摘 要
本文以元素疊代（Element-by-Element）為基礎的投射有限元素流體解析法（projection finite element fluid analysis）為主，對於均勻紊流流過二維混合對流通道之無障礙物，具障礙物及三維強制對流通道之無障礙物，具障礙物的暫態流動及其傳熱現象進行分析。以EBE-PCG投射有限元素法取代以往有限元素法解無因次之Navier-Stokes Equation及能量方程式，乃是為了能減少矩陣的儲存量，及減少電腦上的計算時間。並且運用Large Eddy Simulation的紊流模式來模擬紊流流場，以前置處理之共軛梯度法（preconditioned conjugate gradient method）加以疊代而解出其速度場，壓力場和溫度場。
本文提供了一套EBE-PCG數值模擬二維和三維紊流流場的計算方法及結果，經由文獻的結果驗証，確認本計算方法的準確及可靠性。這些結果可以瞭解二維及三維通道內混合對流的紊流流場現象及熱傳效應。

ABSTRACT
This paper used Element-by-Element projection finite element fluid analysis turbulent flow and heat transfer for uniform turbulent flow in a 2D mixed convection channel and 3D force convection channel with heated block. Using Element-by-Element finite element preconditioned conjugate gradient method replaces the traditional finite element method for the non-dimensional Navier-Stokes Equation and Energy Equation. It can reduce matrix storage and computational time. Using large eddy simulation method turbulent model simulates turbulent flow with preconditioned conjugate gradient method and iterates to obtain velocity field, pressure field, and temperature field.
This paper offered a set of EBE-PCG numerical simulation method to simulate 2D and 3D turbulent flow. It can confirm that this method is precise and reliable by references. These conclusions can help us understand the phenomenon of 2D and 3D mixing convection of turbulent flow in the channel and heat transfer.

目 錄
摘要 I
目錄 II
圖目錄 Ⅳ
符號說明 ⅩII
第一章、 前言
1-1 研究動機及目的 1
1-2 文獻回顧 2
第二章、 EBE-PCG
2-1 利用Element-By-Element觀念 5
2-2 利用Preconditioned共軛梯度法觀念 6
第三章、 數學模式及數值演算法
3-1 介紹 9
3-2 數學方程式 9
3-3 基本統御方程式之無因次化 13
3-4 紊流模式 19
3-5 利用FEM方法求解 21
3-5 利用投射觀念(Projection method) 25
3-6 對於通道出口的處理 27
第四章、 結果與討論
4-1 本文之數值解與參考文獻之比較 31
4-2 風道內具一方形障礙物之模式 32
4-2-1 在混合對流下，不同Gr的值對流場的影響 33
(Re=1200)
4-2-2 在混合對流下，不同Gr的值對流場的影響 35
(Re=2500，3800)
4-2-3 在混合對流下，不同 的值對流場之影響 37
4-3 風道內無障礙物之模式 37
4-4 3D風道內無障礙物之模式 39
4-5 3D風道內具有一方形障礙物之模式 41

第五章、 總結 43
參考文獻 101

參考文獻
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