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研究生:季彥成
研究生(外文):Yan-Cheng Ji
論文名稱:微極流體在充滿多孔介質之方形移動蓋口容器中混合對流熱傳研究
論文名稱(外文):Mixed convection of micropolar fluids in a lid-driven enclosure filled with a fluid-saturated porous medium
指導教授:許燦輝
指導教授(外文):Tsan-Hui Hsu
學位類別:碩士
校院名稱:國立高雄應用科技大學
系所名稱:機械與精密工程研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:中文
論文頁數:88
中文關鍵詞:微極流體多孔介質達西數混合對流三次樣線交換方向定置
外文關鍵詞:Mixed convectionMicropolar fluidsPorous mediumDarcy numberSpline Alternating-Direction Implicit Method
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本文係以數值計算方法來模擬求解多孔介質下微極流體在方形移動蓋口容器之混合對流熱傳分析問題,在二維的方形容器充滿一種相同的密集氣孔和滲透性的流動飽和的多孔的介質。 正上方以恆定的速度從左到右移動, 蓋子和底部表面被保持在恆溫,左右為兩堵垂直絕熱的牆,重力方向為垂直朝下。統制方程式之推導由完整的 Navier-Stokes 方程式著手,配合微極流體之定律將牛頓流體擴展至非牛頓流體的應用。數值計算上是以三次樣線交換方向定置法(SADI;Spline Alternating-Direction Implicit Method)在個人電腦上求解。無因次化的轉換後的統馭方程式以流線、旋渦函數、角動量及溫度函數等表示,並得到穩態的熱傳效應。而影響熱場的數值參數主要有 Pr、Gr、達西數和微極流體特有的參數。數值模擬顯示出,一般牛頓流體比微極流體的熱傳效果較佳,多孔性介質俱有提昇熱傳效率的功能,本文會將封閉內穴所模擬結果的流場以及溫度場繪製並討論之。
A number of applications in thermal technology require an analysis of convective flow and heat transfer near the thermal boundary condition. The influences of these effects on heat transfer result are much significant. In addition, the study of convection heat transfer in a porous medium has attracted considerable interest because of its important applications in several engineering process, such as chemical, cooling and drying process, etc.
Mixed convection heat transfer of micropolar fluids in a lid-driven enclosure filled with a fluid-saturated porous medium is numerically investigated in this study. The governing equations for micropolar fluid were first presented by A.C. Eringen, wherein we furthermore expand the applications to non-Newtonian fluids. The numerical computations were obtained using the cubic spline collocation method in a personal computer. The governing equations, including stream function, vorticity, microrotation and energy, were first put in dimensionless form. The governing parameters appearing in present study are Pr, Gr, R, λ, Darcy number, and several micropolar parameters. The numerical results of the flow fields are discussed with plot of isotherms, streamlines and velocity vectors. The results indicate that the Newtonian fluid has more significant convection heat transfer effect than that of micropolar fluids.
中文摘要(橫式)……………………………………………………………. i
英文摘要(橫式)……………………………………………………………. ii
致謝…………………………………………………………………………… iii
目錄…………………………………………………………………………… iv
表目錄………………………………………………………………………… vi
圖目錄…………………………………………………………….................... vii
符號說明………………………………………………………….................... xi
第一章 緒論………………………………………………………………….. 1
1-1 研究目的與動機及其背景……………………………………... 1
1-2 相關文獻回顧…………………………………………………... 2
1-3 研究方法……………………………………………………….. 5
1-4 本文架構……………………………………………………….. 5
第二章 理論分析與數值方法……………………………………………….. 6
2-1 物理模型……………………………………………………….. 6
2-2 基本假設……………………………………………………….. 7
2-3 統御方程式…………………………………………………….. 7
2-4 系統的邊界狀況……………………………………………….. 8
2-5 無因次化分析………………………………………………….. 8
2-6 邊界條件……………………………………………………….. 10
第三章 數值方法…………...……………………………………...………… 12
3-1 數值解析…………….…….......................................................... 12
3-2 數值方法……………………………………………................. 14
3-2.1 線函數表示法及其性質…………………….................. 15
3-2.2 利用三次樣線函數求解…………...……………..……. 18
3-3.3 邊界條件之處理…………………………...…..………. 22
3-4 解題方法與程序……………………………….……………….. 23
第四章 結果與討論………………………………………………………….. 25
4-1 數值方法正確性之測試……………...………………………… 25
4-2 格點測試…………………………..………………………………….. 25
4-3 微極流體參數R之影響……………………………................... 25
4-4 達西數Da與Richardson number Ri之影響………….................. 26
4-5 暫態流場與溫度場之分析……………………………………... 28
4-5.1 不同達西數的暫態影響……………………………….. 28
4-5.2 不同微極流體參數的暫態影響……………………….. 28
4-5.3 不同Richardson number的暫態影響…………………. 29
4-5.4 無因次溫度梯度在不同的參數下之暫態分佈圖…….. 29
4-6 穩態之Nusselt數分析…………………………………………... 29
4-6.1 Nusselt數在不同微極流體參數R下的穩態分佈……… 30
4-6.2 Nusselt數在不同Richardson number數下之穩態分佈 30
第五章 結論與建議………………………………………………………….. 81
5-1 結論……………………………………...……………………… 81
5-2 對未來研究之建議…………………………………………… 82
參考文獻……………………………………………………………………… 83


表 目 錄
表 3-1 係數 , 和 之形式……………………………………………
13


圖 目 錄
圖2-1 物理模型圖……………………………………………………………… 6
圖3-1 三次樣線之基本型式-………………………………………………….. 16
圖3-2 三次樣線函數之二次微分區間圖……………………………………… 17
圖4-1 數值方法比較圖(X=0.5、Re=400,Gr=10 、R=0、 =0)………………
31
圖4-2 格點測試圖(Pr=0.71、R=0、 =0、Re=1000、Gr=100)…………………
31
圖4-3 R=0、1、3、5、10,流線圖(Da=0.001,Ri=1)…………………………… 32
圖4-4 R=0、1、3、5、10,等溫圖(Da=0.001,Ri=1)…………………………… 32
圖4-5 R=0、1、3、5、10,流線圖(Da=0.01,Ri=1)…………………………… 34
圖4-6 R=0、1、3、5、10,等溫圖(Da=0.01,Ri=1)…………………………… 34
圖4-7 R=0、1、3、5、10,流線圖(Da=0.1,Ri=1)…………………………… 36
圖4-8 R=0、1、3、5、10,等溫圖(Da=0.1,Ri=1)…………………………… 36
圖4-9 R=0、1、3、5、10,流線圖(Da=∞,Ri=1)…………………………… 38
圖4-10 R=0、1、3、5、10,等溫圖(Da=∞,Ri=1)…………………………… 38
圖4-11 R=0、1、3、5、10,流線圖(Da=0.001,Ri=10 )……………………
40
圖4-12 R=0、1、3、5、10,等溫圖(Da=0.001,Ri=10 )……………………
40
圖4-13 R=0、1、3、5、10,流線圖(Da=0.01,Ri=10 )……………………
42
圖4-14 R=0、1、3、5、10,等溫圖(Da=0.01,Ri=10 )……………………
42
圖4-15 R=0、1、3、5、10,流線圖(Da=0.1,Ri=10 )……………………
44
圖4-16 R=0、1、3、5、10,等溫圖(Da=0.1,Ri=10 )……………………
44
圖4-17 R=0、1、3、5、10,流線圖(Da=∞,Ri=10 )……………………
46
圖4-18 R=0、1、3、5、10,等溫圖(Da=∞,Ri=10 )……………………
46
圖4-19 R=0、1、3、5、10,流線圖(Da=0.001,Ri=6.25x10 )……………
48
圖4-20 R=0、1、3、5、10,等溫圖(Da=0.001,Ri=6.25x10 )……………
48
圖4-21 R=0、1、3、5、10,流線圖(Da=0.01,Ri=6.25x10 )……………
50
圖4-22 R=0、1、3、5、10,等溫圖(Da=0.01,Ri=6.25x10 )……………
50
圖4-23 R=0、1、3、5、10,流線圖(Da=0.1,Ri=6.25x10 )……………
52
圖4-24 R=0、1、3、5、10,等溫圖(Da=0.1,Ri=6.25x10 )……………
52
圖4-25 R=0、1、3、5、10,流線圖(Da=∞,Ri=6.25x10 )……………
54
圖4-26 R=0、1、3、5、10,等溫圖(Da=∞,Ri=6.25x10 )……………
54
圖4-27 Ri=1、6.25x10 、10 ,流線圖(Da=0.001,R=0)………………
56
圖4-28 Ri=1、6.25x10 、10 ,等溫圖(Da=0.001,R=0)………………
56
圖4-29 Ri=1、6.25x10 、10 ,流線圖(Da=0.001,R=3)………………
57
圖4-30 Ri=1、6.25x10 、10 ,等溫圖(Da=0.001,R=3)………………
57
圖4-31 Ri=1、6.25x10 、10 ,流線圖(Da=0.001,R=10)………………
58
圖4-32 Ri=1、6.25x10 、10 ,等溫圖(Da=0.001,R=10)………………
58
圖4-33 Ri=1、6.25x10 、10 ,流線圖(Da=0.01,R=0)………………
59
圖4-34 Ri=1、6.25x10 、10 ,等溫圖(Da=0.01,R=0)………………
59
圖4-35 Ri=1、6.25x10 、10 ,流線圖(Da=0.01,R=3)………………
60
圖4-36 Ri=1、6.25x10 、10 ,等溫圖(Da=0.01,R=3)………………
60
圖4-37 Ri=1、6.25x10 、10 ,流線圖(Da=0.01,R=10)………………
61
圖4-38 Ri=1、6.25x10 、10 ,等溫圖(Da=0.01,R=10)………………
61
圖4-39 Ri=1、6.25x10 、10 ,流線圖(Da=0.1,R=0)………………
62
圖4-40 Ri=1、6.25x10 、10 ,等溫圖(Da=0.1,R=0)………………
62
圖4-41 Ri=1、6.25x10 、10 ,流線圖(Da=0.1,R=3)………………
63
圖4-42 Ri=1、6.25x10 、10 ,等溫圖(Da=0.1,R=3)………………
63
圖4-43 Ri=1、6.25x10 、10 ,流線圖(Da=0.1,R=10)………………
64
圖4-44 Ri=1、6.25x10 、10 ,等溫圖(Da=0.1,R=10)………………
64
圖4-45 Ri=1、6.25x10 、10 ,流線圖(Da=∞,R=0)………………
65
圖4-46 Ri=1、6.25x10 、10 ,等溫圖(Da=∞,R=0)………………
65
圖4-47 Ri=1、6.25x10 、10 ,流線圖(Da=∞,R=3)………………
66
圖4-48 Ri=1、6.25x10 、10 ,等溫圖(Da=∞,R=3)………………
66
圖4-49 Ri=1、6.25x10 、10 ,流線圖(Da=∞,R=10)………………
67
圖4-50 Ri=1、6.25x10 、10 ,等溫圖(Da=∞,R=10)………………
67
圖4-51 τ=0.15、0.5、1,流線圖(Da=0.001,R=0)…………..……..…… 68
圖4-52 τ=0.15、0.5、1,等溫圖(Da=0.001,R=0)…………..………….. 68
圖4-53 τ=0.15、0.5、1,流線圖(Da=∞,R=0)……………………..…… 69
圖4-54 τ=0.15、0.5、1,等溫圖(Da=∞,R=0)……………..…………….. 69
圖4-55 τ=0.15、0.5、1,流線圖(Ri= ,R=0)…………………..……
70
圖4-56 τ=0.15、0.5、1,等溫圖(Ri= ,R=0)…………..…………..
70
圖4-57 τ=0.15、0.5、1,流線圖(Ri= ,R=10)………………..……
71
圖4-58 τ=0.15、0.5、1,等溫圖(Ri= ,R=10)………..……………..
71
圖4-59 τ=0.15、0.5、1,流線圖( ,Da=∞)…………..……
72
圖4-60 τ=0.15、0.5、1,等溫圖( ,Da=∞)…………..……
72
圖4-61 τ=0.15、0.5、1,流線圖(Ri=1,Da=∞)………………..…… 73
圖4-62 τ=0.15、0.5、1,等溫圖(Ri=1,Da=∞)………..…………….. 73
圖4-63 無因次溫度梯度在不同的達西數Da下之暫態分佈圖……………….. 74
圖4-64 無因次溫度梯度在不同的微極流體參數R下之暫態分佈圖……….. 75
圖4-65 無因次溫度梯度在不同的Richardson number下之暫態分佈圖……... 76
圖4-66 蓋口平均Nusselt數在不同微極流體參數R下之穩態分佈圖……....... 77
圖4-67 蓋口平均Nusselt數在不同的Richardson number下之穩態分佈圖… 78
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