A Fast Inverse Solution for One-Dimensional Heat Conduction and Phase Change Problem

• Main Authors: Ching- hao Lin, 林慶豪
• Other Authors: Wu-Yao Chiou
• Format: Others
• Language: zh-TW
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/37460632215479454529

碩士 === 國立高雄應用科技大學 === 模具工程系 === 99 === ABSTRACT A numerical analysis of one-dimensional fast inverse heat conduction and phase change problem with semi-infinite boundary is presented in this paper. In real engineering utilization, such as welding, casting, electrical discharge machining…and so on, belong to this kind of problem categories. The numerical model is developed by the finite element method and the least-square method. With the measured temperature, the inverse thermal properties, such as thermal conductivity and specific heat, are estimated by this numerical model. As the nonlinear heat transfer problems caused by the phase change of released latent heat, the numerical model is coupled by the averaged specific heat method. For the better acceleration of numerical convergence, the gradients of numerical model are modified by the Heun’s method, Midpoint method, Ralston’s method and classical fourth-order Runge-Kutta method. The results show that for the one-dimensional semi-infinite length of inverse heat conduction problem, the Midpoint method of the most excellent to accelerate numerical convergence, and the classical fourth-order Runge-Kutta method also has the almost same effect, followed by the Ralston’s method, the last is the Heun’s method, in addition, all of the gradient modify method can accelerate the numerical convergence with same errors. As for the phase change in the one-dimensional semi-infinite length of inverse heat conduction problem, based on the subject a considerable degree of complexity, a variety of improved numerical methods accelerates the convergence and stability are not efficiency obviously, it cannot compare their superiority. Keywords：inverse heat conduction problem, inverse phase change heat conduction problem, least-square method, averaged specific heat method, finite element method, Heun’s method, Midpoint method, Ralston’s method and classical fourth-order Runge-Kutta method