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研究生: 王世杰
Wang, Shih-Chieh
論文名稱: 多孔介質層於具有壁吸流效應的水平平板與圓盤上之薄膜凝結熱傳研究
Investigation of Laminar Film Condensation Heat Transfer on Finite Horizontal Plates and Disks with Suction under a Porous Layer
指導教授: 楊玉姿
Yang, Yue-Tzu
陳朝光
Chen, Chao-Kung
學位類別: 博士
Doctor
系所名稱: 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年: 2004
畢業學年度: 92
語文別: 中文
論文頁數: 194
中文關鍵詞: 多孔隙介質達西定律布立曼模式膜狀凝結最小機械能流動原理孔隙率滲透性達西數傑寇數普納德數修正瑞利數
外文關鍵詞: Modified Rayleigh number., Porous medium, Darcy law, Brinkman model, Filmwise condensation, Minimum mechanical energy principle, Porosity, Permeability, Darcy number, Jacob number, Prandtl number
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  •   本文係探討多孔介質層置於低溫有限長水平平板與圓盤上,且有限長水平平板與圓盤表面具壁吸流效應,則當高溫蒸汽於多孔介質層中凝結時,對此穩態薄膜凝結熱傳特性加以探討。其中水平平板則考慮以平滑水平平板與波形水平波型板兩種幾何模型作解析。本文沿用紐塞(Nusselt) 之穩定層流連續膜狀凝結理論之假設與均勻孔隙率之多孔隙介質為本文之基本假設。其中亦忽略慣性與對流效應、液汽兩相間之表面張力、凝結液於多孔介質層之表面張力與毛細現象之作用力等。
      冷凝液於多孔介質層流動特性則本文採用兩種模式:達西定律與布立曼模式為統御方程式中之動量方程式。於水平平板與水平圓盤邊緣處的邊界條件,乃應用開放渠流之最小機械能原理以獲得另一個關鍵性的邊界條件;在數值求解方面,本文使用四階郎奇庫塔法與射擊法求解耦合常微分方程式,以及於第二章中一部分應用牛頓法解多項式方程式;本文在分析薄膜凝結熱傳特性方面,將統御方程式無因次化後,本文歸納出幾個的重要參數:達西數 、無因次波形高度比 、傑寇數 、波形板特徵波數 、普納德數 、修正瑞利數 、壁吸流效應參數 、孔隙率-滲透性比之參數 等;以上各種參數對薄膜凝結熱傳之凝結率、臨界薄膜厚度 、無因次平均薄膜厚度 及平均紐塞數 等之影響,分別於各章中加以討論,並將低溫水平平板或低溫水平圓盤模型在相同的參數條件下,比較其凝結熱傳效率的差異性。
      當固定Da,Ja,Pr,Ra與Lamda之值,板中央液膜厚度隨著壁吸流效應的增加而減少。當Pr值增加或Ra值增加時Nu之值亦隨之增加。對於邊界黏滯效應而言,邊界之摩擦阻力影響凝結熱傳是不容忽視的,尤其是對於較大的Ra值或存在較薄的液膜層時更是需要考慮邊界摩擦阻力效應,因此考慮以布立曼模式分析較能符合實際情形。和無多孔介質層者之結果比較,顯示水平板上方增加多孔介質層將有助於凝結熱傳之進行。對於具波形表面效應之熱對流特性方面,當有相同的奇數n值時,則平均紐塞數Nu隨著波形高度與特徵長度比值(即F值)增加而增高;當有相同的偶數n值時,則平均紐塞數Nu隨著F值增加而減少。當有相同的Nu值時,則平均紐塞數Nu隨著F值增加而增加,而且以較大的Nu值時n隨著F值增加的比率較大。

      Reported herein presents the problems of steady filmwise condensation outside a finite-size horizontal plate and disk which cover a homogeneous porous medium layer filled with a dry saturated vapor have been investigated by boundary layer approximations. The analysis is conducted to study film condensation in a porous layer with the effects of applied suction action onto a finite horizontal plate and disk. The classical condensation model of Nusselt analysis combined with the set of Darcy and Brinkman equations is utilized to treat the behavior of condensate in a porous layer. It is assumed that the inertia and energy convection terms, surface tension force of two-phase zone, the form drag of a porous medium, and capillary suction of two-phase zone are could plausibly neglected.
      Darcy law and Brinkman model are applied to be physical model in this analysis. An essential part of the present analysis is that the boundary condition at the plate edge is established by the application of Minimum mechanical energy principle from the open channel flow theory. To obtain the critical condensate layer thickness, the mass and energy equations must satisfy the conservation balance at the interface. Numerical solutions are obtained by using the fourth-order Runge-Kutta scheme method and shooting method. A theoretical analysis is performed to predict the effects of a condensation with suction action. To sum up the physical phenomena, results of the complete model were discussed in dimensionless form. The dimensionless average Nusselt number and the dimensionless liquid film thickness on the surface are investigated as a function of Darcy number , wave amplitude ratio , Jakob number , wave number , Prandtl number , modified Rayleigh number , permeance parameter and suction parameter . It is also to consider the Brinkman model and Darcy model equations of motion for the condensate flow in a porous medium layer and examine the significance of each term.
      At fixed values of Da,Ja,Pr,Ra and Lamda, the central film thickness decreases as the value of Sw increases. An increase in value of Ra or Pr increases the average Nusselt number Nu . The viscous boundary effects of the BD model largely reduce the heat transfer rate as the Ra increases. As for the influence of wavy surface effect on the mean heat transfer coefficient, the results shows that if the total waviness number is odd, the value of Nu will be proportional to the waviness amplitude. If the total waviness number is even, the value of Nu strictly decreases as the waviness amplitude increases.

    中文摘要…………………………………………………………………...Ⅰ ABSTRACT……………………………………………………………….. Ⅲ 誌 謝………………………………………………………………….……. Ⅴ 目 錄………………………………………………………………………...Ⅶ 表目錄………………………………………………………………..….ⅩⅡ 圖目錄……………………………………………..……………………ⅩⅢ 符號說明………………………………………………………………...ⅩⅩ 第一章 緒 論 § 1–1 研究背景與目的前言………..…………………………...…..…1 § 1–2 文獻回顧……..………………………………………....……….8 § 1–2–1 膜狀凝結熱傳研究之文獻回顧………………...…………8 § 1–2–1 膜狀凝結熱傳研究之文獻回顧……...…………………..17 § 1–3 論文結構…………………....………………………...…..……19 第二章 應用達西定律之多孔介質層於水平平板上的層流薄膜凝結熱傳研究 § 2–1 簡 介…………..……………………………...…………..……23 § 2–2 理 論 分 析……….……………………………………………24 § 2–2–1統御方程式………………………………….………24 § 2–2–2統御方程式無因次化之推導……………….………28 § 2–2–3 不考慮壁吸流效應之解析……...…………………..35 § 2–2–4 考慮壁吸流效應之解析…….…..…………………..36 § 2–3 結果與討論….……………..……..….…………………………38 § 2–3–1 數值方法….………..……....…………………………38 § 2–3–2不考慮壁吸流效應…………....………………………39 § 2–3–3考慮壁吸流效應……………....………………………44 第三章 應用布立曼模式之多孔介質層 於水平平板上的層流薄膜凝結熱傳研究 § 3–1 簡 介…………..……………………………...…………..……61 § 3–2 理 論 分 析……….…………………………………….………62 § 3–2–1統制方程式……………………………………………62 § 3–2–2統御方程式無因次化之推導………………….………64 § 3–3 結果與討論….……………..…….….….………………………70 § 3–3–1 數值方法….………..……....…………………………70 § 3–3–2數值結果與討論……………...………………………71 第四章 應用達西模式之多孔介質層於水平圓盤上的層流薄膜凝結熱傳研究 § 4–1 簡 介…………..……………………………...…………..……85 § 4–2 理 論 分 析……….…………………………………….………86 § 4–2–1統制方程式……………………………………………86 § 4–2–2統御方程式無因次化之推導………………….………88 § 4–3 結果與討論….……………..……..…….………………………94 § 4–3–1 數值方法….………..……....…………………………94 § 4–3–2數值結果與討論……………...………………………95 第五章 應用布立曼模式分析多孔介質層於水平圓盤上的層流薄膜凝結熱傳研究 § 5–1 簡 介…………..………………………..…...…………..……115 § 5–2 理 論 分 析……….…...………………………………….……116 § 5–2–1統制方程式………………………………………..…116 § 5–2–2統御方程式無因次化之推導…….………….………117 § 5–3 結果與討論….……………..…...…..….….…………………..123 § 5–3–1 數值方法….………....……....………………………123 § 5–3–2數值結果與討論…..…………...……………………124 第六章 多孔介質層於水平波形板上的薄膜凝結熱傳研究 § 6–1 簡 介…………..………………………..…...…………..……134 § 6–2 理 論 分 析……….…...………………………………….……135 § 6–2–1統制方程式…..…….…………………………..……135 § 6–2–2統御方程式無因次化之推導……………….………138 § 6–3 結果與討論….…………….……..….….……………………..145 § 6–3–1 數值方法….…….…....……....………………………146 § 6–3–2數值結果與討論…...…………...……………………147 第七章 總結 §7–1 綜合結論………...…………………………………………….158 § 7–1–1 第二章之綜合結論………………………………….159 § 7–1–2 第三章之綜合結論………………………………….160 § 7–1–3 第四章之綜合結論………………………………….161 § 7–1–4 第五章之綜合結論………………………………….163 § 7–1–5 第六章之綜合結論………………………………….164 §7–2 建議及展望...….………………………………………………166 附 錄 附錄一………………………………………….…………………………168 附錄二…………………………………………………………………….169 附錄三…………………………………………………………………….171 附錄四…………………………………………………………………….173 附錄五…………………………………………………………………….175 附錄六…………………………………………………………………….176 附錄七…………………………………………………………………….178 附錄八…………………………………………………………………….179 參考文獻……………………..………………….………………………180 自述……….……………………………………………………………194

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