A numerical solution for non-linear heat flow problem using boundary integral method

In the present paper, the problem of heat flow during laser heat treatment of surfaces is analyzed due to its practical importance in industry. The problem is highly nonlinear due to the dependence of thermal conductivity and the heat capacity on the temperature and the existence of the moving interface. For such a problem no analytical solution is available. In the present paper, a mathematical analysis for the laser beam parameters is introduced through a numerical solution for the problem. This analysis is based on solving an integral equation for each phase using a proposed new numerical algorithm. The results gave a good agreement with a previous finite difference solution.