An Application of the Hybrid Differential Transform Method for Studying a Thin Film Exposed to Ultrashort Pulsed Lasers

• Main Authors: Kuei-Lin Pai, 白桂霖
• Other Authors: 駱正穎
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/qbdst8

碩士 === 國立虎尾科技大學 === 航空與電子科技研究所 === 97 === Ultrashort-pulsed lasers have been extensively applied in engineering problems, especially in the manufacture of micro size parts or systems. Studying the thermal deformation induced by ultrashort-pulsed lasers is important for preventing thermal damage. This article presents an application of the hybrid differential transform and finite difference method for studying thermal deformation in a thin film exposed to ultrashort pulsed lasers. The mathematic model of the problem is based on two-step hyperbolic transfer equations. Firstly, the differential transform technique is used to transform the governing equations as well as boundary conditions from the time domains into the spectrum domain. Secondly, the resulting transformed equations are discretized by the finite difference method. Thirdly, the spectrum functions are determined through a recursive procedure. Finally, all system variables are obtained by using the numerical inversion of differential transform. The merit of the present method lies on the transformation of differential equation into the recursive forms which are much easier to solve systematically. The present study obtains the full field solutions of electronic temperature, lattice temperature, heat flux stresses and strains of a thin film in the manufacturing process. It accounts for the coupling effects between lattice temperature and strain rate, as well as for the hot-electron-blast effect in momentum transfer .The numerical oscillations which often arise in the vicinity of sharp discontinuities can be successfully suppressed with an appropriate grid number used in the model. The thesis demonstrates the feasible application of the hybrid differential transform technique in solving the two-step hyperbolic heat transfer problems.