Phase-change heat transfer in laser transformation hardening by moving Gaussian rectangular heat source

An analytical solution is developed for a quasi-steady phase-change heat transfer problem in which a plane slab is heated by a Gaussian rectangular heat source moving at a constant speed over the upper surface. The physical model is set up to simulate a laser transformation hardening process. In the mathematical formulation, nonhomogeneous terms arise from the Gaussian heat flux and the heat absorption and release at the moving phase-change interfaces. After conversion to dimensionless variables, a source-and-sink method in conjunction with the superposition technique and the method of undetermined parameters is applied to derive the body temperature of the workpiece. An iteration method based on the concept of perturbation methods is employed to obtain the numerical results. The high convergence rate of the numerical solutions reveals the efficacy of the method used. The theoretical predictions are in reasonable agreement with published experimental results. The effects of the heat flux distribution and the Peclet number on the penetration depth and the material cooling rate are discussed in a parametric study.