隨著半導體製程及元件科技的進步，積體電路內晶體管數量持續增加，其單位面積產生的熱量也快速上升，傳統的散熱技術已無法滿足部分高階晶片散熱需求。本研究開發一種新型的脈動式入口具多孔介質肋條微通道熱沉(Heat sink)，並藉由晶格波茲曼方法(Lattice-Boltzmann Method, 簡稱LBM)和機器學習(Machine learning, 簡稱ML)優化其熱性能。其中ML使用徑向基類神經網絡(Radial basis neural network, 簡稱RBNN)、最小二乘支持向量機(Least square support vector machine, 簡稱LSSVM)及隨機森林(Random forest, 簡稱RF) 等模型進行測試，並以雷諾數(Reynolds number, Re=100-300)、斯特勞哈爾數(Strouhal number, St=0.4-3.6)、多孔介質無因次化肋條高度(〖Hr〗^*=0-1)、孔隙度(Porosity, ε=0.4-0.8)作為模型輸入參數，訓練後之輸出分別為平均努賽數((Nu) ̅/〖Nu〗_0)與平均摩擦係數(f ̅/f_0)。相比於LBM模擬結果，LSSVM模型在預測(Nu) ̅/〖Nu〗_0與f ̅/f_0的準確度最佳，其最大相對誤差(Max relative error, 簡稱MRE)分別為3.5%與3.3%，準確度較前人經驗公式分別提升20.2%和39.7%。為找尋具有最佳熱性能因子(Thermal performance factor, 簡稱TPF)的參數配置，引入實驗設計法 (Design of experiment, 簡稱DoE)並結合粒子群優化演算法(Particle swarm optimization, 簡稱PSO)進行優化，結果發現在設定的參數範圍內，Re=300、St=2.01、〖Hr〗^*=0.45、ε=0.4時，獲得最佳TPF=2.64，相比前人在最佳設計，在類似(Nu) ̅⁄〖Nu〗_0 =13.31下，f ̅/f_0降低23.9%，TPF則提升6.5%。

With the advancement of semiconductor fabrication and device technology, the number of transistors in an integrated circuits continue to increase. This causes a surge of heat generation per unit area so that the conventional cooling techniques can no longer meet the heat load requirement of some advanced chips.Thus, a novel microchannel channel heat sink with pulsatile flow inlet and porous ribs is proposed. The lattice-boltzmann method (LBM) and machine learning (ML) are adopted to optimize its thermal performance. The ML methods examined include radial basis neural network (RBNN), least square support vector machine (LSSVM), and random forest (RF). The input parameters selected for training these models include Reynolds number (Re=100~300), Strouhal number (St=0.4~3.6), porous media rib height (〖Hr〗^*=0~1), and porosity (ε=0.4~0.8), while the output parameters are the average Nusselt number ((Nu) ̅⁄〖Nu〗_0 ) and average friction coefficient (f ̅⁄f_0 ). The training results reveal that the LSSVM model achieves the best accuracy with a max relative error (MRE) of 3.5% and 3.3% for the predicted (Nu) ̅⁄〖Nu〗_0 and f ̅⁄f_0 respectively, compared to the LBM calculations, which are 20.2% and 39.7% more accurate than conventional empirical correlations. To determine the optimal parameter design for the best thermal performance factor (TPF), the design of experiment (DoE) methodology is employed with the particle swarm optimization (PSO) algorithm to optimize the model. It is found that the optimal TPF is 2.64 at Re=300, St=2.01,〖Hr〗^*=0.45, and ε=0.4 for the examined ranges of parameters. Compared to the previous best design, the present microchannel shows 24% reduction in f ̅⁄f_0 and a 6.5% improvement in TPF for similar value of (Nu) ̅⁄〖Nu〗_0 =13.31.

目錄
摘要 II
Abstract IV
誌謝 VI
目錄 VI
表目錄 IX
圖目錄 X
符號表 XII
1. 前言 1
1.1. 研究動機 1
1.2. 研究背景 2
1.3. 文獻回顧 3
1.3.1. 機器學習方法於熱傳 3
1.3.2. 多孔介質 7
1.3.3. 脈動流 10
1.4. 研究目的 11
2. 數值方法 22
2.1. 晶格波茲曼模型 22
2.1.1. 宏觀統治方程式 22
2.1.2. 晶格波茲曼模型 23
2.2. 機器學習模型與優化演算法 25
2.2.1. 人工神經網絡模型—徑向基類神經網絡 25
2.2.2. 支持向量機模型—最小二乘支持向量機 26
2.2.3. 決策樹模型—隨機森林 27
2.2.4. 模型評估 28
2.2.5. 優化方法—粒子群優化演算法 30
2.2.6. 優化方法—最佳化迭代流程 31
2.3. 模型驗證 32
2.3.1. LBM模型驗證 32
2.3.2. ML模型與優化演算法驗證 32
3. 建構微通道之機器學習模型 41
3.1. 模擬問題 41
3.1.1. 問題描述與計算座標系統 41
3.1.2. 邊界條件 42
3.1.3. 計算參數 42
3.1.4. 多孔介質參數 44
3.2. 建立機器學習模型 45
3.2.1. 徑向基類神經網絡 45
3.2.2. 最小二乘支持向量機 47
3.2.3. 隨機森林的參數 47
3.2.4. 機器學習模型比較 48
4. 優化機器學習模型之結果 60
4.1. 優化機器學習模型 60
4.1.1. 優化具多孔介質肋條微通道 60
4.1.2. 脈動流之速度場與溫度場 61
4.2. 脈動頻率及肋條高度的影響 62
4.2.1. 脈動頻率及肋條高度對摩擦係數的影響 62
4.2.2. 脈動頻率及肋條高度對熱傳增益的影響 63
4.2.3. 脈動頻率及肋條高度對熱性能參數的影響 63
4.3. 孔隙度的影響 64
4.4. 熱性能結果與前人數據進行比較 65
5. 結論與未來建議 76
5.1. 結論 76
5.2. 重要研究貢獻 76
5.3. 未來建議 78
參考文獻 79

 
表目錄
表 1 1機器學習模型於熱傳文獻整理 14
表 1 2多孔介質熱傳增益整理 19
表 1 3脈動流熱傳增益整理 21
表 3 1 本文與Wang等人[33]參數變化範圍比較 51
表 3 2 三種ML模型摩擦係數與努賽數的RMSE、MRE、R2 51
表 3 3 在Re=300、Hr*=0.5、ε=0.4時三種ML模型預測值與LBM結果在不同St下的誤差比較 51
表 4 1 LSSVM模型與LBM結果在最佳TPF配置下的比較 66

 
圖目錄
圖 1 1近20年晶片最大功耗、熱通量、晶體管數量的發展趨勢、電子設備故障原因分佈[1] 13
圖 2 1 D2Q9模型晶格速度遷移方向示意圖[33] 34
圖 2 2 D2Q5模型晶格速度遷移方向示意圖[33] 34
圖 2 3徑向基神經元示意圖 35
圖 2 4最佳化迭代過程 36
圖 2 5在Re=100,St=1.2,Hr*=0.5下的局部努賽數的分布與Wang等人[33]的結果比較圖 37
圖 2 6目標函數與RBNN模型比較 38
圖 2 7目標函數與LSSVM模型比較 38
圖 2 8目標函數與RF模型比較 39
圖 2 9 z=xexp(-(x2+y2))函式的空間直角座標圖 39
圖 2 10 初始粒子的位置與方向 40
圖 2 11 PSO收斂結果在X=-0.7071, Y=-0.0007(Z=-0.4289) 40
圖 3 1模擬對象座標與尺寸示意圖[33] 52
圖 3 2脈動流入口速度隨時間的變化[33] 52
圖 3 3 RBNN模型擴展常數與交叉驗證誤差 53
圖 3 4 RBNN模型的摩擦係數預測值與LBM結果的比較圖 53
圖 3 5 LSSVM模型的摩擦係數預測值與LBM結果的比較圖 54
圖 3 6 RF模型的摩擦係數預測值與LBM結果的比較圖 54
圖 3 7 Wang等人[33]相關性公式的摩擦係數估計值與LBM結果的比較圖 55
圖 3 8 RBNN模型的努賽數預測值與LBM結果的比較圖 55
圖 3 9 LSSVM模型的努賽數預測值與LBM結果的比較圖 56
圖 3 10 RF模型的努賽數預測值與LBM結果的比較圖 56
圖 3 11 Wang等人[33]相關性公式的努賽數估計值與LBM結果的比較圖 57
圖 3 12 ML模型摩擦係數預測值與LBM結果的決定係數 57
圖 3 13 ML模型努賽數預測值與LBM結果的決定係數 58
圖 3 14 Re=200,Hr*=0.5時ML模型摩擦係數預測值與LBM結果的比較圖 58
圖 3 15 Re=200,Hr*=0.5時ML模型努賽數預測值與LBM結果的比較圖 59
圖 4 1最佳TPF的週期平均速度場 66
圖 4 2最佳TPF的週期平均溫度場 66
圖 4 3 最佳TPF的配置在不同時刻下的瞬時速度場 67
圖 4 4最佳TPF的配置不同時刻下的瞬時溫度場 68
圖 4 5 Re=300,ε=0.4時摩擦係數隨St,Hr*的變化 69
圖 4 6 Re=300,ε=0.4時努賽數隨St,Hr*的變化 69
圖 4 7 Re=300,ε=0.4時TPF隨St,Hr*的變化 70
圖 4 8 Re=300,St=2.01,Hr*=0.45時不同孔隙度的週期平均速度場 71
圖 4 9 Re=300,St=2.01,Hr*=0.45時不同孔隙度的週期平均溫度場 72
圖 4 10 Re=300,St=2.01,Hr*=0.45時不同孔隙度的局部努賽數變化 73
圖 4 11 Re=300,St=2.01,Hr*=0.45時LSSVM模型預測不同孔隙度下壓力損失變化 73
圖 4 12 Re=300,St=2.01,Hr*=0.45時LSSVM模型預測不同孔隙度下熱傳增益變化 74
圖 4 13 本文最佳TPF結果與前人文獻[23,24][33] [50-55]的數據比較圖 75

參考文獻
[1] Z. Zhang, X. Wang, and Y. Yan, "A review of the state-of-the-art in electronic cooling," e-Prime-Advances in Electrical Engineering, Electronics and Energy, 1,　(2021) pp.100009.
[2] G. Xie, B. Sunden, Q. Wang, and L. Tang, "Performance predictions of laminar and turbulent heat transfer and fluid flow of heat exchangers having large tube-diameter and large tube-row by artificial neural networks," International Journal of Heat and Mass Transfer, 52, (2009) pp.2484-2497.
[3] Ş. Ö. Atayılmaz, H. Demir, and Ö. Ağra, "Application of artificial neural networks for prediction of natural convection from a heated horizontal cylinder," International Communications in Heat and Mass Transfer, 37.1, (2010) pp.68-73.
[4] H. Peng, and X. Ling, "Neural networks analysis of thermal characteristics on plate-fin heat exchangers with limited experimental data," Applied Thermal Engineering, 29, (2009) pp.2251-2256.
[5] R. Beigzadeh, and M. Rahimi, "Prediction of heat transfer and flow characteristics in helically coiled tubes using artificial neural networks," International Communications in Heat and Mass Transfer, 39.8, (2012) pp.1279-1285.
[6] M. Sheikholeslami, F. Bani Sheykholeslami, S. Khoshhal, H. Mola-Abasia, D. D. Ganji, and H. B. Rokni, "Effect of magnetic field on Cu–water nanofluid heat transfer using GMDH-type neural network," Neural Computing and Applications, 25, (2014) pp.171-178.
[7] U. Akdag, M. A. Komur, and S. Akcay, "Prediction of heat transfer on a flat plate subjected to a transversely pulsating jet using artificial neural networks," Applied Thermal Engineering, 100, (2016) pp.412-420.
[8] S. Chokphoemphun, S. Hongkong, S. Thongdaeng, and S. Chokphoemphun, "Experimental study and neural networks prediction on thermal performance assessment of grooved channel air heater," International Journal of Heat and Mass Transfer, 163, (2020) pp. 120397.
[9] R. V. Rao, and V. K. Patel, "Thermodynamic optimization of cross flow plate-fin heat exchanger using a particle swarm optimization algorithm," International Journal of Thermal Sciences, 49.9, (2010) pp.1712-1721.
[10] V. K. Patel, and R. V. Rao, "Design optimization of shell-and-tube heat exchanger using particle swarm optimization technique," Applied Thermal Engineering, 30, (2010) pp.1417-1425.
[11] M. D. Damavandi, M. Forouzanmehr, and H. Safikhani, "Modeling and Pareto based multi-objective optimization of wavy fin-and-elliptical tube heat exchangers using CFD and NSGA-II algorithm," Applied Thermal Engineering, 111, (2017) pp.325-339.
[12] S. Wang, J. Xiao, J. Wang, G. Jian, J. Wen, and Z. Zhang, "Application of response surface method and multi-objective genetic algorithm to configuration optimization of Shell-and-tube heat exchanger with fold helical baffles," Applied Thermal Engineering, 129, (2018) pp.512-520.
[13] H. Ke, T. A. Khan, W. Li, Y. Lin, Z. Ke, H. Zhu, and Z. Zhang, "Thermal-hydraulic performance and optimization of attack angle of delta winglets in plain and wavy finned-tube heat exchangers," Applied Thermal Engineering, 150, (2019) pp.1054-1065.
[14] A. Afzal, H. Chung, K. Muralidhar, and H. H. Cho, "Neural-network-assisted optimization of rectangular channels with intersecting ribs for enhanced thermal performance," Heat Transfer Engineering, 41, (2020) pp.1609-1625.
[15] M. Algarni, M. A. Alazwari, and M. R. Safaei, "Optimization of nano-additive characteristics to improve the efficiency of a shell and tube thermal energy storage system using a hybrid procedure: DOE, ANN, MCDM, MOO, and CFD modeling," Mathematics, 9.24, (2021) pp.3235.
[16] T. Wen, G. Zhu, K. Jiao, and L. Lu, "Experimental study on the thermal and flow characteristics of ZnO/water nanofluid in mini-channels integrated with GA-optimized ANN prediction and CFD simulation," International Journal of Heat and Mass Transfer, 178, (2021) pp.121617.
[17] A. Baghban, M. Kahani, M. A. Nazari, M. H. Ahmadi, and W. M. Yan, "Sensitivity analysis and application of machine learning methods to predict the heat transfer performance of CNT/water nanofluid flows through coils," International Journal of Heat and Mass Transfer, 128, (2019) pp.825-835.
[18] L. Zhou, D. Garg, Y. Qiu, S. M. Kim, I. Mudawar, and C. R. Kharangate, "Machine learning algorithms to predict flow condensation heat transfer coefficient in mini/micro-channel utilizing universal data," International Journal of Heat and Mass Transfer, 162, (2020) pp.120351.
[19] K. Kim, H. Lee, M. Kang, G. Lee, K. Jung, C. R. Kharangate, and H. Lee, "A machine learning approach for predicting heat transfer characteristics in micro-pin fin heat sinks," International Journal of Heat and Mass Transfer, 194, (2022) pp.123087.
[20] A. Saravanan, S. Parida, M. Murugan, M. S. Reddy, Elumalai, P. V. Elumalai, and S. K. Dash, "Thermal performance prediction of a solar air heater with a C-shape finned absorber plate using RF, LR and KNN models of Machine learning," Thermal Science and Engineering Progress, 38, (2023) pp.101630.
[21] M. Ghalandari, M. I. Shahrestani, A. Maleki, M. S. Shadloo, and M. E. H. Assad, "Applications of intelligent methods in various types of heat exchangers: a review," Journal of Thermal Analysis and Calorimetry, 145, (2021) pp.1837-1848.
[22] P. C. Huang, and C. F. Yang, "Analysis of pulsating convection from two heat sources mounted with porous blocks," International Journal of Heat and Mass Transfer, 51.25-26, (2008) pp.6294-6311.
[23] H. Shokouhmand, F. Jam, and M. R. Salimpour, "Simulation of laminar flow and convective heat transfer in conduits filled with porous media using Lattice Boltzmann Method," International Communications in Heat and Mass Transfer, 36.4, (2009) pp.378-384.
[24] J. Yang, M. Zeng, and Q. Wang, "Forced convection heat transfer enhancement by porous pin fins in rectangular channels," Journal of Heat Transfer,48, (2010) pp.1-8aswqaz
[25] N. Guerroudj, and H. Kahalerras, "Mixed convection in a channel provided with heated porous blocks of various shapes," Energy Conversion and Management, 51, (2010) pp.505–517.
[26] H. J. Xu, Z. G. Qu, Lu, T. J. Lu, Y. L. He, and W. Q. Tao, "Thermal modeling of forced convection in a parallel-plate channel partially filled with metallic foams," Journal of Heat Transfer, 133.9, (2011).
[27] M. E. Nimvari, M. Maerefat, and M. K. El-Hossaini, "Numerical simulation of turbulent flow and heat transfer in a channel partially filled with a porous media," International Journal of Thermal Sciences, 60, (2012) pp.131-141.
[28] A. A. Mehrizi, M. Farhadi, K. Sedighi, and M. A. Delavar, "Effect of fin position and porosity on heat transfer improvement in a plate porous media heat exchanger," Journal of the Taiwan Institute of Chemical Engineers ,44.3, (2013) pp.420-431.
[29] R. A. Mahdi, H. A. Mohammed, K. M. Munisamy, and N. H. Saeid, "Influence of various geometrical shapes on mixed convection through an open-cell aluminium foam filled with nanofluid," Journal of Computational and Theoretical Nanoscience, 11.5, (2014) pp.1275-1289.
[30] A. Davari, and M. Maerefat, "Numerical analysis of fluid flow and heat transfer in entrance and fully developed regions of a channel with porous baffles," Journal of Heat Transfer, 138.6, (2016).
[31] S. Saedodin, S. A. H. Zamzamian, M. Eshagh Nimvari, S. Wongwises, and H. Javaniyan Jouybari, "Performance evaluation of a flat-plate solar collector filled with porous metal foam: Experimental and numerical analysis," Energy Conversion and Management, 153, (2017) pp.278-287.
[32] K. Anirudh and S. Dhinakaran, "Performance improvement of a flat-plate solar collector by inserting intermittent porous blocks," Renewable Energy, 145, (2020) pp.428-441.
[33] C.S. Wang, P.Y. Shen, and T.M. Liou, "Evaluation of porous rib and flow pulsation on microchannel thermal performance using a novel thermal lattice Boltzmann method," International Journal of Thermal Sciences, 172, (2022) pp.1290-0729.
[34] S. Y. Kim, B. H. Kang, and J. M. Hyun, "Heat transfer in the thermally developing region of a pulsating channel flow," International Journal of Heat and Mass Transfer, 36.17, (1993) pp.4257-4266.
[35] S. Y. Kim, B. H. Kang, and J. M. Hyun, "Heat transfer from pulsating flow in a channel filled with porous media," International Journal of Heat and Mass Transfer, 37.14, (1994) pp.2025-2033.
[36] Z. Guo, and H. J. Sung, "Analysis of the Nusselt number in pulsating pipe flow," International Journal of Heat and Mass Transfer, 40.10, (1997) pp.2486-2489.
[37] P. C. Huang, and C. F. Yang, "Analysis of pulsating convection from two heat sources mounted with porous blocks," International Journal of Heat and Mass Transfer, 51.25-26, (2008) pp.6294-6311.
[38] M. Jafari, M. Farhadi, and K. Sedighi, "Pulsating flow effects on convection heat transfer in a corrugated channel: A LBM approach," International Communications in Heat and Mass Transfer, 45, (2013) pp.146-154.
[39] D. Zheng, X. Wang, and Q. Yuan, "The effect of pulsating parameters on the spatiotemporal variation of flow and heat transfer characteristics in a ribbed channel of a gas turbine blade with the pulsating inlet flow," International Journal of Heat and Mass Transfer, 153, (2020) pp.119609.
[40] C. S. Wang, T. C. Wei, P. Y. Shen, and T. M. Liou, "Lattice Boltzmann study of flow pulsation on heat transfer augmentation in a louvered microchannel heat sink," International Journal of Heat and Mass Transfer, 148, (2020) pp.119139.
[41] Q. Ye, Y. Zhang, and J. Wei, "A comprehensive review of pulsating flow on heat transfer enhancement," Applied Thermal Engineering, 196, (2021) pp.117275.
[42] P. Nithiarasu, K. N. Seetharamu, and T. Sundararajan, "Natural convective heat transfer in a fluid saturated variable porosity medium," International Journal of Heat and Mass Transfer, 40.16, (1997) pp.3955-3967.
[43] Y. H. Qian, "Simulating thermohydrodynamics with lattice BGK Models," Journal of Scientific Computing, 8.3, (1993) pp.231-242.
[44] J. Kennedy, and R. Eberhart, "Particle swarm optimization," Proceedings of ICNN'95-International Conference on Neural Networks, Vol. 4, IEEE, (1995).
[45] P. Li, X. Lian, Y. Chen, Y. Zhang, W. Zhao, and C. Ma, "Multiple-relaxation-time lattice Boltzmann simulation of natural convection with multiple heat sources in a rectangular cavity," Canadian Journal of Physics, 98.4, (2020) pp.332-343.
[46] K. Vafai, "Convective flow and heat transfer in variable-porosity media," Journal of Fluid Mechanics, 147, (1984) pp.233-259.
[47] S. Ergun, and A. A. Orning, "Fluid flow through randomly packed columns and fluidized beds," Industrial & Engineering Chemistry, 41.6, (1949) pp.1179-1184.
[48] M. A. Combarnous, and S. A. Bories, "Hydrothermal convection in saturated porous media," Advances in Hydroscience, 10, (1975) pp.231-307.
[49] K. De Brabanter, P. Karsmakers, F. Ojeda, C. Alzate, J. De Brabanter, K. Pelckmans, and J. A. Suykens, LS-SVMlab toolbox user's guide: version 1.7, (2010).
[50] A. Bhattacharya, and R. L. Mahajan, "Finned metal foam heat sinks for electronics cooling in forced convection," Journal of Electronic Packaging, 124, (2002) pp.154-163.
[51] S. Y. Kim, J. W. Paek, and B. H. Kang, "Thermal performance of aluminum-foam heat sinks by forced air cooling," IEEE Transactions on Components and Packaging Technologies, 26(1), (2003) pp.262-267.
[52] C. Y. Zhao, T. Kim, T. J. Lu, and H. P. Hodson, "Thermal transport in high porosity cellular metal foams," Journal of Thermophysics and Heat Transfer, 18(3), (2004) pp.309-317.
[53] S. S. Mousavi, and K. Hooman, "Heat and fluid flow in entrance region of a channel with staggered baffles," Energy Conversion and Management, 47(15), (2006) pp.2011-2019.
[54] T. Desrues, P. Marty, and J. F. Fourmigué, "Numerical prediction of heat transfer and pressure drop in three-dimensional channels with alternated opposed ribs," Applied Thermal Engineering, 45, (2012) pp.52-63.
[55] L. Lin, J. Zhao, G. Lu, X.D. Wang, and W.M. Yan, "Heat transfer enhancement in microchannel heat sink by wavy channel with changing wavelength/amplitude," International Journal of Thermal Sciences,118, (2017) pp.423-434.