Heat Exchanger Design Handbook Edgar Miller Heat Exchanger Design Handbook "This page is Intentionally Left Blank" Heat Exchanger Design Handbook Edited by Edgar Miller Heat Exchanger Design Handbook Edited by Edgar Miller The publisher’s policy is to use permanent paper from mills that operate a sustainable forestry policy. Furthermore, the publisher ensures that the text paper and cover boards used have met acceptable environmental accreditation standards. Trademark Notice: Registered trademark of products or corporate names are used only for explanation and identification without intent to infringe. This book contains information obtained from authentic and highly regarded sources. Copyright for all individual chapters remain with the respective authors as indicated. A wide variety of references are listed. Permission and sources are indicated; for detailed attributions, please refer to the permis- sions page. Reasonable efforts have been made to publish reliable data and information, but the au- thors, editors and publisher cannot assume any responsibility for the validity of all materials or the consequences of their use. Copyright of this ebook is with University Publications, rights acquired from the original print publisher, NY Research Press. Published by University Publications, 5 Penn Plaza, 19th Floor, New York, NY 10001, USA © 2018 University Publications International Standard Book Number: 978-1-9789-1213-7 Contents Preface VII Part 1 General Aspects 1 Chapter 1 Thermodynamic Optimization 3 M.M. Awad and Y.S. Muzychka Chapter 2 Analytical Solution of Dynamic Response of Heat Exchanger 53 D. Gvozdenac Chapter 3 Development of High Efficiency Two-Phase Thermosyphons for Heat Recovery 79 Ignacio Carvajal-Mariscal, Florencio Sanchez-Silva and Georgiy Polupan Chapter 4 Impact of a Medium Flow Maldistribution on a Cross-Flow Heat Exchanger Performance 99 Tomasz Bury Chapter 5 Numerical Analysis of the Structural Stability of Heat Exchangers – The FEM Approach 125 Agnieszka A. Chudzik Chapter 6 Control of LNG Pyrolysis and Application to Regenerative Cooling Rocket Engine 147 R. Minato, K. Higashino, M. Sugioka and Y. Sasayama Chapter 7 Self-Heat Recuperation: Theory and Applications 169 Yasuki Kansha, Akira Kishimoto, Muhammad Aziz and Atsushi Tsutsumi ________________ WORLD TECHNOLOGIES ________________ Part 2 Micro-Channels and Compact Heat Exchangers 187 Chapter 8 Compact Heat Exchange Reformer Used for High Temperature Fuel Cell Systems 189 Huisheng Zhang, Shilie Weng and Ming Su Chapter 9 Microchannel Simulation 217 Mohammad Hassan Saidi, Omid Asgari and Hadis Hemati Chapter 10 Single-Phase Heat Transfer and Fluid Flow Phenomena of Microchannel Heat Exchangers 249 Thanhtrung Dang, Jyh-tong Teng, Jiann-cherng Chu, Tingting Xu, Suyi Huang, Shiping Jin and Jieqing Zheng Chapter 11 Heat Exchangers for Thermoelectric Devices 289 David Astrain and Álvaro Martínez Part 3 Helical Coils and Finned Surfaces 309 Chapter 12 Fin-Tube Heat Exchanger Optimization 311 Piotr Wais Chapter 13 Thermal Design of Cooling and Dehumidifying Coils 335 M. Khamis Mansour and M. Hassab Chapter 14 Helically Coiled Heat Exchangers 363 J. S. Jayakumar Permissions List of Contributors VI Contents ________________ WORLD TECHNOLOGIES ________________ Preface The contents of this book offer extensive information on specific cases of heat exchangers. The selection was directed by seeking future prospects of applied research and industry, particularly aiming on the effective use and conversion energy in shifting environment. Besides the questions of thermodynamic basics, the contributions of this book are thematically grouped which presents various critical issues grouped under three sections, namely general aspects, micro-channels and compact heat exchangers, and plate heat exchangers. The book is not necessarily focused to be a fundamental source of the knowledge in the area it covers, but rather serves as a mentor while practising expansive solutions of particular technical issues which are faced by engineers and technicians occupied in research and development in the subjects of heat transfer and heat exchangers. This book unites the global concepts and researches in an organized manner for a comprehensive understanding of the subject. It is a ripe text for all researchers, students, scientists or anyone else who is interested in acquiring a better knowledge of this dynamic field. I extend my sincere thanks to the contributors for such eloquent research chapters. Finally, I thank my family for being a source of support and help. Editor ________________ WORLD TECHNOLOGIES ________________ "This page is Intentionally Left Blank" ________________ WORLD TECHNOLOGIES ________________ Part 1 General Aspects ________________ WORLD TECHNOLOGIES ________________ "This page is Intentionally Left Blank" ________________ WORLD TECHNOLOGIES ________________ 1 Thermodynamic Optimization* M.M. Awad1 and Y.S. Muzychka2 1Mechanical Power Engineering Department, Faculty of Engineering, Mansoura University, 2Faculty of Engineering and Applied Science, St. John's, NL, Memorial University of Newfoundland, 1Egypt 2Canada 1. Introduction Second law analysis in the design of thermal and chemical processes has received considerable attention since 1970s. For example, Gaggioli and Petit (1977) reviewed the first and second laws of thermodynamics as an introduction to an explanation of the thesis that energy analyses of plants, components, and processes should be made by application of the second law that deals with the availability of energy or the potential energy. They illustrated their methodology suggested by applying it to an analysis of the Koppers-Totzek gasification system. Optimization of heat exchangers based on second-law rather than first- law considerations ensures that the most efficient use of available energy is being made. Second-law analysis has affected the design methodology of different heat and mass transfer systems to minimize the entropy generation rate, and so to maximize system available work. Many researchers considered these processes in terms of one of two entities: exergy (available energy) and irreversibility (entropy production). For instance, McClintock (1951) described irreversibility analysis of heat exchangers, designed to transfer a specified amount of heat between the fluid streams. He gave explicit equations for the local optimum design of fluid passages for either side of a heat exchanger. To the knowledge of authors, McClintock (1951) was the first researcher who employed the irreversibility concept for estimating and minimizing the usable energy wasted in heat exchangers design. Bejan (1977) introduced the concept of designing heat exchangers for specified irreversibility rather than specified amount of heat transferred. Many authors used this technique in the field of cryogenic engineering (Bejan and Smith (1974, 1976), Bejan (1975), and Hilal and Boom (1976)). One of the first examinations of entropy generation in convective heat transfer was conducted by Bejan (1979) for a number of fundamental applications. Much of the early * The part of this chapter was presented by Y. S. Muzychka in fall 2005 as Part III during the short course: Adrian Bejan, Sylvie Lorente, and Yuri Muzychka, Constructal Design of Porous and Complex Flow Structures, Memorial University of Newfoundland, Faculty of Engineering and Applied Science, St. John's, NL, Canada, September 21-23, 2005. ________________ WORLD TECHNOLOGIES ________________ work is well documented in his books (Bejan, 1982a and 1996a). Since the publication of (Bejan, 1996a), entropy generation in internal structure has been examined by numerous researchers. In this section, we will examine these studies that include the optimization of heat exchangers, and enhancement of internal flows. Also, we will proceed to develop some of the basic principles and examine selected results from the published literature. 1.1 Optimization of heat exchangers In the past thirty five years, much work relating to heat exchanger design based on the second law of thermodynamics was presented by researchers (Bejan, 1988). Heat exchangers have often been subjected to thermodynamic optimization (or entropy generation minimization) in isolation, i.e., removed from the larger installation, which uses them. Examples include the parallel flow, counterflow, crossflow, and phase-change heat exchanger optimizations. We will talk in details about this in this section. Bejan (1977) presented a heat exchanger design method for fixed or for minimum irreversibility (number of entropy generation units, Ns). The researcher obtained the number of entropy generation units (Ns) by dividing entropy generation rate by the smallest heat capacity rate of the fluids. The value of Ns can range between 0-∞. The heat exchanger would have a better performance if the entropy generation was at its minimum (Ns0). This dimensionless number can clearly express how a heat exchanger performance is close to an ideal heat exchanger in terms of thermal losses. He showed that entropy generation in a heat exchanger is due to heat transfer through temperature gradient and fluid friction. In contrast with traditional design procedures, the amount of heat transferred between streams and the pumping power for every side became outputs of the Ns design approach. Also, he proposed a methodology for designing heat exchangers based on entropy generation minimization. To illustrate the use of his method, the paper developed the design of regenerative heat exchangers with minimum heat transfer surface and with fixed irreversibility Ns. The thermal design of counterflow heat exchangers for gas-to-gas applications is based on the thermodynamic irreversibility rate or useful power no longer available as a result of heat exchanger frictional pressure drops and stream-to-stream temperature differences. The irreversibility (entropy production) concept establishes a direct relationship between the heat exchanger design parameters and the useful power wasted due to heat exchanger nonideality. Bejan (1978) demonstrated the use of irreversibility as a criterion for evaluation of the efficiency of a heat exchanger. The researcher minimized the wasted energy using the optimum design of fluid passages in a heat exchanger. He studied the interrelationship between the losses caused by heat transfer across the stream-to-stream due to differences in temperatures and losses caused by fluid friction. He obtained the following relation for the entropy generation rate per unit length as follows: . . . 2 2 0 1 1 gen dS dq dq m dP T m dP T T T dx T dx dx T dx dx T T T T                                        (1) 4 Heat Exchanger Design Handbook ________________ WORLD TECHNOLOGIES ________________ The first term in expression (1) is the entropy production contribution due to fluid friction in the fluid duct. The second term in expression (1) represents the contribution due to heat transfer across the wall-fluid temperature difference. These two contributions were strongly interrelated through the geometric characteristics of the heat exchanger. It should be noted that the use of density () instead of the inverse of specific volume (v) in the first term on the right hand side. Also, the denominator of the second term on the right hand side was simplified by assuming that the local temperature difference (T) was negligible compared with the local absolute temperature (T). Heat transfer losses could be reduced by increasing the heat transfer area, but in this case pressure drops in the channels increased. Both heat transfer losses and frictional pressure drops in channels determined the irreversibility level of heat exchanger. A remarkable feature of Eq. (1) and of many like it for other simple devices is that a proposed design change (for instance, making the passage narrower) induces changes of opposite signs in the two terms of the expression. Then, an optimal trade-off exists between the fluid friction irreversibility and the heat transfer irreversibility contributions, an optimal design for which the overall measure of exergy destruction is minimum, while the system continues to serve its specified function. In order to illustrate this trade-off, use the definition of friction factor (f), Stanton number (St), mass flux (G), Reynolds number (Re), and hydraulic diameter (dh): 2 2 h d dP f dx G          (2) 1 p dq St dx p Tc G   (3) . m G A  (4) Re h Gd   (5) 4 h A d p  (6) In Eq. (3), the quantity (dq/dx)/(pT) is better known as the average heat transfer coefficient. The entropy generation rate, Eq. (1) becomes 3 . . 2 . 2 2 2 2 4 gen h h p dS dq m f d dx dx Td A T mc St          (7) Where heat transfer rate per unit length and mass flow rate are fixed. The geometric configuration of the exchanger passage has two degrees of freedom, the perimeter (p) and the cross-sectional area (A), or any other pair of independent parameters, like (Re; dh) or (G; 5 Thermodynamic Optimization ________________ WORLD TECHNOLOGIES ________________ dh). If the passage is a straight pipe with circular cross-section, p and A are related through the pipe inner diameter d that is the only degree of freedom left in the design process. Writing 2 , /4, h d d A d and p d      (8) Equation (7) becomes 3 . . 2 2 2 2 5 32 gen h dS dq m f d dx dx T kNu Td            (9) Where Re = 4 m /d. The Nusselt number (Nu) definition, and the relation between Nu, St, Re, and the Prandtl number (Pr = /) .Re.Pr .. av h h d Nu St St Pe k    (10) Introducing two classical correlations for fully developed turbulent pipe flow (Bejan, 1993), 0.8 0.4 4 0.023Re Pr (0.7 Pr 160 : Re 10 ) Nu     (11) -0.2 4 6 0.046 Re (10 Re 10 ) f    (12) and combining them with Eq. (9), yields an expression for exergy destruction, which depends only on Re. Differentiating the exergy destruction with respect to the Reynolds number (Re) and equaling the result with zero, we find that the entropy generation rate is minimized when the Reynolds number (or pipe diameter) reaches the optimal value (Bejan, 1982a) -0.071 0.358 opt Re 2.023Pr B  (13) Equation (13) shows how to select the optimal pipe size for minimal irreversibility. Parameter B is a heat and fluid flow ‘‘duty’’ parameter that accounts for the constraints of heat transfer rate per unit length, and mass flow rate: . 5/2 1/2 ( ) dq p B m dx kT         (14) Additional results may be obtained for non-circular ducts using the appropriate expressions for the geometry A and p, and appropriate models for heat transfer and friction coefficients. The Reynolds number (Re) effect on the exergy destruction can be expressed in relative terms as . 0.8 4.8 . min / Re Re 0.856 0.144 Re Re ( / ) gen opt opt gen dS dx dS dx                    (15) 6 Heat Exchanger Design Handbook ________________ WORLD TECHNOLOGIES ________________