Analytical Model of Heating an Isotropic Half-Space by a Moving Laser Source with a Gaussian Distribution

Abstract

This study presents the solution of the transient spatial problem of the impact of a moving source of heat flux induced by laser radiation on the surface of a half-space using the superposition principle and the method of transient functions. The solution is based on the Green’s function method, according to which the influence function of a surface-concentrated heat source is found at the first stage. The influence function has axial symmetry and the problem of finding the influence function is axisymmetric. To find the Green’s function, Laplace and Fourier integral transforms are used. The novelty of the obtained analytical solution is that the heat transfer at the free surface of the half-space is taken into account. The Green’s function that was obtained is used to construct an analytical solution to the moving heat-source problem in the integral form. The kernel of the advising integral operator is the constructed Green’s function. The Gaussian distribution is used to calculate integrals on spatial variables analytically. Gaussian law models the distribution of heat flux in the laser beam. As a result, the corresponding integrals on the spatial variables can be calculated analytically. A convenient formula that allows one to study the non-stationary temperature distribution when the heat source moves along arbitrary trajectories is obtained. A numerical, analytical algorithm has been developed and implemented that allows one to determine temperature distribution both on the surface and on the depth of a half-space. For verification purposes, the results were compared with the solution obtained using FEM.