Application of Hybrid Differential Transformation and Finite Difference Method on the Laser Heating Problem

Abstract

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.

The support of the National Science Council of Taiwan under the grant no. NSC 98-2221-E-006-209-MY2, and National Cheng Kung University under the grant no. D98-1500 is gratefully acknowledged.