近年來，隨著電子晶片微型化與效能上升，單一晶片的熱通量已經超過傳統強制對流的散熱能力，在冷卻通道內擺放金屬多孔介質是較為簡單且能有效解決散熱問題的新方式。本文提出一種新型熱晶格波茲曼法(Thermal Lattice Boltzmann Method, 簡稱TLBM)在表徵體元尺度(Representative Element Volume, 簡稱REV)下模擬多孔介質於二維層流微流道的熱傳特性，相較於前人模型，新模型在模擬流體、多孔介質與固體之耦合熱傳時不須特別定義熱容比，且計算過程上更為簡潔。本文利用此一模型來模擬具有多孔介質的微管道，並在多孔介質內部放入一固體來使溫度邊界層變薄來增益熱傳效果，在固定雷諾數(Re)下藉由改變固體的厚度(S/H)來觀察其熱傳增益與壓力損失的變化。模擬結果發現熱傳增益與壓力損失皆會隨著S/H下降而單調上升。固體在S/H=0.125的情形下擁有最高的熱傳增益與熱性能係數(Thermal Performance Factor, 簡稱TPF)，其值分別為全展平滑管道的61.3倍和3.23倍。之後為了進一步提升熱傳效果而將管道的穩態流入口改為脈動入口，但多孔介質填滿管道時會使得渦旋難以產生，使得脈動效果不佳。為了改善脈動效果不佳的缺點，本文將原本填滿多孔介質的管道改為多孔介質肋條管道，並改變Re與脈動頻率(St)來觀察熱傳增益與壓力損失的變化情形。模擬結果發現，脈動流會使通道內產生膨脹收縮渦旋，將壁面上的高溫流體捲至中心與中心的冷流體產生混合來增益熱傳，在特定頻率St=2下會有最高的熱傳增益，其熱傳增益為平滑管道的14.4倍，相較於穩態時也高出了2.14倍。

With the miniaturization and increasing efficiency of electronic chips in recent years, the heat flux generated per unit area has exceeded the cooling capacity of conventional forced convection. The use of metal porous media in microchannel heat sinks has emerged as a relatively simple and effective way to address this issue. In this paper, a novel thermal lattice Boltzmann method (TLBM) based on the representative elementary volume (REV) scale is developed to simulate the laminar flow and heat transfer in a two-dimensional microchannels partially filled with porous media. Compared with previous TLBMs, the present model possesses a simpler computational procedure and consistent definition of heat capacity ratio in simulating conjugate heat transfer in fluid, porous media, and solid regions. The model is then used to study the heat transfer in a microchannel partially filled with porous media and solid obstacles. For fixed Reynolds number (Re), as the height of the solid obstacle (S/H) increases, both the averaged Nusselt number ratio and friction factor increase.The highest heat transfer and thermal performance factor occur at S/H=0.125, are 61.3 and 3.23 times those of smooth channel, respectively. To further improve the heat transfer, the inlet condition of the microchannel is changed from steady state flow to pulsating flow. It is found that the pulsating effect has minor effect on heat transfer since there is no vortex induced in porous blocks. Therefore, the porous blocks are further replaced with porous ribs whose effect on heat transfer and friction factor is then studied by varying Re and pulsating frequency (St). The simulation results show that there exist contraction and expanding vortices which effectively promote the mixing of fluid between near wall and core region, and in turn augment the heat transfer. The maximum appears at St=2 and is respectively 2.14 and 14.4 times that of the steady state condition and smooth channel.

目錄
摘要 I
Abstract II
表目錄 VIII
圖目錄 IX
符號表 XII
第一章、前言 1
1.1研究動機 1
1.2研究背景 2
1.3文獻回顧 2
1.3.1傳統擾流器 2
1.3.2多孔介質 5
1.3.3脈動流 9
1.4研究目的 14
第二章、數值方法 25
2.1 多孔介質熱晶格波茲曼模型 25
2.1.1模型假設與宏觀統治方程式 25
2.1.2速度場晶格波茲曼模型 27
2.1.3溫度場的晶格波茲曼模型 29
2.1.3.1前人的溫度場模型 29
2.1.3.2本文的溫度場模型 32
2.1.4計算流程 34
2.2 模型驗證 35
2.2.1穩態流 35
2.2.1.1兩固體間的熱傳導 35
2.2.1.2同時有多孔介質與流體的拖曳流動(Couette flow) 36
2.2.1.3固體與多孔介質自然對流 37
2.2.1.4流體、固體與多孔介質並存的自然對流 38
2.2.2 脈動流 39
2.2.2.1 全展脈動平行板流 40
2.2.2.2熱發展脈動平行板流 40
第三章、固體與多孔介質耦合管道穩態流 51
3.1模擬問題 51
3.1.1計算座標系統 51
3.1.2邊界條件 51
3.1.3計算參數 52
3.1.4多孔介質參數 53
3.2網格獨立測試 54
3.3 固體厚度的影響 54
3.3.1速度場分析 54
3.3.2熱傳分析 55
3.3.3壓損與熱性能係數分析 56
3.4總體熱性能與前人數據比較 56
第四章、多孔介質肋條管道脈動流 63
4.1問題描述 63
4.1.1計算區域與座標系統 63
4.1.2邊界條件 63
4.1.3計算參數 64
4.2網格獨立測試 65
4.3脈動下的速度場與溫度場 65
4.3.1速度場 66
4.3.2溫度場 66
4.4肋條高度的影響 67
4.5 脈動頻率的影響 68
4.5.1 脈動頻率對熱傳增益的影響 68
4.5.2脈動頻率對壓力損失的影響 70
4.5.3脈動頻率對熱性能係數的影響 70
4.6雷諾數的影響 71
4.7熱傳關係式 72
4.8總體熱性能與前人數據比較 73
第五章、結論與未來建議 87
5.1結論 87
5.1.1多孔介質算法 87
5.1.2穩態流 87
5.1.3脈動流 88
5.2未來工作 89
附錄A 固體與多孔介質耦合管道的脈動流 91
A.1問題描述 91
A.2 脈動頻率的影響 91
附錄B 論文口試之補充答辯 95
參考文獻 101

[1] L. Chai, G. D. Xia, H. S. Wang, “Numerical study of laminar flow and heat transfer in microchannel heat sink with offset ribs on sidewalls,” Applied Thermal Engineering, 92, (2016) pp.32-41.
[2] B. W. Webb, S. Ramadhyani, “Conjugate heat transfer in a channel with staggered ribs,” International Journal of Heat and Mass Transfer, 28(9), (1985) pp.1679-1687.
[3] L. Gong, K. Kota, W. Tao, Y. Joshi, “Parametric numerical study of flow and heat transfer in microchannels with wavy walls,” Journal of Heat Transfer, 133(5), (2011) pp.1-10.
[4] S. V. Patankar, C. H. Liu, E. M. Sparrow, “Fully developed flow and heat transfer in ducts having streamwise-periodic variations of cross-sectional area,” ASME Journal of Heat Transfer, 99(2), (1977) pp.180-186.
[5] C. H. Cheng, W. H. Hung, “Numerical prediction for laminar forced convection in parallel-plate channels with transverse fin arrays,” International Journal of Heat and Mass Transfer, 34(11), (1991) pp.2739-2749.
[6] S. Sripattanapipat, P. Promvonge, “Numerical analysis of laminar heat transfer in a channel with diamond-shaped baffles,” International Communications in Heat and Mass Transfer, 36(1), (2009) pp.32-38.
[7] T. M. Liou, T. C. Wei, C. S. Wang, “Investigation of nanofluids on heat transfer enhancement in a louvered microchannel with lattice Boltzmann method,” Journal of Thermal Analysis and Calorimetry, 135(1), (2019) pp. 751–762.
[8] R. Singh, A. Akbarzadeh, M. Mochizuki, “Sintered porous heat sink for cooling of high-powered microprocessors for server applications,” International Journal of Heat and Mass Transfer, 52, (2009) pp.2289-2299.
[9] S. Kim, B. H. Kang, J. H. Kim, “Forced convection from aluminum foam materials in an asymmetrically heated channel,” International Journal of Heat and Mass Transfer ,44, (2001) pp.1451-1454.
[10] P. X. Jiang, M. Li, T. J. Lu, L. Yu, Z. P. Ren, “Experimental research on convection heat transfer in sintered porous plate channels,” International Journal of Heat and Mass Transfer, 47, (2004) pp.2085-2096.
[11] V. V. Calmidi1, R. L. Mahajan, “Forced convection in high porosity metal foams,” Journal of Heat Transfer, 122, (2000) pp.557-565.
[12] W.H. Hsieh, J.Y. Wu, W.H. Shih, W.C. Chiu, “Experimental investigation of heat-transfer characteristics of aluminum-foam heat sinks,” International Journal of Heat and Mass Transfer, 47, (2004) pp.5149-5157.
[13] A. Hadim, “Forced convection in a porous channel with localized heat sources,” Journal of Heat Transfer, 116, (1994) pp.465-472.
[14] J. Yang, M. Zeng, Q. Wang, “Forced Convection Heat Transfer Enhancement by Porous Pin Fins in Rectangular Channels,” Journal of Heat Transfer, 132, (2010) pp.1-8.
[15] P.C. Huang, C.F. Yang, J.J. Hwang, M.T. Chiu, “Enhancement of forced-convection cooling of multiple heated blocks in a channel using porous covers,” International Journal of Heat and Mass Transfer, 48, (2005) pp.647-664.
[16] H. Shokouhmand, F. Jam, M.R. Salimpour, “Simulation of laminar flowand convective heat transfer in conduits filled with porous media using Lattice Boltzmann Method,” International Communications in Heat and Mass Transfer, 36, (2009) pp.378-384.
[17] H. R. Seyf, M. Layeghi, “Numerical analysis of convective heat transfer from an elliptic pin fin heat sink with and without metal foam insert,” Journal of Heat Transfer, 132, (2010) pp.1-9.
[18] Y. Ould-Amer, S. Chikh, K. Bouhadef, G. Lauriat, “Forced convection cooling enhancement by use of porous materials,” International Journal of Heat and Fluid Flow, 19, (1998) pp.251-258.
[19] R. A. Mahdi, H. A. Mohammed, K. M. Munisamy, N. H. Saeid, “Influence of various geometrical shapes on mixed convection through an open-cell aluminium foam,” Journal of Computational and Theoretical Nanoscience Filled with Nanofluid, 11, (2014) pp.1-15.
[20] R. Siegel, M. Perlmutter, “Heat transfer for pulsating laminar duct flow,” Journal of Heat Transfer, 84, (1962) pp.111-122.
[21] T. Nishimura, A. M. Morega, K. Kunitsugu, “Vortex structure and fluid mixing in pulsatile flow through periodically grooved channels at low Reynolds numbers,” JSME International Journal Series B Fluids and Thermal Engineering, 40, (1997) pp.377-385.
[22] M. Jafari, M. Farhadi, 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.
[23] T. Fukue, W. Hiratsuka, H. Shirakawa, K. Hirose, J. Suzuki, “Numerical investigation of effects of pulsating wave pattern on heat transfer enhancement around square ribs by pulsating flow,” International Symposium on Transport Phenomena, (2017).
[24] H. L. Fu, K. C. Leong, X. Y. Huang, C. Y. Liu, “An experimental study of heat transfer of porous channel subjected to oscillating flow,” Journal of Heat Transfer, 123, (2001) pp.162-170.
[25] G. F. Al-Sumaily, M. C. Tompson, “Forced convection from a circular cylinder in pulsating flow with and without the presence of porous media,” International Journal of Heat and Mass Transfer, 61, (2013) pp.226-244.
[26] P. C. Huang, C. F. Yang, “Analysis of pulsating convection from two heat sources mounted with porous blocks,” International Journal of Heat and Mass Transfer, 51, (2008) pp.6294-6311.
[27] T. M. Liou, C. S. Wang, “Three-dimensional multidomain lattice Boltzmann grid refinement for passive scalar transport,” Physical Review E, 98, (2018) pp.1-9.
[28] T. M. Liou, C. S. Wang, “Large eddy simulation of rotating turbulent flows and heat transfer by the lattice Boltzmann method,” Physics of Fluids, 30, (2018) pp.1-13.
[29] A. Nabovati, E. W. Llewellin, A. C. M. Sousa, “A general model for the permeability of fibrous porous media based on fluid flow simulations using the lattice Boltzmann method,” Composites: Part A, 40, (2009) pp.860-869.
[30] L. Hao, P. Cheng, “Pore-scale simulations on relative permeabilities of porous media by lattice Boltzmann method,” International Journal of Heat and Mass Transfer, 53, (2010) pp.1908-1913.
[31] M. E. Kutay, A. H. Aydilek, E. Masad, “Laboratory validation of lattice Boltzmann method for modeling pore-scale flow in granular materials,” Computers and Geotechnics, 33, (2006) pp.381-395.
[32] Z. Guo, T. S. Zhao, “Lattice Boltzmann model for incompressible flows through porous media,” PHYSICAL REVIEW E ,66, (2002) pp.1-9.
[33] P. Nithiarasu, K. N. Seetharamu, T. Sundararajan, “Natural convective heat transfer in a fluid saturated variable porosity medium,” International Journal of Heat and Mass Transfer ,40, (1997) pp.3955-3967.
[34] D. Kashyap, A. K. Dass, “Two-phase lattice Boltzmann simulation of natural convectionin a Cu-water nanofluid-filled porous cavity: Effects of thermalboundary conditions on heat transfer and entropy generation,” Advanced Powder Technology ,29, (2018) pp.2707–2724.
[35] Z. Guo, T. S. Zhao, “Lattice Boltzmann simulation of natural convection with temperature-dependent viscosity in a porous cavity,” Computational Fluid Dynamics ,5, (2005) pp.110-117.
[36] D. Gao, Z. Chen, “Lattice Boltzmann simulation of natural convection dominated melting in a rectangular cavity filled with porous media,” International Journal of Thermal Sciences ,50, (2011) pp.493-501.
[37] T. Seta, E. Takegoshi, K. Okui, “Lattice Boltzmann simulation of natural convectionin porous media,” Mathematics and Computers in Simulation ,72, (2006) pp.195-200.
[38] H. Shokouhmand, F. Jam, M.R. Salimpour, “Simulation of laminar flow and convective heat transfer in conduits filled with porousmedia using Lattice Boltzmann Method,” International Communications in Heat and Mass Transfer ,36, (2009) pp.378-384.
[39] H. Shokouhmand, F. Jam, M.R. Salimpour, “The effect of porous insert position on the enhanced heat transfer in partially filled channels,” International Communications in Heat and Mass Transfer ,38, (2011) pp.1162-1167.
[40] Z. Guo, T. S. Zhao, “A Lattice Boltzmann model for convection heat transfer in porous media,” Numerical Heat Transfer: Part B ,47, (2005) pp.157-177.
[41] W. Wu, S. Zhang, S. Wang, “A novel lattice Boltzmann model for the solid-liquid phase change with the convection heat transfer in the porous media,” International Journal of Heat transfer ,104, (2017) pp.675-687.
[42] S. Chen, B. Yang, C.G. Zheng, “A lattice Boltzmann model for heat transfer in porous media,” International Journal of Heat and Mass Transfer ,111, (2017) pp.1019-1022.
[43] D.Y. Gao, Z.Q. Chen, L.H. Chen, D.L Zhang, “A modified lattice Boltzmann model for conjugate heat transfer in porous media,” International Journal of Heat and Mass Transfer ,105, (2017) pp.673-683.
[44] 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.
[45] L. Lin, J. Zhao, G. Lu, X.D. Wang, 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.
[46] 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.
[47] A. Bhattacharya, R. L. Mahajan, “Finned Metal Foam Heat Sinks for Electronics Cooling in Forced Convection,” Journal of Electronic Packaging,124, (2002) pp.154-163.
[48] S. Y. Kim, J. W. Paek, 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.
[49] C. Y. Zhao, T. Kim, T. J. Lu, H. P. Hodson, “Thermal Transport in High Porosity Cellular Metal Foams,” Journal of Thermophysics and Heat Transfer, 18(3), (2004) pp.309-317.
[50] N. Guerroudj, H. Kahalerras, “Mixed convection in a channel provided with heated porous blocks of various shapes,” Energy Conversion and Management, 51, (2010) pp.505–517.
[51] K. C. Leong, L.W. Jin, “An experimental study of heat transfer in oscillating flow through a channel filled with an aluminum foam,” International Journal of Heat and Mass Transfer, 48, (2005) pp.243-253.
[52] H. S. Carslaw, J. C. Jaeger, “Conduction of Heat in Solids, second ed., Oxford University Press,” New York, (1959).
[53] A. V. Kuznetsov, “Analytical investigation of Couette flow in a composite channel partially filled with a porous medium and partially with a clear fluid,” International Journal of Heat and Mass Transfer, 41, (1998) pp.2556-2560.
[54] N. C. Markatos, K. A. Pericleous, “Laminar and turbulent natural convection in an enclosed cavity,” International Journal of Heat and Mass Transfer, 27, (1984) pp.755-772.
[55] A. Al-Amiri, K. Khanafer, I. Pop, “Steady-state conjugate natural convection in a fluid-saturated porous cavity,” International Journal of Heat and Mass Transfer, 51, (2008) pp.4260–4275.
[56] C. Beckermann, R. Viskanta, S. Ramadhyani, “Natural convection in vertical enclosures containing simultaneously fluid and porous layers,” Journal Fluid Nech , 186, (1988) pp.257-284.
[57] A. Faghri, M. Faghri, and K. Javdani, “Effect of flow pulsation on laminar heat transfer between two parallel plates,” Wärme-und Stoffübertragung, 13(1-2), (1980) pp.97-103.
[58] K. Vafai, “Convective flow and heat transfer in variable-porosity media,” Journal of Fluid Mechanics, 147, (1984) pp.233-259.
[59] S. Ergun, “Fluid flow through packed columns,” Chemical Engineering Progress, (1952).
[60] M. A. Combarnous, S. A. Bories, “Hydrothermal convection in saturated porous media,” Advances in Hydroscience, 10, (1975) pp.231-307.