophysical parameters of the medium from temperature and an exponential law of radiation absorption with depth. An approximate solution to the heat conduction equation for the half-space heating problem is given by representing the expressions for the intensity distribution and temperature field as a product of functions. This solution is applicable for wide beams and if radial heat propagation is neglected during the initial phase of radiation absorption. Formulas for the maximum excess temperature in the half-space were derived for rectangular and Gaussian temporal optical pulses.