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研究生:王耀鋐
研究生(外文):Yao-HongWang
論文名稱:COMSOL之凝固與熱傳問題分析
論文名稱(外文):Analysis of Solidification and Heat Transfer Problems with COMSOL
指導教授:趙隆山
指導教授(外文):Long-Sun Chao
學位類別:碩士
校院名稱:國立成功大學
系所名稱:工程科學系碩博士班
學門:工程學門
學類:綜合工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:60
中文關鍵詞:COMSOL Multiphysics熱傳學凝固
外文關鍵詞:COMSOL MultiphysicsHeat TransferSolidification
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  • 被引用被引用:11
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本文利用COMSOL Multiphysics分析非線性的凝固相變化問題、自然對流問題、對流凝固問題以及平板加熱器之均溫性分析問題。比較套裝軟體COMSOL Multiphysics對於非線性問題與不連續界面以及應用於實務設計時,其計算的精確度。本文先以具有解析解的相變化問題如史蒂芬問題、Rathjen問題來作分析比較。再針對溫度與流場耦合的自然對流與凝固對流問題,使用COMSOL進行熱流耦合運算,並分析其計算結果。最後進行實務設計的平板加熱器之均溫性分析,經由前次設計之實驗數據來反推其設計參數,進而對現有的加熱器進行改良。分析後發現,COMSOL在實務設計上求解相當便利,對於耦合問題上面亦具有優異的求解能力,但對於非線性的液固界面追蹤誤差較大。
Abstract
This study is to use the software package COMSOL Multiphysics to analyze the nonlinear solidification or phase-change problems, the natural convection problems, the coupling of convection and solidification problems and the thermal problems in the designed Susceptor. The accuracy of COMSOL for solving nonlinear and discontinuous interface problems and that of the practical design problem are compared and analyzed. First, the Stefan and Rathjen solidification problems with exact solutions are investigated by using COMSOL. Furthermore, COMSOL is employed to study the natural convection problems and the convection and solidification problems in which the temperature and flow fields are coupled with each other. Finally, COMSOL is applied to the heater design of a Susceptor for obtaining the uniform temperature distribution. Inverse calculation is utilized to acquire the design parameters from the experimental data of the previously designed Susceptor. The heater design is modified by the COMSOL analysis. From the analysis results, it can be found that COMSOL works very well for the heater design of the Susceptor and for solving the coupling problems. However, the location prediction of the solid/liquid interface of a solidified problem is not very accurate.


摘要 I
Abstract II
致謝 III
目錄 IV
圖目錄 VII
符號說明 X
第一章 緒論 1
前言 1
  1.1-1有限差分法 1
  1.1-2有限元素法 2
  1.1-3邊界元素法 2
  1.1-4無元素法 3
  1.2研究動機 3
  1.2-1 COMSOL Multiphysics介紹 3
  1.3 熱傳與凝固問題 4
  1.4熱傳與對流耦合問題 4
  1.5文獻回顧 5
  1.5-1有限元素法 5
  1.5-2凝固問題 5
  1.5-3凝固與對流問題 6
第二章 有限元素法理論分析 7
  2.1 前言 7
2.2 有限元素基礎理論 7
2.3 有限元素之數值方法 9
2.3.1迦勒金法(Galerkin method) 10
2.4 COMSOL基本功能簡介 10
第三章 凝固熱傳問題數學模式與數值方法分析 15
  3.1 一維史蒂芬問題 15
    3.3.1等效比熱法(Effective specific heat method) 16
  3.2 二維Rathjen問題 18
  3.3 二維自然對流問題 19
  3.4 二維對流凝固問題 20
  3.5 三維平板加熱器均溫性分析問題 22
第四章 結果與討論 32
  4.1一維史蒂芬問題 32
4.2二維Rathjen問題 33
  4.3二維自然對流問題 33
  4.4二維對流凝固問題 34
  4.5三維平板加熱器均溫性分析問題 35
第五章 結論與未來展望 56
參考文獻 58

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[11] Crank J. Free and Moving Boundary Problem. Oxford Uni. Press, Oxford, 1984.
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[15] Nasch P. M., Steinemann S. G., Density and thermal expansion of molten manganese, iron, nickel, copper, aluminum and tin by means of the gamma-ray attenuation technique, Physics and Chemistry of Liquids 29(1995) 43-58.
[16] Chen Y., Im Y. T., Yoo J., Finite element analysis of solidification of aluminum with natural convection, Journal of Materials Processing Technology 52(1995) 592-609.
[17] 彭勳章,“以修正結尾誤差為基礎之可變時間步伐控制策略建立從澆鑄到凝固鑄造過程之數值模式研究,國立成功大學工程科學系研究所博士論文,2010
[18] Lee J., Mok J. and Hong C. P., Straightforward numerical analysis of casting process in a rectangular mold : from filling to solidification , ISIJ international 39(1999) 1252-1261.
[19] Chalmers B., “Principles of solidification Wiley, New York, 1964.
[20] COMSOL MULTIPHYSICS, Modeling Guide, Version3.5a.


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