Application of the Differential Transformation Method for the Heat Transfer Analysis of an Incompressible Viscous Flow

• Main Authors: Te-Chih Chuang, 莊德志
• Other Authors: Bor-Lih Kuo
• Format: Others
• Language: zh-TW
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/36680531424295591514

碩士 === 正修科技大學 === 機電工程研究所 === 93 === This paper presents the differential transformation method to investigate the heat transfer analysis for the plane and axisymmetric stagnation flow, and combine finite difference method to solve two-dimensional heat transfer problem and Burger’s equation. The study begins by using a group of transformations to reduce the third-order nonlinear boundary-layer equation and the second-order linear thermal boundary-layer equation to a pair of initial value problems. The differential transformation method is then employed to solve the velocity and temperature distribution of the plane and axisymmetric stagnation flow. Another purpose of this paper is to present the use of a hybrid method, which combines differential transformation and finite difference approximation, in the analysis of two-dimensional heat transfer problem and Burgers’ equation with specified initial conditions and boundary conditions. Some numerical results of the thermal boundary-layer problems have been presented in order to demonstrate the accuracy and adaptability of the differential transformation method. It has been demonstrated that the results for the velocity and temperature field obtained by the present method are in good agreement with those provided by other numerical approximation methods. And in order to demonstrate the accuracy and validity of the hybrid differential transformation and finite difference method, it is used to solve several examples of two dimensional heat transfer problem and Burgers’ equation, with each example having different initial conditions and boundary conditions. It is found that the results obtained are in good agreement with the analytical solutions, and that the results are more accurate than those provided by other approximate numerical methods. Hence, the hybrid method is one of the most accurate and effective techniques for this kind of nonlinear problems.