Analysis of Laser Pulse Heating Model Using the Finite Element Analysis

Abstract

The Model equation for the laser heating process is a two dimensional partial differential equation in cylindrical coordinate that is time dependent and involves a source term. This work presents a sequential method in obtaining solution to the laser heat equation using a unique method of solution known as Finite Element Method; a numerical approach as against the analytical method. The approach was used in analyzing the temperature of the irradiated material within the domain of the material. This was done by multiplying the model differential equation by a weighted function and carrying out integration over the domain of the problem to obtain the weak form of the equation. Triangular and rectangular Langrage interpolation functions were used for the spatial discretization and Alpha family of approximation was used for the time approximation. The domain of the problem was discretized manually using eight triangular and 4 rectangular finite element mesh. To obtain more accurate solutions, a programme written with MATLAB software was used to further discretize the domain into smaller finite elements (4000 triangular element mesh and 2000 rectangular element mesh). The results obtained was plotted and compared with literature.