臺灣博碩士論文加值系統

本文探討變孔隙率及熱逸散等非達西效應在部份充填多孔性介質之熱特性
及在水平板多孔性介質中熱對流邊界層流場渦漩不穩定性問題.在部份充
填多孔性介質中,多孔性介質區域的動量方程式係常微分方程式,使用朗
吉-庫塔 (Runge-Kutta) 法求解,而流體區域的動量方程式有閉合解
(closed form solution) 存在. 至於能量方程式係特徵值問題,使用朗
吉-庫塔積分法求解. 變孔隙率或熱逸散效應在水平板混合對流場的基本
流場有相似解 (similarity solution) 存在,本文採用朗吉-庫塔積分法
求解. 至於考慮變孔隙率及熱逸散之混合效應時,在水平板自然對流的基
本流場有非相似解(non-similarity solution) 存在,本文利用凱拉盒子
(Keller Box)數值方法求解.關於渦漩不穩定性分析,則採用線性穩定理
論 (linear stability theory) 和局部相似假設 (local similarity
assumption) 推導擾動流場統御方程式.由數值分析結果得知 : 在水平板
多孔性介質中,熱逸散效應愈強,則流流場熱傳量愈大及使得擾動流場愈趨
於穩定;當考慮變孔隙率效應時,因壁面渠道效應使得流場熱傳量增加,然
而擾動流場則越趨於不穩定. 當流場越趨於下游處 (down stream) 熱逸
散效應對流場不穩定性所造成的影響較變孔隙率大.

The problems of non Darcy effects (variable porosity and
thermal dispersion) on forced convection in a duct partially
filled with a porous medium and vortex mode of instability for
flat plate boundary layer flow saturated with porous medium
have been investigated. For the case of a duct partially filled
with a porous medium, the momentum equation in the fluid region
exists closed form solution, while the momentum equation in the
porous region has to be solved numerically by Runge-Kutta
method. The temperature distribution in both fluid and porous
regions are the eigenvalue problem, solved by the Runge-Kutta
method. For the case of variable porosity or thermal dispersion
effect, it is shown that similarity solutions exist for the
mixed convection over a horizontal plate saturated with porous
medium. For the combined effects of variable porosity and
thermal dispersion over a horizontal natural convection flow do
not permit similarity solutions. An efficient implicit Keller-
Box finite difference method is employed to solve the non-
similarity governing equations of the base flow. In stability
analysis, the linear stability theory and local approximation
are applied in deriving the disturbance equations. The
numerical results show that : The thermal dispersion effect
enhances the heat transfer rate and stabilizes the flow; while
variable porosity effect tends to enhance the heat transfer
rate and destabilize the flow. The variable porosity effect is
found to be of minor importance on the flow at downstream as
compared with the thermal dispersion effect.

目錄
中文摘要
英文摘要
誌謝
表目錄
圖目錄
符號說明
第一章 緒論
1.1 研究目的及背景
1.2 文獻回顧
1.3 本文結構及研究方法
第二章 多孔性介質之概識
2.1 達西定律
2.2 非達西定律
第三章 數學分析
3.1 部份充填多孔性介質
3.2 變孔隙率應
3.3 熱逸散效應
3.4 考慮變孔隙率及熱逸散效應
第四章 數值方法
4.1 基本流場
4.2 擾動流場
第五章 結果與討論
5.1 部份充填多孔性介質
5.2 變孔隙率效應
5.3 熱逸散效應
5.4 考慮變孔隙率及熱逸散效應
第六章 結論及未來研究重點
6.1 結論
6.2 未來研究重點
附錄
參考文獻
自述