因應電子產品對微型化與高效能的需求，微型熱交換器之研究在近年成為熱傳領域中的一門顯學，然而多數文獻僅著重對稱截面形狀的交換器流道，卻無人同時探究平行四邊形管道寬高比及側壁傾角對層性熱流場的影響。本篇研究以數值模擬分析在穩態不可壓縮流條件下，單、雙通道平行四邊形截面平滑管道中，層性熱流場隨通道側壁傾角及寬高比之變化。使用 SIMPLE 演算法對速度、壓力項作耦合，並以二階上風法對壓力項進行空間離散；動量及能量方程式使用QUICK算法；格點交介面上以Least Squares Cell-Based方法估算純量。在單通道的部分，以通道水利直徑為特徵長度之雷諾數(Re)固定為100；在幾何參數為側壁傾角45°~90°以及寬高比1~10的範圍內，分別觀察在等壁溫(TBC)、沿軸向單位長度熱傳量保持定值且周界均溫(H1BC)、以及等熱通量(H2BC) 三種熱邊界下熱流場的變化。發現於H2BC條件下，側壁傾角存在一臨界值: 𝜃 = 70°，低於此值則紐賽數隨寬高比增大而增加，而反之亦然，此現象在TBC及H1BC兩種條件下皆未見;本篇歸納出TBC是H1BC在使用數值模擬方法時的經濟替代方案；並整理出側壁傾角及寬高比對紐賽數(Nu)、摩擦因子(f)在三種熱邊界條件下之關係，且以精簡的多項式函數表示。在雙通道的部分，在幾何參數為側壁傾角45°~90°及寬高比1~10的範圍中，選定雷諾數從100變化至300，並由單通道部分之結論選擇TBC為熱邊界。發現側壁的傾斜將加劇紐賽數於上、下壁面分布的不對稱性；另外發現紐賽數的分佈在第一、第二通道受對流熱傳主導，然而在轉彎區則受衝擊效應所統領；本篇亦歸納出以管道寬高比及側壁傾角對平均紐賽數(〖Nu〗_m)與摩擦因子的兩條耦合函數，與模擬結果相比的誤差分別落在10% 與 20%的範圍，說明此耦合函數在微型熱交換器設計上十分具有參考性。

The topic of micro heat exchanger is one of the most active areas in heat transfer research today due to the rapid growth of power consuming and miniaturization of electronics size. Nonetheless, to author’s knowledge, previous studies have primarily concentrated on the channels with symmetric cross-section, which have equal heat transfer distribution on opposite walls. There is a lack of research regarding the combined effect of aspect ratios (α) and included angles (𝜃) on laminar flow and heat transfer in parallelogram channels. In this study, the attention is focused on the numerical simulations of laminar fluid flow and heat transfer in single and two-pass smooth-walled parallelogram channels with various aspect ratios (α) and included angles (𝜃). The SIMPLE algorithm is employed for velocity–pressure coupling with the algebraic multigrid method, while the second-order upwind scheme is utilized for spatial discretization in pressure term; the momentum and energy equations are solved with a QUICK scheme; Least Squares Cell-Based Gradient Evaluation is applied for predicting scalar values at the cell faces and for computing secondary diffusion terms and velocity derivatives. For the single pass channels, the Reynolds number (Re), characterized by the channel hydraulic diameter and the working fluid of water, is kept at 100; the parameters investigated are the α and 𝜃 ranging from 1 to 10 and ranged from 45° to 90°, respectively. Their effects on the thermal fluid features are explored in single channels under three thermal boundary conditions: constant wall temperature (TBC), constant axial heat transfer rate with constant peripheral temperature (H1BC), and constant wall heat flux (H2BC). One of the new findings is that there exists a critical value of 𝜃 = 70° below which the Nusselt number under H2BC increases with increasing α whereas beyond which the trend reverses, a result distinct from those computed with TBC and H1BC. Also, TBC is found to be a time-saving alternative to H1BC. Moreover, both Nusselt numbers (Nu) under the three thermal boundary conditions and friction factor (f) times Re are successfully and compactly correlated with α and 𝜃. For two-pass channels, the Re is ranged from 100 to 300, while the α and 𝜃 ranging from 0.25 to 4 and ranged from 45° to 90°, respectively. According to the previous results, TBC are chosen as the thermal boundary conditions in the two-pass channel studies. It was found that the Nu distributions on bottom and top walls in the channels with slant wall (𝜃 ≠ 90°) are asymmetric and generally lower compared to that of 90° channel (rectangular channel). Additionally, the Nu distributions in the first and second pass are mainly dominated by convection cooling, whereas those in the turn region are ruled by the impingement cooling. Furthermore, two correlations of overall mean Nusselt number (〖Nu〗_m) and f with respect to α, 𝜃, and Re are proposed for laminar flow in parallelogram two-pass channels. The maximum errors of the correlations of 〖Nu〗_m and f compared to the CFD results are within 10% and 20%, respectively. These correlations offer useful reference for designing micro serpentine channels.

中文摘要 I
ABSTRACT II
ACKNOWLEDGEMENT IV
CONTENTS V
LIST OF TABLES VII
LIST OF FIGURES VIII
LIST OF SYMBOLS X
English symbols x
Greek Symbols xi
Subscripts xi
CHAPTER 1 INTRODUCTION 1
1-1 Opening Remarks 1
1-2 Literature Survey 3
1-2-1 Thermal boundary conditions 3
1-2-2 Channel cross-sectional shapes 5
1-2-3 Various channel patterns 7
1-3 Objectives 11
1-3-1 Fully developed laminar flow in single pass channels 11
1-3-2 Developing laminar flow in two-pass channels 11
CHAPTER 2 METHDOLODGY 16
2-1 Governing Equations 16
2-2 Numerical Method 17
CHAPTER 3 SINGLE PASS PARALLELOGRAM CHANNELS 19
3-1 Description of Problem 19
3-1-1 Boundary conditions 19
3-1-2 Data reduction 21
3-1-3 Computational grid details 23
3-2 Validation of Numerical Model 24
3-3 Friction Factor 24
3-4 Nusselt Number under T and H1 Boundary Conditions 25
3-5 Nusselt Number under H2 Boundary Condition 27
3-6 Generalized Correlations in Single Channels 28
CHAPTER 4 TWO-PASS PARALLELOGRAM CHANNELS 42
4-1 Description of Problem 42
4-1-1 Boundary conditions 42
4-1-2 Data reduction 43
4-1-3 Computational grid details 43
4-2 Effect of Aspect Ratio 44
4-2-1 Local Nusselt number ratios and corresponding flow fields 44
4-2-2 Correlations between fluid flow and heat transfer 47
4-3 Effect of Included Angle 48
4-3-1 Local Nusselt number ratios and corresponding flow fields 48
4-3-2 Correlations between fluid flow and heat transfer 50
4-4 Generalized Correlations in Two-Pass Channels 52
CHAPTER 5 CONCLUSIONS AND FUTURE WORKS 67
5-1 Conclusions 67
5-1-1 Fully developed laminar flow in single pass channels 67
5-1-2 Developing laminar flow in two-pass channels 68
5-2 Contributions 69
5-3 Future Works 70
REFERENCES 72

Cengel, Y.A., Heat transfer: a practical approach. 2004: McGraw-Hill.
[2] Zhang, L.-Y., et al., Fluid flow and heat transfer characteristics of liquid cooling microchannels in LTCC multilayered packaging substrate. International Journal of Heat and Mass Transfer, 2015. 84: p. 339-345.
[3] Yuan, L., et al. Thermal Analysis of High Power LED Array Packaging with Microchannel Cooler. in 2006 7th International Conference on Electronic Packaging Technology. 2006.
[4] Goebel, S.G., Evaporative cooled fuel cell. 2005, General Motors Corporation.
[5] Kandlikar, S.G. and Z. Lu, Thermal management issues in a PEMFC stack – A brief review of current status. Applied Thermal Engineering, 2009. 29(7): p. 1276-1280.
[6] Faghri, A. and Z. Guo, Challenges and opportunities of thermal management issues related to fuel cell technology and modeling. International Journal of Heat and Mass Transfer, 2005. 48(19–20): p. 3891-3920.
[7] Lasbet, Y., et al., A chaotic heat-exchanger for PEMFC cooling applications. Journal of Power Sources, 2006. 156(1): p. 114-118.
[8] Inoue, G., et al., Effect of flow pattern of gas and cooling water on relative humidity distribution in polymer electrolyte fuel cell. Journal of Power Sources, 2006. 162(1): p. 94-104.
[9] Inoue, G., et al., Numerical analysis of relative humidity distribution in polymer electrolyte fuel cell stack including cooling water. Journal of Power Sources, 2006. 162(1): p. 81-93.
[10] Xu, C. and T.S. Zhao, A new flow field design for polymer electrolyte-based fuel cells. Electrochemistry Communications, 2007. 9(3): p. 497-503.
[11] Yu, S.H., et al., Numerical study to examine the performance of multi-pass serpentine flow-fields for cooling plates in polymer electrolyte membrane fuel cells. Journal of Power Sources, 2009. 194(2): p. 697-703.
[12] Kurnia, J.C., A.P. Sasmito, and A.S. Mujumdar, Numerical investigation of laminar heat transfer performance of various cooling channel designs. Applied Thermal Engineering, 2011. 31(6–7): p. 1293-1304.
[13] Shah, R.K. and A.L. London, Advances in heat transfer, supplement 1, laminar flow forced convection in ducts. 1978, New York: Academic Press.
[14] Kakaç, S., R.K. Shah, and W. Aung, Handbook of single-phase convective heat transfer. 1987: Wiley New York et al.
[15] Lee, P.-S., S.V. Garimella, and D. Liu, Investigation of heat transfer in rectangular microchannels. International Journal of Heat and Mass Transfer, 2005. 48(9): p. 1688-1704.
[16] Geyer, P.E., D.F. Fletcher, and B.S. Haynes, Laminar flow and heat transfer in a periodic trapezoidal channel with semi-circular cross-section. International Journal of Heat and Mass Transfer, 2007. 50(17–18): p. 3471-3480.
[17] Rosaguti, N.R., D.F. Fletcher, and B.S. Haynes, A general implementation of the H1 boundary condition in CFD simulations of heat transfer in swept passages. International Journal of Heat and Mass Transfer, 2007. 50(9–10): p. 1833-1842.
[18] Wibulswas, P., Laminar-flow heat-transfer in non-circular ducts. 1966, University of London.
[19] Schmidt, F.W. and M.E. Newell, Heat transfer in fully developed laminar flow through rectangular and isosceles triangular ducts. International Journal of Heat and Mass Transfer, 1967. 10(8): p. 1121-1123.
[20] Aparecido, J.B. and R.M. Cotta, Thermally developing laminar flow inside rectangular ducts. International Journal of Heat and Mass Transfer, 1990. 33(2): p. 341-347.
[21] Shah, R.K., Laminar flow friction and forced convection heat transfer in ducts of arbitrary geometry. International Journal of Heat and Mass Transfer, 1975. 18(7–8): p. 849-862.
[22] Lee, P.-S. and S.V. Garimella, Thermally developing flow and heat transfer in rectangular microchannels of different aspect ratios. International Journal of Heat and Mass Transfer, 2006. 49(17–18): p. 3060-3067.
[23] Dharaiya, V.V. and S.G. Kandlikar, Numerical Investigation of Heat Transfer in Rectangular Microchannels Under H2 Boundary Condition During Developing and Fully Developed Laminar Flow. Journal of Heat Transfer, 2011. 134(2): p. 020911-020911.
[24] Rostami, A.A. and S.S. Mortazavi, Analytical prediction of Nusselt number in a simultaneously developing laminar flow between parallel plates. International Journal of Heat and Fluid Flow, 1990. 11(1): p. 44-47.
[25] Silva, J.B.C., R.M. Cotta, and J.B. Aparecido, Analytical solutions to simultaneously developing laminar flow inside parallel-plate channels. International Journal of Heat and Mass Transfer, 1992. 35(4): p. 887-895.
[26] Spiga, M. and G.L. Morini, Nusselt numbers in laminar flow for H2 boundary conditions. International Journal of Heat and Mass Transfer, 1996. 39(6): p. 1165-1174.
[27] Spiga, M. and G.L. Morini, Laminar heat transfer between parallel plates as the limiting solution for the rectangular duct. International Communications in Heat and Mass Transfer, 1996. 23(4): p. 555-562.
[28] Savino, J.M. and R. Siegel, Laminar forced convection in rectangular channels with unequal heat addition on adjacent sides. International Journal of Heat and Mass Transfer, 1964. 7(7): p. 733-741.
[29] Gilbert, D.E., R.W. Leay, and H. Barrow, Theoretical analysis of forced laminar convection heat transfer in the entrance region of an elliptic duct. International Journal of Heat and Mass Transfer, 1973. 16(7): p. 1501-1503.
[30] Abdel-Wahed, R.M., A.E. Attia, and M.A. Hifni, Experiments on laminar flow and heat transfer in an elliptical duct. International Journal of Heat and Mass Transfer, 1984. 27(12): p. 2397-2413.
[31] Iqbal, M., A.K. Khatry, and B.D. Aggarwala, On the second fundamental problem of combined free and forced convection through vertical noncircular ducts. Applied Scientific Research, 1972. 26(1): p. 183-208.
[32] Yilmaz, T. and E. Cihan, General equation for heat transfer for laminar flow in ducts of arbitrary cross-sections. International Journal of Heat and Mass Transfer, 1993. 36(13): p. 3265-3270.
[33] Dean, W., XVI. Note on the motion of fluid in a curved pipe. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1927. 4(20): p. 208-223.
[34] Dennis, S. and M. NG, Dual solutions for steady laminar flow through a curved tube. The Quarterly Journal of Mechanics and Applied Mathematics, 1982. 35(3): p. 305-324.
[35] Wang, L. and F. Liu, Forced convection in slightly curved microchannels. International Journal of Heat and Mass Transfer, 2007. 50(5–6): p. 881-896.
[36] Wang, T.-S. and M.K. Chyu, Heat convection in a 180-deg turning duct with different turn configurations. Journal of Thermophysics and Heat Transfer, 1994. 8(3): p. 595-601.
[37] Sailesh Chintada, K.-H.K.N.K.A., Heat transfer in 3-D serpentine channels with right-angle turns. Numerical Heat Transfer, Part A: Applications, 1999. 36(8): p. 781-806.
[38] Rosaguti, N.R., D.F. Fletcher, and B.S. Haynes, Laminar flow and heat transfer in a periodic serpentine channel. Chemical engineering & technology, 2005. 28(3): p. 353-361.
[39] Aref, H., Stirring by chaotic advection. Journal of fluid mechanics, 1984. 143: p. 1-21.
[40] Zheng, Z., D.F. Fletcher, and B.S. Haynes, Chaotic advection in steady laminar heat transfer simulations: Periodic zigzag channels with square cross-sections. International Journal of Heat and Mass Transfer, 2013. 57(1): p. 274-284.
[41] Zheng, Z., D.F. Fletcher, and B.S. Haynes, Laminar heat transfer simulations for periodic zigzag semicircular channels: Chaotic advection and geometric effects. International Journal of Heat and Mass Transfer, 2013. 62(0): p. 391-401.
[42] Zheng, Z., D.F. Fletcher, and B.S. Haynes, Transient laminar heat transfer simulations in periodic zigzag channels. International Journal of Heat and Mass Transfer, 2014. 71(0): p. 758-768.
[43] Gupta, R., et al., Thermohydraulic performance of a periodic trapezoidal channel with a triangular cross-section. International Journal of Heat and Mass Transfer, 2008. 51(11–12): p. 2925-2929.
[44] Rosaguti, N.R., D.F. Fletcher, and B.S. Haynes, Low-Reynolds number heat transfer enhancement in sinusoidal channels. Chemical Engineering Science, 2007. 62(3): p. 694-702.
[45] Guzmán, A.M., et al., Heat transfer enhancement by flow bifurcations in asymmetric wavy wall channels. International Journal of Heat and Mass Transfer, 2009. 52(15–16): p. 3778-3789.
[46] Rosaguti, N.R., D.F. Fletcher, and B.S. Haynes, Laminar flow and heat transfer in a periodic serpentine channel with semi-circular cross-section. International Journal of Heat and Mass Transfer, 2006. 49(17–18): p. 2912-2923.
[47] Zhang, G. and S.G. Kandlikar, A critical review of cooling techniques in proton exchange membrane fuel cell stacks. International Journal of Hydrogen Energy, 2012. 37(3): p. 2412-2429.
[48] Dittus, F.W. and L.M.K. Boelter, Heat transfer in automobile radiators of the tubular type. International Communications in Heat and Mass Transfer, 1985. 12(1): p. 3-22.
[49] Gnielinski, V., New equations for heat and mass transfer in the turbulent flow in pipes and channels. NASA STI/Recon Technical Report A, 1975. 75: p. 22028.
[50] ANSYS, I., ANSYS Fluent User’s Guide. 2014.
[51] Leonard, B.P., A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Computer Methods in Applied Mechanics and Engineering, 1979. 19(1): p. 59-98.
[52] Bejan, A., Convection heat transfer. 2013: John wiley & sons.