Application of hybrid differential transformation and finite difference method on the laser heating problem

A hybrid numerical technique which combines the differential transformation and finite difference approximation is employed to predict the laser heating problem. The energy transfer induced by laser irradiation in the solid is described by Fourier's law of conduction with an energy source modeled by Beer's law. The influences of convective boundary and dimensionless energy absorption at the surface are examined. It is found that at low Biot number, the peak temperature occurs at the surface. As the biot number increases, the location of the peak temperature moves inwards. In addition, the differential transformation results in a concise procedure than other integral transform methods.