FUNDAMENTALS OF HEAT EXCHANGER DESIGN

(1)

(2)

FUNDAMENTALS OF HEAT

EXCHANGER DESIGN

(3)

FUNDAMENTALS OF

HEAT EXCHANGER

DESIGN

Ramesh K. Shah

Rochester Institute of Technology, Rochester, New York

Formerly at Delphi Harrison Thermal Systems, Lockport, New York

Dusˇan P. Sekulic´

University of Kentucky, Lexington, Kentucky

(4)

This book is printed on acid-free paper._*1

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008,

e-mail: permcoordinator@wiley.com.

Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002.

Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. For more information about Wiley products, visit our web site at www.wiley.com

Library of Congress Cataloging-in-Publication Data: Shah, R. K.

Fundamentals of heat exchanger design / Ramesh K. Shah, Dusˇan P. Sekulic´. p. cm.

Includes index.

ISBN 0-471-32171-0

1. Heat exchangers–Design and construction. I. Sekulic´, Dusˇan P. II. Title. TJ263 .S42 2003

621.40205–dc21

2002010161 Printed in the United States of America

(5)

Over the past quarter century, the importance of heat exchangers has increased immen-sely from the viewpoint of energy conservation, conversion, recovery, and successful implementation of new energy sources. Its importance is also increasing from the stand-point of environmental concerns such as thermal pollution, air pollution, water pollu-tion, and waste disposal. Heat exchangers are used in the process, power, transportapollu-tion, air-conditioning and refrigeration, cryogenic, heat recovery, alternate fuels, and manufacturing industries, as well as being key components of many industrial products available in the marketplace. From an educational point of view, heat exchangers illustrate in one way or another most of the fundamental principles of the thermal sciences, thus serving as an excellent vehicle for review and application, meeting the guidelines for university studies in the United States and oversees. Signiﬁcant advances have taken place in the development of heat exchanger manufacturing technology as well as design theory. Many books have been published on the subject, as summarized in the General References at the end of the book. However, our assessment is that none of the books available seems to provide an in-depth coverage of the intricacies of heat exchanger design and theory so as to fully support both a student and a practicing engineer in the quest for creative mastering of both theory and design. Our book was motivated by this consideration. Coverage includes the theory and design of exchangers for many industries (not restricted to, say, the process industry) for a broader, in-depth foundation.

The objective of this book is to provide in-depth thermal and hydraulic design theory of two-ﬂuid single-phase heat exchangers for steady-state operation. Three important goals were borne in mind during the preparation of this book:

1. To introduce and apply concepts learned in ﬁrst courses in heat transfer, ﬂuid mechanics, thermodynamics, and calculus, to develop heat exchanger design theory. Thus, the book will serve as a link between fundamental subjects men-tioned and thermal engineering design practice in industry.

2. To introduce and apply basic heat exchanger design concepts to the solution of industrial heat exchanger problems. Primary emphasis is placed on fundamental concepts and applications. Also, more emphasis is placed on analysis and less on empiricism.

(15)

To provide comprehensive information for heat exchanger design and analysis in a book of reasonable length, we have opted not to include detailed theoretical derivations of many results, as they can be found in advanced convection heat transfer textbooks. Instead, we have presented some basic derivations and then presented comprehensive information through text and concise tables.

An industrial heat exchanger design problem consists of coupling component and system design considerations to ensure proper functioning. Accordingly, a good design engineer must be familiar with both system and component design aspects. Based on industrial experience of over three decades in designing compact heat exchangers for automobiles and other industrial applications and more than twenty years of teaching, we have endeavored to demonstrate interrelationships between the component and sys-tem design aspects, as well as between the needs of industrial and learning environments. Some of the details of component design presented are also based on our own system design experience.

Considering the fact that heat exchangers constitute a multibillion-dollar industry in the United States alone, and there are over 300 companies engaged in the manufacture of a wide array of heat exchangers, it is difficult to select appropriate material for an introductory course. We have included more material than is necessary for a one-semester course, placing equal emphasis on four basic heat exchanger types: shell-and-tube, plate, extended surface, and regenerator. The choice of the teaching material to cover in one semester is up to the instructor, depending on his or her desire to focus on specific exchanger types and specific topics in each chapter. The prerequisites for this course are first undergraduate courses in fluid mechanics, thermodynamics, and heat transfer. It is expected that the student is familiar with the basics of forced convection and the basic concepts of the heat transfer coefficient, heat exchanger effectiveness, and mean temperature difference.

(16)

develop good understanding of the intricacies of heat exchanger design after going through this material and prior to embarking on specialized work in their areas of greatest interest.

For the thermal design of a heat exchanger for an application, considerable intellec-tual effort is needed in selecting heat exchanger type and determining the appropriate value of the heat transfer coefficients and friction factors; a relatively small effort is needed for executing sizing and optimizing the exchanger because of the computer-based calculations. Thus, Chapters 7, 9, and 10 are very important, in addition to Chapter 3, for basic understanding of theory, design, analysis, and selection of heat exchangers.

Material presented in Chapters 11 through 13 is signiﬁcantly more interdisciplinary than the rest of the book and is presented here in a modiﬁed methodological approach. In Chapter 11 in particular, analytical modeling is used extensively. Readers will participate actively through a set of examples and problems thatextendthe breadth and depth of the material given in the main body of the text. A number of examples and problems in Chapter 11 require analytical derivations and more elaborate analysis, instead of illus-trating the topics with examples that favor only utilization of the formulas and comput-ing numerical values for a problem. The complexity of topics requires a more diverse approach to terminology, less routine treatment of established conventions, and a more creative approach to some unresolved dilemmas.

Because of the breadth of the subject, the coverage includes various design aspects and problems for indirect-contact two-fluid heat exchangers with primarily single-phase fluids on each side. Heat exchangers with condensing and evaporating fluids on one side can also be analyzed using the design methods presented as long as the thermal resistance on the condensing or evaporating side is small or the heat transfer coefficient on that side can be treated as a constant. Design theory for the following exchangers is not covered in this book, due to their complexity and space limitations: two-phase and multiphase heat exchangers (such as condensers and vaporizers), direct-contact heat exchangers (such as humidifiers, dehumidifiers, cooling towers), and multifluid and multistream heat exchangers. Coverage of mechanical design, exchanger fabrication methods, and manufacturing techniques is also deemed beyond the scope of the book.

Books by M. Jakob, D. Q. Kern, and W. M. Kays and A. L. London were considered to be the best and most comprehensive texts on heat exchanger design and analysis following World War II. In the last thirty or so years, a signiﬁcant number of books have been published on heat exchangers. These are summarized in the General References at the end of the book.

This text is an outgrowth of lecture notes prepared by the authors in teaching courses on heat exchanger design, heat transfer, and design and optimization of thermal systems to senior and graduate students. These courses were taught at the State University of New York at Buffalo and the University of Novi Sad, Yugoslavia. Over the past fifteen years or more, the notes of the first author have been used for teaching purposes at a number of institutions, including the University of Miami by Professor S. Kakaç, Rensselaer Polytechnic Institute by Professors A. E. Bergles and R. N. Smith, Rochester Institute of Technology by Professor S. G. Kandlikar, Rice University by Professor Y. Bayazitogˇlu, University of Tennessee Space Center by Dr. R. Schultz, University of Texas at Arlington by Professor A. Haji-Sheikh, University of Cincinnati by Professor R. M. Manglik, Northeastern University by Professor Yaman Yener, North Carolina A&T State University by Professor Lonnie Sharpe, Auburn

(17)

University by Dr. Peter Jones, Southern Methodist University by Dr. Donald Price, University of Tennessee by Professor Edward Keshock, and Gonzaga University by Professor A. Aziz. In addition, these course notes have been used occasionally at a number of other U.S. and foreign institutions. The notes of the second author have also been used for a number of undergraduate and graduate courses at Marquette University and the University of Kentucky.

The first author would like to express his sincere appreciation to the management of Harrison Thermal Systems, Delphi Corporation (formerly General Motors Corporation), for their varied support activities over an extended period of time. The second author acknowledges with appreciation many years of support by his colleagues and friends on the faculty of the School of Engineering, University of Novi Sad, and more recently at Marquette University and the University of Kentucky. We are also thankful for the support provided by the College of Engineering, University of Kentucky, for preparation of the first five and final three chapters of the book. A special word of appreciation is in order for the diligence and care exercised by Messrs. Dale Hall and Mack Mosley in preparing the manuscript and drawings through Chapter 5.

The first author is grateful to Professor A. L. London of Stanford University for teaching him the ABCs of heat exchangers and for providing constant inspiration and encouragement throughout his professional career and particularly during the course of preparation of this book. The first author would also like to thank Professors Sadik Kakaç of the University of Miami and Ralph Webb of the Pennsylvania State University for their support, encouragement, and involvement in many professional activities related to heat exchangers. The second author is grateful to his colleague and friend Professor B. S. Bacˇlic´, University of Novi Sad, for many years of joint work and teaching in the fields of heat exchanger design theory. Numerous discussions the second author have had with Dr. R. Gregory of the University of Kentucky regarding not only what one has to say about a technical topic, but in particular how to formulate it for a reader, were of a great help in resolving some dilemmas. Also, the continuous support and encouragement of Dr. Frederick Edeskuty of Los Alamos National Laboratory, and Professor Richard Gaggioli of Marquette University were immensely important to the second author in an effort to exercise his academic experience on both sides of the Atlantic Ocean. We appreciate Professor P. V. Kadaba of the Georgia Institute of Technology and James Seebald of ABB Alstom Air Preheater for reviewing the complete manuscript and providing constructive suggestions, and Dr. M. S. Bhatti of Delphi Harrison Thermal Systems for reviewing Chapters 1 through 6 and Dr. T. Skiepko of Bialystok Technical University for reviewing Chapter 5 and providing constructive suggestions. The constructive feedback over a period of time provided by many students (too numerous to mention by name) merits a special word of appreciation.

Finally, we must acknowledge the roles played by our wives, Rekha and Gorana, and our children, Nilay and Nirav Shah and Visˇnja and Aleksandar Sekulic´, during the course of preparation of this book. Their loving care, emotional support, assistance, and understanding provided continuing motivation to compete the book.

We welcome suggestions and comments from readers.

(18)

NOMENCLATURE

The dimensions for each symbol are represented in both the SI and English systems of units, where applicable. Note that both the hour and second are commonly used as units for time in the English system of units; hence a conversion factor of 3600 should be employed at appropriate places in dimensionless groups.

A total heat transfer surface area (both primary and secondary, if any) on one side of a direct transfer type exchanger (recuperator), total heat transfer surface area of all matrices of a regenerator,{m2, ft2

Ac total heat transfer area (both primary and secondary, if any) on the cold side of an exchanger, m2, ft2

A_eff eﬀective surface area on one side of an extended surface exchanger [deﬁned by Eq. (4.167)], m2, ft2

A_f ﬁn or extended surface area on one side of the exchanger, m2, ft2 A_fr frontal or face area on one side of an exchanger, m2, ft2

A_fr;t window area occupied by tubes, m2, ft2 A_fr;w gross (total) window area, m2, ft2

A_h total heat transfer surface area (both primary and secondary, if any) on the hot ﬂuid side of an exchanger, m2, ft2

A_k ﬁn cross-sectional area for heat conduction in Section 4.3 (A_k_;_o isA_kat the ﬁn base), m2, ft2

Ak total wall cross-sectional area for longitudinal conduction [additional subscriptsc,h, andt, if present, denote cold side, hot side, and total (hotþ cold) for a regenerator] in Section 5.4, m2, ft2

A*_k ratio of Ak on the Cmin side to that on the Cmax side [see Eq. (5.117)], dimensionless

Ao minimum free-ﬂow (or open) area on one ﬂuid side of an exchanger, heat transfer surface area on tube outside in a tubular exchanger in Chapter 13 only, m2, ft2

Ao;bp ﬂow bypass area of one baffle, m2, ft2

Ao;cr ﬂow area at or near the shell centerline for one crossﬂow section in a shell-and-tube exchanger, m2, ft2

A_o;sb shell-to-baffle leakage flow area, m2, ft2 A_o;tb tube-to-baffle leakage flow area, m2, ft2 Ao;w flow area through window zone, m2, ft2

Ap primary surface area on one side of an exchanger, m2, ft2

Aw total wall area for heat conduction from the hot ﬂuid to the cold ﬂuid, or total wall area for transverse heat conduction (in the matrix wall thickness direc-tion), m2, ft2

a short side (unless speciﬁed) of a rectangular cross section, m, ft

a amplitude of chevron plate corrugation (see Fig. 7.28), m, ft

NOMENCLATURE xix

{

(19)

B parameter for a thin ﬁn with end leakage allowed,h_e=mk_f, dimensionless Bi Biot number, Bi¼hð=2Þ=k_f for the ﬁn analysis; Bi¼hð=2Þ=k_w for the

regenerator analysis, dimensionless

b distance between two plates in a plate-ﬁn heat exchanger [see Fig. 8.7 forb₁ orb2(bon ﬂuid 1 or 2 side)], m, ft

b long side (unless speciﬁed) of a rectangular cross section, m, ft

c some arbitrary monetary unit (instead of $, £, etc.), money

C ﬂow stream heat capacity rate with a subscriptcorh,_m_mc_ _p_{, W=K, Btu/hr-}₈_F

C correction factor when used with a subscript diﬀerent fromc,h, min, or max, dimensionless

C unit cost,c/J(c/Btu),c/kg (c/lbm),c/kW [c/(Btu/hr)],c/kWyr(c/Btu on yearly basis),c/m2(c/ft2)

C annual cost,c/yr

C* heat capacity rate ratio,C_min=C_max, dimensionless

C

C ﬂow stream heat capacitance,Mc_p,Cd, Ws=K, Btu/8F CD drag coeﬃcient,p=ðu21=2gcÞ, dimensionless

Cmax maximum ofCcandCh, W=K, Btu/hr-8F C_min minimum ofC_candC_h, W/K, Btu/hr-8F

C_ms heat capacity rate of the maldistributed stream, W/K, Btu/hr-8F

Cr heat capacity rate of a regenerator,MwcwNorMwcw=Pt[see Eq. (5.7) for the hot- and cold-side matrix heat capacity ratesC_r;handCr;c], W/K, Btu/hr-8F C*_r total matrix heat capacity rate ratio,Cr=Cmin,C*r;h¼Cr;h=Ch,C*r;c¼Cr;c=Cc,

dimensionless

C

C_r total matrix wall heat capacitance,M_wc_worC_rP_t [see Eq. (5.6) for hot- and cold-side matrix heat capacitancesCC_r_;_handCC_r_;_c], Ws=K, Btu/8F

C

C*_r ratio ofCC_rtoCC_min, dimensionless

C_UA cost per unit thermal size (see Fig. 10.13 and Appendix D),c/W/K Cus heat capacity rate of the uniform stream, W/K, Btu/hr-8F

C_w matrix heat capacity rate; same asC_r, W/K, Btu/hr-8F

C

C_w total wall heat capacitance for a recuperator,M_wc_w, Ws=K, Btu/8F

C

Cw* ratio ofCCw toCCmin, dimensionless CF cleanliness factor,Uf=Uc, dimensionless

c speciﬁc heat of solid, J=kgK,{_Btu/lbm-₈_F c annual cost of operation percentile, dimensionless

cp specific heat of fluid at constant pressure, J=kgK, Btu/lbm-8F c_w specific heat of wall material, J=kgK, Btu/lbm-8F

d exergy destruction rate, W, Btu/hr Dbaffle baffle diameter, m, ft

Dctl diameter of the circle through the centers of the outermost tubes,Dotl do, m, ft

Dh hydraulic diameter of ﬂow passages, 4rh, 4Ao=P, 4AoL=A, or 4=, m, ft {

(20)

D_h;w hydraulic diameter of the window section, m, ft Dotl diameter of the outer tube limit (see Fig. 8.9), m, ft D_p port or manifold diameter in a plate heat exchanger, m, ft Ds shell inside diameter, m, ft

d diﬀerential operator

d_c collar diameter in a round tube and fin exchanger,d_oþ2, m, ft de fin tip diameter of a disk (radial) fin, m, ft

d_i tube inside diameter, m, ft

do tube (or pin) outside diameter, tube outside diameter at the ﬁn root for a ﬁnned tube after tube expansion, if any, m, ft

dw wire diameter, m, ft

d₁ tube hole diameter in a baffle, m, ft

_ e

e exergy rate, W, Btu/hr E energy, J, Btu

E activation energy in Chapter 13 [see Eq. (13.12)], J=kgmol, Btu/lbm-mole

E ﬂuid pumping power per unit surface area,_m_m_p=A, W=m2, hp/ft2

Eu row average Euler number per tube row, p=ðu2_mN_r=2g_cÞ or

p=ðG2Nr=2gcÞ, dimensionless

e surface roughness size, m, ft

eþ roughness Reynolds number,eu*=, dimensionless

F log-mean temperature diﬀerence correction factor [deﬁned by Eq. (3.183)], dimensionless

f Fanning friction factor,w=ðu2m=2gcÞ, pgcDh=ð2LG2Þ, dimensionless fD Darcy friction factor, 4f, dimensionless

f_tb row average Fanning friction factor per tube for crossﬂow to tubes, used in Chapter 7,p=ð4G2Nr=2gcÞ, Eu/4, dimensionless

G ﬂuid mass velocity based on theminimumfree area,mm_=A_o(replaceA_obyA_o_;_c for the crossﬂow section of a tube bundle in a shell-and-tube heat exchan-ger), kg=m2s, lbm/hr-ft2

Gr Grashof number [deﬁned by Eq. (7.159)], dimensionless

Gz Graetz number,_m_mc_ _p₌_kL_{[see Eqs. (7.39) and (12.53)], dimensionless}

Gzx local Graetz number,mmc_ p=kx, dimensionless

g gravitational acceleration, m/s2, ft/sec2

g_c proportionality constant in Newton’s second law of motion, g_c¼1 and dimensionless in SI units,gc¼32:174 lbm-ft/lbf-sec2

H head or velocity head, m, ft

H ﬂuid enthalpy, J, Btu

_ H

H enthalpy rate, used in Chapter 11, W, Btu/hr Hg Hagen number, deﬁned by Eq. (7.23), dimensionless

*

H thermal boundary condition referring to constant axial as well as peripheral wall heat ﬂux; also constant peripheral wall temperature; boundary condition valid only for the circular tube, parallel plates, and concentric annular ducts when symmetrically heated

(21)

*

H1 thermal boundary condition referring to constant axial wall heat ﬂux with constant peripheral wall temperature

*

H2 thermal boundary condition referring to constant axial wall heat ﬂux with constant peripheral wall heat ﬂux

h heat transfer coeﬃcient [deﬁned by Eqs. (7.11) and (7.12)], W=m2K, Btu/ hr-ft2-8F

h speciﬁc enthalpy, J/kg, Btu/lbm

he heat transfer coefficient at the fin tip, W=m2K, Btu/hr-ft2-8F h‘g specific enthalpy of phase change, J/kg, Btu/lbm

_

II_irr irreversibility rate (defined in Table 11.3), W, Btu/hr InðÞ modified Bessel function of the first kind andnth order

ij ﬂow direction indicator,ij¼ þ1 or 1, ﬂuidj¼1 or 2, dimensionless

J mechanical to thermal energy conversion factor,J¼1 and dimensionless in SI units,J¼778:163 lbf-ft/Btu

Ji correction factors for the shell-side heat transfer coefficient for the Bell– Delaware method [see Eq. (9.50)];i¼cfor baffle cut and spacing;i¼‘for baffle leakage effects, including both shell-to-baffle and tube-to-baffle leak-age;i¼bfor the bundle bypass flow (C and F streams);i¼sfor variable baffle spacing in the inlet and outlet sections;i¼rfor adverse temperature gradient buildup in laminar flow, dimensionless

j Colburn factor, St Pr2/3_,_ð_h₌_Gc

pÞPr2=3, dimensionless

K pressure loss coeﬃcient,p=ðum2=2gcÞ; subscripts:bfor a circular bend,sfor a miter bend, andvfor a screwed valve in Chapter 6, andbrfor branches in Chapter 12, dimensionless

Kð1Þ incremental pressure drop number for fully developed ﬂow (see Table 7.2 for the deﬁnition), dimensionless

Kc contraction loss coefficient for flow at heat exchanger entrance, dimensionless Ke expansion loss coefficient for flow at heat exchanger exit, dimensionless K_nðÞ modified Bessel function of the second kind andnth order

k fluid thermal conductivity for fluid if no subscript, W=mK, Btu/hr-ft-8F kf thermal conductivity of the fin material in Chapter 4 and of the foulant

material in Chapter 13, W=mK, Btu/hr-ft-8F

k_w thermal conductivity of the matrix (wall) material, W=mK, Btu/hr-ft-8F L ﬂuid ﬂow (core) length on one side of an exchanger, m, ft

(22)

‘ fin height or fin length for heat conduction from primary surface to either fin tip or midpoint between plates for symmetric heating,‘¼ ðde doÞ=2 for individually finned tubes,‘with this meaning used only in the fin analysis and in the definition off, m, ft

‘c baffle cut, distance from the baffle tip to the shell inside diameter (see Fig. 8.9), m, ft

‘ef eﬀective ﬂow length between major boundary layer disturbances, distance between interruptions, m, ft

‘s strip length of an oﬀset strip ﬁn, m, ft

‘* ﬂow length between interruptions,‘ef=ðDhRePrÞ, dimensionless ‘c* baffle cut,‘c=Ds, dimensionless

m molecular weight (molar mass) of a gas, kg/kmol, lbm/lb mole

M_A foulant material mass per unit heat transfer surface area in Chapter 13, m/A, kg/m2, lbm/ft2

M_w mass of a heat exchanger core or the total mass of all matrices of a regenerator, kg, lbm

m fin parameter [defined by Eqs. (4.62) and (4.65); see also Table 4.5 for other definitions], 1/m, 1/ft

m mass of a body or ﬂuid in a control volume, kg, lbm

_ m

m ﬂuid mass ﬂow rate,u_mA_o, kg/s, 1bm/hr

_ m

mn fluid mass flow rate for nominal flow passages in Chapter 12, kg/s, 1bm/hr

N number of subexchangers in gross ﬂow maldistributed exchanger or a number of diﬀerently sized/shaped passages in passage-to-passage nonuniformity, used in Chapter 12

N rotational speed for a rotary regenerator, rev/s, rpm Nb number of baffles in a plate-baffled shell-and-tube exchanger N_c number of ﬂuid channels in a plate heat exchanger

N_f number of fins per unit length in the fin pitch direction, l/m, l/ft N_p number of fluid 1 passages in a two-fluid heat exchanger

N_p number of pass divider lanes through the tube ﬁeld that are parallel to the crossﬂow stream in a shell-and-tube exchanger

N_p0 number of separating plates in a plate-ﬁn exchanger, number of pass divider lanes in a shell-and-tube exchanger

Nr number of tube rows in the ﬂow direction

Nr;c number of eﬀective tube rows crossed during ﬂow through one baffle section, Nr;ccþNr;cw

N_r;cc number of effective tube rows crossed during flow through one crossflow section (between baffle tips)

Nr;cw number of eﬀective tube rows crossed during ﬂow through one window zone in a segmental baffled shell-and-tube heat exchanger

N_t total number of tubes in an exchanger, total number of holes in a tubesheet, or total number of plates in a plate heat exchanger

Nt;b total number of tubes associated with one segmental baffle

(23)

N_t;c number of tubes at the tube bundle centerline cross section N_t;p number of tubes per pass

N_t;w number of tubes in the window zone N_t0 number of tubes in a speciﬁed row

NTU number of exchanger heat transfer units, UA=C_min [deﬁned by Eqs. (3.59) through (3.64)], it represents the total number of transfer units in a multipass

unit, dimensionless

NTU1 number of exchanger heat transfer units based on ﬂuid 1 heat capacity rate, UA=C₁; similarly, NTU2¼UA=C2, dimensionless

NTUc number of exchanger heat transfer units based onCc,UA=Cc, dimensionless NTUh number of exchanger heat transfer units based onCh,UA=Ch, dimensionless NTUo modiﬁed number of heat transfer units for a regenerator [deﬁned by Eq.

(5.48)], dimensionless

NTU* number of heat transfer units at maximum entropy generation, dimensionless Nu Nusselt number [deﬁned by Eqs. (7.26) and (7.27)], dimensionless

n,n_p number of passes in an exchanger

n_c number of cells of a regenerator matrix per unit of frontal area, 1/m2_{, 1/ft}2 n_f total number of ﬁns on one ﬂuid side of an extended-surface exchanger n_t number of tubes in each pass

ntuc number of heat transfer units based on the cold ﬂuid side, ðohAÞc=Cc, dimensionless

ntu*cost reduction in ntu [deﬁned by Eq. (12.44)], dimensionless

ntuh number of heat transfer units based on the hot ﬂuid side, ðohAÞh=Ch, dimensionless

P ﬂuid pumping power,mm_p=, W, hp

P temperature effectiveness for one fluid stream [defined by Eqs. (3.96) and (3.97)], dimensionless

P wetted perimeter of exchanger passages on one ﬂuid side, P¼A=L¼ Afr, m, ft

} deposition probability function, dimensionless

P_c cold-gas ﬂow period, duration of the cold-gas stream in the matrix or duration of matrix in the cold-gas stream, used in Chapter 5, s, sec

P_h hot-gas ﬂow period, duration of the hot-gas stream in the matrix or duration of matrix in the hot-gas stream, used in Chapter 5, s, sec

Pr reversal period for switching from hot- to cold-gas stream, or vice versa, in a ﬁxed-matrix regenerator, used in Chapter 5, s, sec

P_t total period between the start of two successive heating (or cooling) periods in a regenerator, used in Chapter 5,Pt¼PhþPcþPrPhþPc, s, sec Pe Pe´clet number, RePr, dimensionless

Pr Prandtl number, cp=k,umDh=, dimensionless

p ﬂuid static pressure, Pa, lbf/ft2(psf ) or lbf/in2(psi){

{

(24)

p porosity of a matrix, a ratio of void volume to total volume of a matrix,r_h, dimensionless

p* ratio of cold-ﬂuid inlet pressure to hot-ﬂuid inlet pressure,p_c;i=ph;i, dimension-less

p_d ﬁn pattern depth, peak-to-valley distance, excluding ﬁn thickness (see Fig. 7.30), m, ft

pf ﬁn pitch, 1=Nf, m, ft

p_t tube pitch, center-to-center distance between tubes, m, ft

p ﬂuid static pressure drop on one ﬂuid side of a heat exchanger core [see Eq. (6.28)], Pa, psf (psi)

p* ¼p=ðu2m=2gcÞ, dimensionless

p_b ﬂuid static pressure drop associated with a pipe bend, Pa, psf (psi)

pb;i ﬂuid static pressure drop associated with an ideal crossﬂow section between two baffles, Pa, psf (psi)

p_c ﬂuid static pressure drop associated with the tube bundle central section (crossﬂow zone) between baffle tips, Pa, psf (psi)

p_gain pressure drop reduction due to passage-to-passage nonuniformity [deﬁned by Eq. (12.36)], Pa, psf (psi)

p_s shell-side pressure drop, Pa, psf (psi)

pw;i ﬂuid static pressure drop associated with an ideal window section, Pa, psf (psi) Q heat transfer in a speciﬁed period or time, J, Btu

q total or local (whatever appropriate) heat transfer rate in an exchanger, or heat ‘‘duty,’’ W, Btu/hr

q* normalized heat transfer rate,q=½ðmmc_ _pÞðT₂_;_i T₁_;_iÞ, dimensionless q0 heat transfer rate per unit length,q=L, W/m, Btu/hr-ft

q00 heat ﬂux, heat transfer rate per unit surface area,q=A, W/m2, Btu/hr-ft2 qe heat transfer rate through the ﬁn tip, W, Btu/hr

q₀ heat transfer rate at the ﬁn base, W, Btu/hr

qmax thermodynamically maximum possible heat transfer rate in a counterﬂow heat exchanger as expressed by Eq. (3.42), and also that through the ﬁn base as expressed by Eq. (4.130), W, Btu/hr

R universal gas constant, 8.3143 kJ=kmolK, 1545.33 1bf-ft/1b mole-8R R heat capacity rate ratio [deﬁned by Eqs. (3.105) and (3.106)], dimensionless

R thermal resistance based on the surface areaA;R¼1=UA¼overall thermal resistance in a two-fluid exchanger,R_h¼1=ðhAÞh¼hot-side film resistance (between the fluid and the wall),Rc¼cold-side film resistance,Rf ¼fouling resistance, and R_w¼wall thermal resistance [definitions found after Eq. (3.24)], K/W, hr-8F/Btu

^ R

R unit thermal resistance, RR^¼RA¼1=U, RR^_h¼1=ðohÞh, RR^w¼1=ðohÞc, ^

R

R_w¼w=Aw, m2K=W, hr-ft28F/Btu

R* ratio of thermal resistances on theCmintoCmaxside, 1=ðohAÞ*; it is also the same as the ratio of hot to cold reduced periods,_h₌_c_{, Chapter 5,}

dimen-sionless

(25)

R* total thermal resistance (wall, fouling, and convective) on the enhanced (or plain with subscriptp) ‘‘outside’’ surface side normalized with respect to the thermal resistance½1=ðhA_i;pÞof ‘‘inside’’ plain tube/surface (see Table 10.5 for explicit formulas), dimensionless

~ R

R gas constant for a particular gas,R/m, J=kgK, 1bf-ft=1bm-8R

^ R

Rf fouling factor or unit thermal resistance (‘‘fouling resistance’’), 1=hf, m2K=W, hr-ft2_-₈_F/Btu

R_i pressure drop correction factor for the Bell–Delaware method, wherei¼bfor bundle bypass flow effects (C stream),i¼‘for baffle leakage effects (A and E streams),i¼sfor unequal inlet/outlet baffle spacing effects, dimension-less

Ra Rayleigh number [deﬁned by Eq. (7.160)], dimensionless

Re Reynolds number based on the hydraulic diameter,GDh= , dimensionless Red Reynolds number based on the tube outside diameter and mean velocity,

umdo= , dimensionless

Redc Reynolds number based on the collar diameter and mean velocity,umdc= , dimensionless

Reo Reynolds number based on the tube outside diameter and free stream (approach or core upstream) velocity,u1do= , dimensionless

r radial coordinate in the cylindrical coordinate system, m, ft r_c radius of curvature of a tube bend (see Fig. 6.5), m, ft

rf fouling factor or fouling resistancerf ¼RR^f ¼1=hf ¼f=kf, m2K=W, hr-ft2 -8F/Btu

rh hydraulic radius,AoL=AorDh=4, m, ft ri tube inside radius, m, ft

S entropy, J/K, Btu/8R

S* normalized entropy generation rate,SS_irr=C2orSS_irr=Cmax, dimensionless _

S

Sirr entropy generation rate, W/K, Btu/hr-8R

St Stanton number,h=Gc_p, Sto¼U=Gcp, dimensionless

s speciﬁc entropy in Chapter 11, J=kgK, Btu/lbm-8R

s complex Laplace independent variable with Laplace transforms only in Chapter 11, dimensionless

s spacing between adjacent ﬁns,pf , m, ft

T fluid static temperature to a specified arbitrary datum, except for Eqs. (7.157) and (7.158) and in Chapter 11 where it is defined on an absolute temperature scale,8C,8F

*T _{thermal boundary condition referring to constant wall temperature, both} axially and peripherally

Tc;o flow area average cold-fluid outlet temperature unless otherwise specified,8C, 8F

T_h;o flow area average hot-fluid outlet temperature unless otherwise specified,8C, 8F

(26)

T_s steam temperature,8C,8F T_w wall temperature,8C,8F

T1 ambient ﬂuid temperature, free stream temperature beyond the extent of the boundary layer on the wall,8C,8F

T* ratio of hot-ﬂuid inlet temperature to cold-ﬂuid inlet temperature,T_h;i=Tc;i, dimensionless

T_c* ¼ ðT_c T_c;iÞ=ðTh;i Tc:iÞ, dimensionless T_h* ¼ ðT_h T_c;iÞ=ðTh;i Tc:iÞ, dimensionless Tw* ¼ ðTw Tc;iÞ=ðTh;i Tc;iÞ, dimensionless T0 temperature of the ﬁn base,8C,8F

T local temperature diﬀerence between two ﬂuids,T_h T_c,8C,8F

T_c temperature rise of the cold fluid in the exchanger,T_c;o Tc;i,8C,8F Th temperature drop of the hot fluid in the exchanger,Th;i Th;o,8C,8F Tlm log-mean temperature difference [defined by Eq. (3.172)],8C,8F

T_m true (effective) mean temperature difference [defined by Eqs. (3.9) and (3.13)],

8C,8F

Tmax inlet temperature diﬀerence (ITD) of the two ﬂuids,ðTh;i Tc;iÞ,ðTw;i Ta;iÞ in Section 7.3.1,8C,8F

U,Um overall heat transfer coeﬃcient [deﬁned by Eq. (3.20) or (3.24)], subscript

m represents mean value when localU is variable (see Table 4.2 for the deﬁnitions of otherU’s), W=m2_{K, Btu/hr-ft}2

-8F

u,um fluid mean axial velocity,um occurs at the minimum free flow area in the exchanger unless specified, m/s, ft/sec

uc fluid mean velocity for flow normal to a tube bank based on the flow area of the gapðX_t d_oÞ; evaluated at or near the shell centerline for a plate-baffled shell-and-tube exchanger, m/s, ft/sec

u_cr critical gap velocity for ﬂuidelastic excitation or critical axial velocity for turbulent buﬀeting, m/s, ft/sec

uz,uw eﬀective and ideal mean velocities in the window zone of a plate-baffled shell-and-tube exchanger [see Eq. (6.41)], m/s, ft/sec

u1 free stream (approach) velocity, m/s, ft/sec u* friction velocity,ðwgc=Þ1=2, m/s, ft/sec

V heat exchanger total volume,V_h¼volume occupied by the hot-fluid-side heat transfer surface area,Vcdefined similarly for the cold fluid side, m3, ft3

V* ratio of the header volume to the matrix total volume, dimensionless

_ V

V volumetric ﬂow rate,VV_¼mm_=¼u_mA_o, m3/s, ft3/sec V_m matrix or core volume, m3, ft3

Vp heat exchanger volume between plates on one ﬂuid side, m3, ft3 Vv void volume of a regenerator, m3, ft3

v speciﬁc volume, 1=, m3=kg, ft3_/1bm

W plate width between gaskets (see Fig. 7.28), m, ft w_p width of the bypass lane (see Fig. 8.9), m, ft X* axial distance or coordinate,x=L, dimensionless

(27)

X_d diagonal pitch,ðX_t2þX‘2Þ1=2, m, ft

X_d* ratio of the diagonal pitch to the tube outside diameter in a circular tube bank, X_d=d_o, dimensionless

X_‘ longitudinal (parallel to the ﬂow) tube pitch (see Table 8.1), m, ft

X‘* ratio of the longitudinal pitch to the tube outside diameter in a circular tube bank,X_‘=d_o, dimensionless

X_t transverse (perpendicular to the ﬂow) tube pitch, m, ft

X_t* ratio of the transverse pitch to the tube diameter in a circular tube bank,X_t=d_o, dimensionless

x Cartesian coordinate along the ﬂow direction, m, ft xþ axial distance,x=D_hRe, dimensionless

x* axial distance,x=DhRePr, dimensionless

xf projected wavy length for one-half wavelength (see Fig. 7.30), m, ft

y transverse Cartesian coordinate, along the matrix wall thickness direction in a regenerator, or along ﬂuid 2 ﬂow direction in other exchangers, m, ft Z capital investment or operating expenses in Chapter 11,c/yr

z Cartesian coordinate, along the noﬂow or stack height direction for a plate-ﬁn exchanger, m, ft

ﬂuid thermal diﬀusivity,k=cp, m2/s, ft2/sec

ratio of total heat transfer area on one ﬂuid side of an exchanger to the total volume of an exchanger,A=V, m2/m3, ft2/ft3

w thermal diﬀusivity of the matrix material,kw=wcw, m2/s, ft2/sec

* aspect ratio of rectangular ducts, ratio of the small to large side length, dimensionless

f* ﬁn aspect ratio, 2‘=, dimensionless

chevron angle for a PHE chevron plate measured from the axis parallel to the plate length (908) (see Fig. 1.18cor 7.28), rad, deg

heat transfer surface area density: ratio of total transfer area on one fluid side of a plate-fin heat exchanger to the volume between the plates on that fluid side,A=A_frL, packing density for a regenerator, m2=m3, ft2=ft3

* coeﬃcient of thermal expansion, 1=T for a perfect gas, 1/K, 1/8R

unbalance factor, ð_c=_cÞ=ð_h=_hÞorC_c=C_h in Chapter 5 [see Eq. (5.92)], dimensionless

speciﬁc heat ratio,c_p=c_v, dimensionless

_{denotes ﬁnite diﬀerence}

@, partial and ﬁnite diﬀerential operators

ﬁn thickness, at the root if the ﬁn is not of constant cross section, m, ft b segmental baffle thickness, m, ft

bb shell-to-tube bundle diametral clearance,Ds Dotl, m, ft

c channel deviation parameter [deﬁned in Eqs. (12.44), (12.46), and (12.47)], dimensionless

(28)

‘ laminar (viscous) sublayer thickness in a turbulent boundary layer, m, ft otl shell-to-tube outer limit diameter clearance,Do Dotl, m, ft

s leakage and bypass stream correction factor to the true mean temperature diﬀerence for the stream analysis method [deﬁned by Eq. (4.170)], dimen-sionless

sb shell-to-baffle diametral clearance,Ds Dbaffle, m, ft tb tube-to-baffle hole diametral clearance,d1 do, m, ft t thermal boundary layer thickness, m, ft

v velocity boundary layer thickness, m, ft w wall or primary surface (plate) thickness, m, ft

" heat exchanger effectiveness [defined by Eq. (3.37) or (3.44) and Table 11.1]; represents an overall exchanger effectiveness for a multipass unit, dimen-sionless

"c temperature effectiveness of the cold fluid [defined by Eq. (3.52)], also as the exchanger effectiveness of the cold fluid in Appendix B, dimensionless "cf counterflow heat exchanger effectiveness [see Eq. (3.83)], dimensionless "h temperature effectiveness of the hot fluid [defined by Eq. (3.51)], also as the

exchange effectiveness of the hot fluid in Appendix B, dimensionless "h;o temperature effectiveness of the hot fluid when flow is uniform onbothfluid

sides of a two-fluid heat exchanger (defined the same as"h), dimensionless "p heat exchanger effectiveness per pass, dimensionless

"r regenerator eﬀectiveness of a single matrix [deﬁned by Eq. (5.81)], dimension-less

"* eﬀectiveness deterioration factor, dimensionless

Cartesian coordinate,ðy=L₂ÞC*NTU [see Eq. (11.21)], dimensionless _i correction factors for shellside pressure drop terms for the Bell–Delaware

method [see Eq. (9.51)];i¼‘for tube-to-baffle and baffle-to-shell leakage; i¼bfor bypass ﬂow;i¼sfor inlet and outlet sections, dimensionless reduced time variable for a regenerator [deﬁned by Eq. (5.69)] with subscripts

j¼candhfor cold- and hot-gas flow periods, dimensionless exergy efficiency [defined by Eq. (11.60)], dimensionless f fin efficiency [defined by Eq. (4.129)], dimensionless

o extended surface efficiency on one fluid side of the extended surface heat exchanger [see Eqs. (4.158) and (4.160) for the definition], dimensionless ðohAÞ* convection conductance ratio [defined by Eq. (4.8)], dimensionless p pump/fan efficiency, dimensionless

" fin effectiveness [defined by Eq. (4.156)], dimensionless

¼1 ¼ ðT T1;iÞ=ðT2;i T1;iÞin Chapter 11 only, dimensionless angular coordinate in the cylindrical coordinate system, rad, deg

excess temperature for the fin analysis in Chapter 4 [defined by Eq. (4.63)]; 0¼T0 T1at the fin base,8C,8F

¼ ðT T2;iÞ=ðT1;i T2;iÞin Chapter 11 only, dimensionless

(29)

b angle between two radii intersected at the inside shell wall with the baffle cut (see Fig. 8.9), rad unless explicitly mentioned in degrees

b bend deﬂection angle (see Fig. 6.5), deg

c disk sector angle for the cold-ﬂuid stream in a rotary regenerator, rad, deg h disk sector angle for the hot-ﬂuid stream in a rotary regenerator, rad, deg _r disk sector angle covered by the radial seals in a rotary regenerator, rad, deg t ¼hþcþr¼2¼3608, rad, deg

# ﬂuid temperature for internal ﬂow in Chapter 7, ðT T_w;mÞ=ðTm Tw;mÞ, dimensionless

# ratio of ﬂuid inlet temperatures,T₁;i=T2;i in Chapter 11 where temperatures are on absolute temperature scale, dimensionless

#* ﬂuid temperature for external ﬂow, ðT T_wÞ=ðT1 TwÞ or

ðT TwÞ=ðTe TwÞ, dimensionless

length eﬀect correction factor for the overall heat transfer coeﬃcient [see Eqs. (4.32) and (4.33)] dimensionless

T isothermal compressibility, 1/Pa, ft 2

/lbf

_{reduced length for a regenerator [deﬁned by Eqs. (5.84), (5.102), and (5.103)],}

dimensionless

_m _{mean reduced length [deﬁned by Eq. (5.91)], dimensionless} _* _¼_h₌_c_{, dimensionless}

, wavelength of chevron plate corrugation (see Fig. 7.28), m, ft

longitudinal wall conduction parameter based on the total conduction area, ¼kwAk;t=CminL,c¼kwAk;c=CcLc,h¼kwAw;h=ChLh, dimensionless ﬂuid dynamic viscosity, Pas, 1bm/hr-ft

ﬂuid kinematic viscosity =, m2

/s, ft2/sec

reduced length variable for regenerator [deﬁned by Eq. (5.69], dimensionless axial coordinate in Chapter 11,x=L, dimensionless

_{reduced period for a regenerator [deﬁned by Eqs. (5.84), (5.104), and (5.105)],}

dimensionless

_m _{harmonic mean reduced period [deﬁned by Eq. 5.90)], dimensionless}

ﬂuid density, kg/m3, 1bm/ft3

ratio of free ﬂow area to frontal area,Ao=Afr, dimensionless

time, s, sec

_d delay period or induction period associated with initiation of fouling in Chapter 13; dwell time, residence time, or transit time of a ﬂuid particle in a heat exchanger in Chapter 5, s, sec

d;min dwell time of theCminﬂuid, s, sec _s ﬂuid shear stress, Pa, psf

w equivalent ﬂuid shear stress at wall, Pa, psf (psi) * time variable,=d;min, dimensionless

c*,h* time variable for the cold and hot ﬂuids [deﬁned by Eq. (5.26)], dimensionless ðÞ denotes a functional relationship

(30)

i fractional distribution of theith shaped passage, dimensionless Tm=ðTh;i Tc;iÞ, dimensionless

removal resistance [scale strength factor; see Eq. (13.12)], dimensionless

_{water quality factor, dimensionless}

Subscripts

A unit (row, section) A

a air side

B unit (row, section) B

b bend, tube bundle, or lateral branch c cold-ﬂuid side, clean surface in Chapter 13

cf counterﬂow

cp constant properties

cr crossﬂow section in a segmental baffled exchanger cv control volume

cu cold utility

d deposit

df displaced ﬂuid

eﬀ eﬀective

f fouling, ﬂuid in Section 7.3.3.2

g gas side

H constant axial wall heat ﬂux boundary condition

h hot-ﬂuid side

hu hot utility hex heat exchanger

H1 thermal boundary condition referring to constant axial wall heat ﬂux with constant peripheral wall temperature

i inlet to the exchanger i inside surface in Chapter 13

id ideal

iso isothermal

L coupled liquid

leak caused by a leak lm logarithmic mean

m mean or bulk mean, manifold (in Chapter 12)

max maximum

min minimum

mixing caused by mixing ms maldistributed ﬂuid

n nominal or reference passage in Chapter 12

o overall

o outside surface in Chapter 13

(31)

o outlet to the exchanger when used as a subscript with the temperature

opt optimal

otl outer tube limit in a shell-and-tube heat exchanger

p pass, except for plain surface in Section 10.3

pf parallelﬂow

r reentrainment

ref referent thermodynamic conditions

s shellside; steam; structural

std arbitrarily selected standard temperature and pressure conditions

T constant wall temperature boundary condition t tubeside, tube

tot total

v viscous

w wall or properties at the wall temperature, window zone for a shell-and-tube exchanger

w water

x local value at sectionxalong the ﬂow length 1 ﬂuid 1; one section (inlet or outlet) of the exchanger

2 ﬂuid 2; other section (outlet or inlet) of the exchanger

(32)

1

Classiﬁcation of Heat Exchangers

A variety of heat exchangers are used in industry and in their products. The objective of this chapter is to describe most of these heat exchangers in some detail using classification schemes. Starting with a definition, heat exchangers are classified according to transfer processes, number of fluids, degree of surface compactness, construction features, flow arrangements, and heat transfer mechanisms. With a detailed classification in each cate-gory, the terminology associated with a variety of these exchangers is introduced and practical applications are outlined. A brief mention is also made of the differences in design procedure for the various types of heat exchangers.

1.1 INTRODUCTION

Aheat exchangeris a device that is used to transfer thermal energy (enthalpy) between two or more fluids, between a solid surface and a fluid, or between solid particulates and a fluid, at different temperatures and in thermal contact. In heat exchangers, there are usually no external heat and work interactions. Typical applications involve heating or cooling of a fluid stream of concern and evaporation or condensation of single- or multicomponent fluid streams. In other applications, the objective may be to recover or reject heat, or sterilize, pasteurize, fractionate, distill, concentrate, crystallize, or con-trol a process fluid. In a few heat exchangers, the fluids exchanging heat are in direct contact. In most heat exchangers, heat transfer between fluids takes place through a separating wall or into and out of a wall in a transient manner. In many heat exchangers, the fluids are separated by a heat transfer surface, and ideally they do not mix or leak. Such exchangers are referred to asdirect transfer type, or simplyrecuperators. In con-trast, exchangers in which there is intermittent heat exchange between the hot and cold fluids—via thermal energy storage and release through the exchanger surface or matrix— are referred to asindirect transfer type, or simplyregenerators. Such exchangers usually have fluid leakage from one fluid stream to the other, due to pressure differences and matrix rotation/valve switching. Common examples of heat exchangers are shell-and-tube exchangers, automobile radiators, condensers, evaporators, air preheaters, and cooling towers. If no phase change occurs in any of the fluids in the exchanger, it is sometimes referred to as a sensible heat exchanger. There could be internal thermal energy sources in the exchangers, such as in electric heaters and nuclear fuel elements. Combustion and chemical reaction may take place within the exchanger, such as in boilers, fired heaters, and fluidized-bed exchangers. Mechanical devices may be used in some exchangers such as in scraped surface exchangers, agitated vessels, and stirred tank reactors. Heat transfer in the separating wall of a recuperator generally takes place by

1

(33)

conduction. However, in a heat pipe heat exchanger, the heat pipe not only acts as a separating wall, but also facilitates the transfer of heat by condensation, evaporation, and conduction of the working fluid inside the heat pipe. In general, if the fluids are immiscible, the separating wall may be eliminated, and the interface between the fluids replaces a heat transfer surface, as in a direct-contact heat exchanger.

(34)

A heat exchanger consists ofheat transfer elementssuch as a core or matrix containing the heat transfer surface, and ﬂuid distribution elements such as headers, manifolds, tanks, inlet and outlet nozzles or pipes, or seals. Usually, there are no moving parts in a heat exchanger; however, there are exceptions, such as a rotary regenerative exchanger (in which the matrix is mechanically driven to rotate at some design speed) or a scraped surface heat exchanger.

The heat transfer surface is a surface of the exchanger core that is in direct contact with fluids and through which heat is transferred by conduction. That portion of the surface that is in direct contact with both the hot and cold fluids and transfers heat between them is referred to as theprimaryordirect surface. To increase the heat transfer area, appendages may be intimately connected to the primary surface to provide an extended,secondary, orindirect surface. These extended surface elements are referred to asfins. Thus, heat is conducted through the fin and convected (and/or radiated) from the fin (through the surface area) to the surrounding fluid, or vice versa, depending on whether the fin is being cooled or heated. As a result, the addition of fins to the primary surface reduces the thermal resistance on that side and thereby increases the total heat transfer from the surface for the same temperature difference. Fins may form flow passages for the individual fluids but do not separate the two (or more) fluids of the exchanger. These secondary surfaces or fins may also be introduced primarily for struc-tural strength purposes or to provide thorough mixing of a highly viscous liquid.

Not only are heat exchangers often used in the process, power, petroleum, transpor-tation, air-conditioning, refrigeration, cryogenic, heat recovery, alternative fuel, and manufacturing industries, they also serve as key components of many industrial products available in the marketplace. These exchangers can be classified in many different ways. We will classify them according to transfer processes, number of fluids, and heat transfer mechanisms. Conventional heat exchangers are further classified according to construc-tion type and flow arrangements. Another arbitrary classificaconstruc-tion can be made, based on the heat transfer surface area/volume ratio, into compact and noncompact heat exchan-gers. This classification is made because the type of equipment, fields of applications, and design techniques generally differ. All these classifications are summarized in Fig. 1.1 and discussed further in this chapter. Heat exchangers can also be classified according to the process function, as outlined in Fig. 1.2. However, they are not discussed here and the reader may refer to Shah and Mueller (1988). Additional ways to classify heat exchangers are by fluid type (gas–gas, gas–liquid, liquid–liquid, gas two-phase, liquid two-phase, etc.), industry, and so on, but we do not cover such classifications in this chapter.

1.2 CLASSIFICATION ACCORDING TO TRANSFER PROCESSES

Heat exchangers are classiﬁed according to transfer processes into in and direct-contact types.

1.2.1 Indirect-Contact Heat Exchangers

In an indirect-contact heat exchanger, the fluid streams remain separate and the heat transfers continuously through an impervious dividing wall or into and out of a wall in a transient manner. Thus, ideally, there is no direct contact between thermally interacting fluids. This type of heat exchanger, also referred to as asurface heat exchanger, can be further classified into direct-transfer type, storage type, and fluidized-bed exchangers.

(35)

1.2.1.1 Direct-Transfer Type Exchangers. In this type, heat transfers continuously from the hot fluid to the cold fluid through a dividing wall. Although a simultaneous flow of two (or more) fluids is required in the exchanger, there is no direct mixing of the two (or more) fluids because each fluid flows in separate fluid passages. In general, there are no moving parts in most such heat exchangers. This type of exchanger is designated as a recuperative heat exchanger or simply as arecuperator.{_{Some examples of}

direct-transfer type heat exchangers are tubular, plate-type, and extended surface exchangers. Note that the termrecuperatoris not commonly used in the process industry for shell-FIGURE 1.2 (a) Classification according to process function; (b) classification of condensers; (c) classification of liquid-to-vapor phase-change exchangers.

{

(36)

and-tube and plate heat exchangers, although they are also considered as recuperators. Recuperators are further subclassified as prime surface exchangers and extended-surface exchangers.Prime surface exchangersdo not employ fins or extended surfaces on any fluid side. Plain tubular exchangers, shell-and-tube exchangers with plain tubes, and plate exchangers are good examples of prime surface exchangers. Recuperators consti-tute a vast majority of all heat exchangers.

1.2.1.2 Storage Type Exchangers. In a storage type exchanger, both fluids flow alter-natively through the same flow passages, and hence heat transfer is intermittent. The heat transfer surface (or flow passages) is generally cellular in structure and is referred to as amatrix(see Fig. 1.43), or it is a permeable (porous) solid material, referred to as a packed bed.When hot gas flows over the heat transfer surface (through flow passages), CLASSIFICATION ACCORDING TO TRANSFER PROCESSES 5

FUNDAMENTALS OF HEAT EXCHANGER DESIGN