KHẢO SÁT ĐA DẠNG DI TRUYỀN VÀ TÍNH GÂY BỆNH CỦA NẤM Corynespora cassiicola (Berk. Curt.) Wei PHÂN LẬP TỪ CÂY CAO SU VÀ CÁC CÂY KÝ CHỦ KHÁC

National Chung Hsing University Department of Mechanical Engineering Master Thesis Heat Transfer Effectiveness and Exergy Recovery Effectiveness of a Spiral Heat Exchanger Advisor: Jung-Yang San Student: Nguyen Duc Khuyen 16th June 2011 Acknowledgement It is my immense pleasure to thank all the people who have helped and inspired me during my two-year master's study at National Chung-Hsing University I would like to express my deep and sincere gratitude to my thesis advisor, Professor Jung-Yang San for his guidance and support during my research and study With his inspiration, I was able to overcome the problems that I faced during my two year study in Taiwan I sincerely thank all the Professors and members in the Departments of Mechanical Engineering of NCHU, especially I am obliged to Professor Jau-Huai Lu, Professor Cheng-Hsiung Kuo, Professor Jerry-Min Chen, Professor JauLiang Chen, Professor Shi-Chang Huang and Professor Quen-Yaw Sheen for teaching, helping and assisting me in many different ways My time at NCHU was largely made enjoyable due to my friends here, who in a short time became a part of my life I thank my fellow labmates and friends: Yuan-Kuei Peng, Hui-Ping Shen, Chih-Hsiang Hsu, Shen-Yang Huang, Ding-Wei Zhen, Thac Dang, Tung Nguyen, Dony Mathew, You-Chen Huang for their help and for all the good times, we had in the last two years Finally I would like to thank my family for all their love and undying support I wish to thank my wife, Tuan Le, whose support was endless and selfless I feel very fortunate to have her as my best friend and wife Thanks to my son, Tuan Linh, for giving me happiness and joy Nguyen Duc Khuyen ( i ) Abstract In the present study, a numerical method was developed to investigate the heat transfer performance of a spiral heat exchanger In the spiral heat exchanger, two long metal strips are wound concentrically to create hot-flow channel and coldflow channel The flow of the two fluids through a spiral heat exchanger was considered counter-current, the hot-flow circulates counter-clockwise and the coldflow circulates clockwise The upper surface, lower surface and outer-most side of the spiral heat exchanger were assumed to be insulated A heat transfer effectiveness (  ) and an exergy recovery effectiveness (ex) were defined and evaluated based on the calculated non-dimensional temperatures of the two counter-flow fluids in the heat exchanger At small NTU value, the  value initially increases with the NTU value; while at higher NTU values, after reaching the maximum heat transfer effectiveness, the  value starts to slightly decrease For a set of Nt and NTU values, the heat transfer effectiveness reaches a minimum value at C*=1.0 As the C* approaches zero or infinity, the  value would approach the maximum Conversely, for a set of NTU, Nt,  c* ,  h* , and FP ,total values, as the C* approaches zero or infinity, the exergy recovery effectiveness of the spiral heat exchanger is at the minimum The exergy recovery effectiveness reaches a maximum as the C* value nears 1.0 The result also shows that, at small values of Nt (Nt < 40), the  value and the ex value slightly increase with the Nt value; while these two values remain almost the same when the number of turns is larger than 40 turns Keywords: exergy, spiral heat exchanger, heat transfer effectiveness, exergy recovery effectiveness ii Table of contents Acknowledgement i Abstract ii Table of contents iii List of Tables and Figures v Nomenclature vii Chapter Introduction 1.1 Preface 1.2 Spiral heat exchanger and main applications 1.3 Survey of literature 1.4 Objective of the Thesis 12 Chapter Energy Equations for a Spiral Heat Exchanger 13 2.1 Length of a Curve in Polar Coordinates 13 2.2 Length of Archimedes’ spiral in polar Coordinates 14 2.3 Geometry of a spiral heat exchanger 17 2.4 Mathematical modeling 20 2.4.1 Energy balance for hot flow 20 2.4.2 Energy balance for cold flow 22 2.4.3 Dimensionless energy equations 24 2.5 Heat transfer effectiveness of heat exchanger 28 Chapter Numerical Analysis 30 3.1 The case for hot-flow capacity rate less than cold flow capacity rate 30 iii 3.1.1 Finite-difference equations for the hot flow: 30 3.1.2 Finite-difference equations for the cold flow: 31 3.2 The case for hot-flow capacity rate lager than cold flow capacity rate 33 3.2.1 Finite-difference equations for the hot flow: 33 3.2.2 Finite-difference equations for the cold flow: 35 3.3 Computer simulation program 36 3.4 Error Analysis of numerical scheme 37 3.4.1 Equation for checking the accuracy of numerical scheme 37 3.4.2 Error analysis of numerical scheme 38 3.5 Results of heat transfer analysis 39 Chapter Exergy Analysis 45 4.1 General form of exergy change rate in a flow 45 4.1.1 Concept of exergy analysis 45 4.1.2 Exergy change rate for ideal gas flow 46 4.1.3 Exergy change rate for incompressible flow 47 4.1.4 General form of exergy change rate in a flow 48 4.2 Exergy analysis for the spiral heat exchanger 49 4.3 Exergy recovery effectiveness 50 4.4 Dimensionless exergy recovery effectiveness equations 56 4.4 Results of exergy analysis and discussion 57 Chapter Conclusions 61 References 63 iv List of Figures Figure 2.1 Length of a Curve in Polar Coordinates 67 Figure 2.2 Archimedes’ spiral 67 Figure 2.3 Archimedes’ spiral is started at   0 68 Figure 2.4 The constructing principle of a spiral heat exchanger 68 Figure 2.5 Schematic of a spiral heat exchanger 69 Figure 2.6 One side of spiral heat exchanger 69 Figure 2.7 Infinitesimal segment dof the spiral heat exchanger 70 Figure 2.8 Control volume of hot flow 70 Figure 2.9 Control volume of cold flow 71 Figure 3.1 Flow chart of the program 72 Figure 3.2 The relationship between NTU and  at Nt=3 73 Figure 3.3 The relationship between NTU and  at Nt=6 74 Figure 3.4 The relationship between NTU and  at Nt=10 75 Figure 3.5 The relationship between NTU and  at Nt=20 76 Figure 3.6 The relationship between NTU and  at Nt=40 77 Figure 3.7 The relationship between NTU and  at Nt=80 78 Figure 3.8 The relationship between NTU and  at Nt=3 79 Figure 3.9 The relationship between NTU and  at Nt=10 80 Figure 3.10 Comparison of heat transfer effectiveness versus NTU at Nt=8 81 Figure 3.11 Comparison of heat transfer effectiveness at C=1.0 82 Figure 3.12 Comparison between spiral heat exchanger at Nt=3 and counter-flow heat exchanger 83 v Figure 3.13 Comparison between spiral heat exchanger at Nt=10 and counter-flow heat exchanger 84 Figure 3.14 Comparison between spiral heat exchanger at Nt=20 and counter-flow heat exchanger 85 Figure 3.15 Comparison between spiral heat exchanger at Nt=40 and counter-flow heat exchanger 86 Figure 3.16 Temperature distributions at Nt=10, C*=1.0 and NTU=5.0 87 Figure 3.17 Temperature distributions at Nt=10, C*=1.0 and NTU=10 88 Figure 3.18 Temperature distributions at Nt=10, C*=1.0 and NTU=5.0 89 Figure 3.19 Temperature distributions at Nt=10, C*=2.0 and NTU=5.0 90 Figure 4.1 The relationship between C* and ex at FP ,total  0.0 ,  h*  1.2 , Nt=3 91 Figure 4.2 The relationship between C* and ex at FP ,total  0.0 ,  h*  1.2 , Nt=10 92 Figure 4.3 Effect of  h* on ex at FP ,total  0.0 and Nt=10 93 Figure 4.4 Effect of Nt on ex at FP ,total  0.0 and  h*  1.2 94 Figure 4.5 Effect of  h* on ex,max at Nt=3 95 Figure 4.6 Effect of  c* on ex,max at Nt=10 96 Figure 4.7 Effect of FP ,total on ex at  h*  1.2 and Nt=10 97 Figure 4.8 Effect of FP ,total on ex at  h*  2.4 and Nt=10 98 vi Nomenclature a constant for the Archimedean spiral, m At total heat transfer area of heat exchanger, m2 C  p ) /(mc  p ) max ratio of capacity rates, (mc C*  p )h /(mc  p )c modified ratio of capacity rates, (mc C1 NTU / L* cp constant-pressure specific heat, kJ/kg-K cv constant-volume specific heat, kJ/kg-K EX rate of exergy, W FP pressure-drop factor FP ,total overall pressure drop factor h specific enthalpy, kJ/kg H height of channel or enthalpy, m or kJ H0 enthalpy of fluid at ambient state, kJ k cp / cv L length of a spiral channel, m L* non-dimensional length, 2L /(2)2 a m mass flowrate, kg/s n number of segments NTU  p ) number of transfer units, UA t /(mc vii NTUh  p )h modified number of transfer units, UA t /(mc Nt total number of turns P pressure, Pa P pressure drop, Pa Q heat transfer rate, W r radius of spiral, m r0 minimum radius of spiral, m rc maximum radius of spiral, m rd maximum radius of dash-line spiral, m rs maximum radius of solid-line spiral, m R gas constant, kJ/kg-K s specific entropy, kJ/kg-K S total entropy, kJ/K S0 entropy of fluid at ambient state, kJ/K T temperature, K T0 ambient temperature or dead-state temperature, K u specific internal energy, J/kg U overall heat transfer coefficient, W/m2-K v specific volume, m3/kg W width of hot or cold flow channel, m Greek symbols heat transfer effectiveness viii Heat Transfer Effectiveness () 0.8 C=1.0 C=0.75 C=0.5 C=0.25 C0 0.6 0.4 0.2  *0 = spiral counter-flow Nt = 10 C = (mcp)min/(mcp)max 0 10 NTU Figure 3.13 Comparison between spiral heat exchanger at Nt=10 and counter-flow heat exchanger 84 Heat Transfer Effectiveness () 0.8 C=1.0 C=0.75 C=0.5 C=0.25 C0 0.6 0.4 0.2 spiral  *0 = counter-flow Nt = 20 C = (mcp)min/(mcp)max 0 10 NTU Figure 3.14 Comparison between spiral heat exchanger at Nt=20 and counter-flow heat exchanger 85 Heat Transfer Effectiveness () 0.8 C=1.0 C=0.75 C=0.5 C=0.25 C0 0.6 0.4 0.2 spiral Nt = 40 counter-flow C = (mcp)min/(mcp)max 0 10 NTU Figure 3.15 Comparison between spiral heat exchanger at Nt=40 and counter-flow heat exchanger 86 1 Dimensionless Temperature () 0.8 0.6 0.4 NTU=5 C=1.0  *0 = 0.2 Nt =10 C* = (mcp)h/(mcp)c hot-flow cold-flow 1: inlet half-turn 2: intermittent turns 3: outer-most half-turn i 10 Turns Figure 3.16 Temperature distributions at Nt=10, C*=1.0 and NTU=5.0 87 1 Dimensionless Temperature () 0.8 0.6 0.4 NTU=10 C=1.0  *0 = Nt =10 0.2 C* = (mcp)h/(mcp)c hot-flow cold-flow 1: inlet half-turn 2: intermittent turns 3: outer-most half-turn i 10 Turns Figure 3.17 Temperature distributions at Nt=10, C*=1.0 and NTU=10 88 hot-flow cold-flow 1: inlet half-turn 2: intermittent turns 3: outer-most half-turn NTU=5 C*=0.5 Dimensionless Temperature () 0.8  *0 = Nt =10 0.6 C* = (mcp)h/(mcp)c 0.4 0.2 i 10 Turns Figure 3.18 Temperature distributions at Nt=10, C*=1.0 and NTU=5.0 89 1 Dimensionless Temperature () 0.8 0.6 0.4 NTU=5 C*=2.0  *0 = Nt =10 0.2 C* = (mcp)h/(mcp)c hot-flow cold-flow 1: inlet half-turn 2: intermittent turns 3: outer-most half-turn i 10 Turns Figure 3.19 Temperature distributions at Nt=10, C*=2.0 and NTU=5.0 90 Exergy Recovery Effectiveness (ex) FP,total=0.0  *c=1.0  *h=1.2 Nt=3 0.8  *0 = 0.6 C  *=2.0 C  *=4.0 C  *=1 C  *=0.5 0.4 C  *=0.25 0.2 C  * 0 10 NTU Figure 4.1 The relationship between C* and ex at FP ,total  0.0 ,  h*  1.2 , Nt=3 91 Exergy Recovery Effectiveness (ex) FP,total=0.0  *c=1.0  *h=1.2 Nt=10 0.8 C  *=1  *0 = C  *=2.0 C  *=4.0 0.6 C  *=0.5 0.4 C  *=0.25 0.2 C  * 0 10 NTU Figure 4.2 The relationship between C* and ex at FP ,total  0.0 ,  h*  1.2 , Nt=10 92 Exergy Recovery Effectiveness (ex) 0.8 Nt =10 FP,total=0.0  *c=1.0  *h=1.2  *h=2.4  *0 = 1: NTU=0.5 2: NTU=1.0 3: NTU=2.0 4: NTU=8.0 0.6 0.4 0.2 0.1 C* Figure 4.3 Effect of  h* on ex at FP ,total  0.0 and Nt=10 93 10 Exergy Recovery Effectiveness (ex) FP,total=0  *c=1.0  *h=1.2 Nt =40 Nt =10 Nt =3  *0 = 0.8 1: NTU=0.5 2: NTU=1.0 3: NTU=2.0 4: NTU=8.0 0.6 0.4 0.2 0.1 C* Figure 4.4 Effect of Nt on ex at FP ,total  0.0 and  h*  1.2 94 10 0.8 FP,total=0.0 Nt =3  *0 =  *c=1.0  *h=1.2  *h=2.4 ex,max 0.6 0.4 0.2 0 NTU Figure 4.5 Effect of  h* on ex,max at Nt=3 95 10 FP,total=0.0 Nt =10  *0 =  *h=2.4  *c=1.0  *c=1.2 0.8 ex,max 0.6 0.4 0.2 0 NTU Figure 4.6 Effect of  c* on ex,max at Nt=10 96 10 FP,total=0.0001 FP,total=0.001 Nt =10  = Exergy Recovery Effectiveness (ex) *  *c=1.0  *h=1.2 0.8 1: NTU=0.5 2: NTU=1.0 3: NTU=2.0 4: NTU=8.0 0.6 0.4 0.2 0.1 C* Figure 4.7 Effect of FP ,total on ex at  h*  1.2 and Nt=10 97 10 Exergy Recovery Effectiveness (ex) FP,total=0.0001 FP,total=0.001 0.8  =1.0  =2.4 1: NTU=0.5 2: NTU=1.0 3: NTU=2.0 4: NTU=8.0 Nt =10  *0 = * c * h 0.6 0.4 0.2 0.1 C* Figure 4.8 Effect of FP ,total on ex at  h*  2.4 and Nt=10 98 10 ... her as my best friend and wife Thanks to my son, Tuan Linh, for giving me happiness and joy Nguyen Duc Khuyen ( i ) Abstract In the present study, a numerical method was developed to investigate... thermal thermal exergy x Chapter Introduction 1.1 Preface In this modern world, energy plays an important role in maintaining or producing different kind of products for the benefit of mankind Human... exchanger A set of entropy production (Ns) equation for some particular cases was derived in terms of relevant dimensionless parameters The result shows that, the entropy production decreases 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