有限元素法分析問題之優點，是它能夠用很準確的近似元素來處理幾何形狀複雜之物體和它的邊界條件。因此本論文主要是以有限元素之數學方法來推導和計算逐漸減少熱傳體積之散熱突出物數學模擬程式，然後利用Fortran90電腦語言來撰寫數值計算的電腦程式來計算鋁製之散熱突出物的溫度分佈。本論文不僅討論各種形狀在固定底部溫度及外界溫度，於不同邊界對流條件下之穩態溫度分佈情形並且討論各形狀效能。 分析的結果顯示，於熱對流係數較高的情形下溫度呈現內高外低之分佈，其中又以外凸型散熱突出物的變化最為顯著，而圓錐型突出物及內凹型突出物則較不明顯；各形狀頂端處溫度均隨熱對流係數增大而降低。總體之散熱量以外凸型為最大，但單位面積熱傳量則是以內凹型的較佳。 The main objective of this research is applied the method of finite element to analyze heat transfer on the extended surfaces. The term extended surface is commonly used to depict an important special case involving heat transfer by conduction within a solid and heat transfer by convection from the boundaries of the solid. The advantage of finite element method is that it can give a better approximation to the complex geometrical shape by dividing the solution region into elements. In this research, from energy conservation we derived governing equation of heat transfer on the extended surface, then we use the finite element method to derive the element equations for the governing equation of heat transfer from the variation principle. Based on the method of finite element and numerical analysis, we develop a computer program with Fortran 90 to translate the numerical method into computer instructions. This computer program is used to compute and analyze the temperature distributions of extended surfaces at steady state with the specified base temperature and the environment temperature. We discuss the efficiency of the extended surfaces with different parabolic profiles. When the coefficient of convection heat transfer at surrounding is higher, the temperature at the center is much higher than the surface of the extended surface, especially the extended surface of parabolic convex profile. The temperature at the top of extended surface decreases when the coefficient of convection heat transfer is increasing. And the extended surface with concave parabolic profile is good at heat flux. The convex parabolic profile can dissipate more heat than others because of its largest surface.
