在本研究中，吾人使用熱晶格波茲曼法來模擬立方腔體中含有一可改變位置之加熱圓柱其產生之自然對流的情形，所研究之雷利數範圍為10^4 ~ 10^6 ，普朗特數則固定為0.7，圓柱的位置沿著正立方腔體的中心線上下移動，藉此研究並分析其從暫態到穩態的完整熱傳過程。我們發現正立方腔體之邊界對熱傳還有流體流動的現象造成之影響除了跟圓柱所放置的位置有關，也與雷利數的大小有密切的關係，詳細的分析包含三維流線、溫度場分析和紐森數的分布。最後，我們試著去分析三維的模擬結果跟二維的模擬結果的差異，並探討其可能的原因，最終我們可以利用此研究的結果，來決定高雷利數的情況下是否應該使用三維的模擬。

In the present study, the thermal lattice Boltzmann scheme is used for simulating the natural convection in cubical enclosure with different inner cylinder position in different Rayleigh numbers of 10^4 ~ 10^6 at Prandtl number of 0.7. The location of the inner cylinder is changed vertically along the centerline of the enclosure. The transient state and steady state results are investigated and analyzed. The effects of the boundary wall on heat transfer and fluid flow in the enclosure depend on both the position of the cylinder and the Rayleigh number. Detailed discussion for the streamline, isotherms, and Nusselt number distribution is presented in this paper.

[論文審定書 i]
[誌謝 ii]
[中文摘要 iii]
[ABSTRACT iv]
[CONTENTS v]
[LIST OF FIGURES vii]
[LIST OF TABLES xi]
[NOMENCLATURE xii]

[CHAPTER 1 INTRODUCTION 1]
[CHAPTER 2 THERMAL LATTICE BOLTZMANN METHODS 5]
[2.1 The Boltzmann equation 5]
[2.2 The BGK approximation 6]
[2.3 Equilibrium Distribution Function 10]
[2.4 Lattice Arrangements 11]
[2.5 The Thermal Lattice Boltzmann Method 12]
[2.6 Buoyancy force 14]
[2.7 Implementation of TLBM algorithm 15]
[CHAPTER 3 BOUNDARY CONDITIONS 16]
[3.1 Wall Boundary Conditions 16]
[3.2 Open Inlet Zou-He Pressure and Velocity boundary condition 18]
[3.3 Thermal Boundary Conditions 23]
[CHAPTER 4 VALIDATION 25]
[4.1 Natural convection in an enclosed cavity 25]
[CHAPTER 5 SIMULATIONS OF THE FREE CONVECTION ABOVE A HEATED HORIZONTAL CYLINDER 30]
[5.1 Numerical simulation of transient laminar natural convection in a cubical enclosure with inner cylinder 30]
[5.2 The wall effect on natural convection 62]
[5.3 Numerical simulation of natural convection in a cubical enclosure with inner cylinder at different positions 64]
[CHAPTER 6 CONCLUSIONS 85]
[REFERNCE 86]

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