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研究生:楊世傳
研究生(外文):Shi-Chuan Yang
論文名稱:應用李群打靶法探討垂直可滲透平板於停滯點附近混合對流之雙重解
論文名稱(外文):Application of the Lie group shooting method to investigate the dual solutions in mixed convection flow near a stagnation-point on a vertical permeable plate
指導教授:賈明益
口試委員:張文政張浮明郭人泰顏增昌
口試日期:2016-06-30
學位類別:博士
校院名稱:國立中興大學
系所名稱:應用數學系所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2016
畢業學年度:104
語文別:中文
論文頁數:60
中文關鍵詞:李群打靶法雙重解混合對流停滯點相似變換
外文關鍵詞:Lie group shooting methoddual solutionsmixed convectionstagnation pointsimilarity transformation
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本文探討混合對流中流經一個具可滲透的垂直平板在停滯點附近,受到熱輻射和流體熱源的作用對雙重解造成的影響。經由相似變換將統御的偏微分方程組轉換成常微分方程組,並以李群打靶法,求解表面摩擦係數(skin friction coefficient, )與局部的紐塞數(local Nusselt number, ),並且得到受到相關參數的作用下的分歧點(bifurcation point),並將相關的結果以表格與圖形的方式呈現,文中針對磁場參數 、浮力或混合對流參數 、普朗特數(the Prandtl number) 、熱輻射參數 與熱源/熱涵參數 對表面摩擦係數(skin friction coefficient, )、局部的紐塞數(local Nusselt number, ),與分歧點(bifurcation point)之影響分別作詳細討論。結果顯示,當熱源/熱涵參數 或熱輻射 值增加,臨界浮力參數 增加。然而,對於臨界浮力參數 減小,即普朗特數 或壁傳質係數 值增加所致。其中當熱源/熱涵參數 減小,使得在上分支解的皮膚摩擦係數 減小而下分支解的值增加。此外,增加的熱源/熱涵參數 導致局部的紐塞數 在上分支解的值減少和下分支解值的增加。為了證明李群打靶法(Lie group shooting method)的準確度,我們將本文特例之結果與相關文獻做一比較,其結果顯示是吻合的。

This article discusses the influences of thermal radiation and fluid heat sources on dual solutions nearby the stagnation point through a permeable vertical flat plate in mixed convection. The governing partial differential equations are converted by similarity transformation into an ordinary differential equation set, where the Lie group shooting method is used to compute the skin friction coefficient and the wall temperature gradient , the bifurcation point under the effects of relevant parameters is obtained, and the results are displayed in the tables and graphs. The effects of the magnetic parameter , the buoyancy or mixed convection parameter , the Prandtl number , the thermal radiation parameter , the heat source or sink number on the skin friction coefficient , the wall temperature gradient and the bifurcation point are discussed in detail. The results indicate that when the value of the heat source or sink number or thermal radiation parameter is increased, the critical buoyancy parameter increases. However, for the critical buoyancy parameter is decreased, that due to the value of Prandtl number or wall mass transfer coefficient is increased. And when the heat source or sink number decreases, the skin friction coefficient in the upper branch solution decreases while in the lower branch solution increases. Moreover, an increase in the heat source or sink number leads to a decrease in the Local Nusselt number in the upper branch solution and an increase in the value of in the lower branch solution. In order to assess the accuracy of the Lie group shooting method, the results of special cases in this study are compared with relevant literature, and the results are found in good agreement.

目錄
謝 誌 i
摘要 ii
Abstract iii
符號表 iv
目錄 vii
表目錄 viii
圖目錄 ix
第一章 前言 1
1.1 研究動機 1
1.2 文獻回顧 2
1.3 研究重點 3
1.4 本文架構 4
第二章 數值方法 5
2.1 保群數值方法 5
2.1.1閔氏空間中增廣動態系統 5
2.1.2 Padé近似求解 7
2.1.3利用Cayley轉換用來構建保群算法 9
2.2 在光錐上兩點之間的李群映射 9
第三章 受熱輻射和熱源的影響於混合對流中流經垂直可滲透平板在停滯點附近的雙重解 13
3.1 簡介 13
3.2 物理模型分析 13
3.3 數值分析 15
3.4 結果與討論 16
第四章 磁性流體流經一個垂直可滲透平板之混合對流中於停滯點附近雙重解受到磁場、熱輻射和熱源效應的影響 18
4.1 簡介 18
4.2 物理模型分析 18
4.3 數值分析 20
4.4結果與討論 21
第五章 結論與建議 23
5.1 結論 23
5.2 建議 24
參考文獻 25



參考文獻

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