Application of Adomian’s Decomposition method on the Analysis of Nonlinear Heat Transfer in Fins

• Main Authors: Ching-Huang Chiu, 邱青煌
• Other Authors: Cha'o-Kuang Chen
• Format: Others
• Language: zh-TW
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/62441639960624613420

博士 === 國立成功大學 === 機械工程學系 === 90 === Abstract The Adomian’s decomposition is extended to predict the efficiency and optimal length of a longitudinal fin with variable thermal conductivity. The solutions of the nonlinear equations have been made for the special cases where the heat exchange of the fins with the surrounding may be caused by the pure radiation or the simultaneous convection and radiation, and the thermal conductivity of the fins is variable. An analytical solution is derived and formed as an infinite power series. This considerably reduces the numerical complexity. The Temperature distributions are obtained for an annular fin of temperature dependent conductivity under periodical heat transfer condition. The heat transfer process is governed by the convectional fin parameter N, the thermal conductivity parameter ε, the frequency parameter B, and the amplitude parameter s. Many of the practical fin problems have been completely performed. （1）The surface heat dissipation include mechanisms of pure convection, pure radiation, and simultaneous convection and radiation. （2）several situations give rise to heat transfer, such as a constant base temperature, convective base boundary condition and periodic oscillating base temperature.（3）the insulated and the convective-radiative fin tip are individually considered for evaluating the effect of the fin tip conditions. The accuracy of The Adomian’s decomposition method with a varying number of terms in the series investigated. The comparison with the finite-difference method, based on a Newton linearization scheme, shown that the Adomian’s decomposition method is one of the most powerful techniques to solve nonlinear problems.