fundamentals of heat exchanger design

side of a direct transfer type exchanger recuperator, total heat transfersurface area of all matrices of a regenerator,{m2, ft2 of an exchanger, m2, ft2 Aeff effective surface area on one

FUNDAMENTALS OF HEAT EXCHANGER DESIGN

Fundamentals of Heat Exchanger Design Ramesh K Shah and Dušan P Sekulic Copyright © 2003 John Wiley & Sons, Inc.

FUNDAMENTALS OF HEAT EXCHANGER DESIGN

Ramesh K Shah

Rochester Institute of Technology, Rochester, New York

Formerly at Delphi Harrison Thermal Systems, Lockport, New YorkDusˇan P Sekulic´

University of Kentucky, Lexington, Kentucky

JOHN WILEY & SONS, INC

This book is printed on acid-free paper * 1

Copyright # 2003 by John Wiley & Sons, Inc All rights reserved

Published by John Wiley & Sons, Inc., Hoboken, New Jersey

Published simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data:

10 9 8 7 6 5 4 3 2 1

2.2 Interactions Among Design Considerations 93

3.11 Solution Methods for Determining Exchanger Effectiveness 212

3.11.7 Rules for the Determination of Exchanger Effectiveness

5.2 The"-NTUoMethod 316

6.8 Pressure Drop Dependence on Geometry and Fluid Properties 418

7.8.2 Gases as Participating Media 538

9.4.3 Rating a PHE 637

10.3.3 Evaluation Criteria Based on the Second Law of

11.2 Modeling a Heat Exchanger Based on the First Law of

11.2.3 Temperature Difference Distributions for Parallelflow and

11.4.3 Thermodynamic Analysis for 1–2 TEMA J Shell-and-Tube

11.6.5 Thermodynamic Figure of Merit for Assessing Heat

Review Questions 855

13.3.1 Fouling Resistance and Overall Heat Transfer Coefficient

Over the past quarter century, the importance of heat exchangers has increased sely from the viewpoint of energy conservation, conversion, recovery, and successfulimplementation 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, transportation,air-conditioning and refrigeration, cryogenic, heat recovery, alternate fuels, andmanufacturing industries, as well as being key components of many industrial productsavailable in the marketplace From an educational point of view, heat exchangersillustrate in one way or another most of the fundamental principles of the thermalsciences, thus serving as an excellent vehicle for review and application, meeting theguidelines for university studies in the United States and oversees Significant advanceshave taken place in the development of heat exchanger manufacturing technology as well

immen-as design theory Many books have been published on the subject, immen-as summarized inthe General References at the end of the book However, our assessment is that none ofthe books available seems to provide an in-depth coverage of the intricacies of heatexchanger design and theory so as to fully support both a student and a practicingengineer in the quest for creative mastering of both theory and design Our book wasmotivated by this consideration Coverage includes the theory and design of exchangersfor many industries (not restricted to, say, the process industry) for a broader, in-depthfoundation

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 importantgoals were borne in mind during the preparation of this book:

1 To introduce and apply concepts learned in first courses in heat transfer, fluidmechanics, thermodynamics, and calculus, to develop heat exchanger designtheory 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 ofindustrial heat exchanger problems Primary emphasis is placed on fundamentalconcepts and applications Also, more emphasis is placed on analysis and less onempiricism

3 The book is also intended for practicing engineers in addition to students.Hence, at a number of places in the text, some redundancy is added to make theconcepts clearer, early theory is developed using constant and mean overall heattransfer coefficients, and more data are added in the text and tables for industrialuse

To provide comprehensive information for heat exchanger design and analysis in abook 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 comprehensiveinformation through text and concise tables

An industrial heat exchanger design problem consists of coupling component andsystem design considerations to ensure proper functioning Accordingly, a good designengineer must be familiar with both system and component design aspects Based onindustrial experience of over three decades in designing compact heat exchangers forautomobiles and other industrial applications and more than twenty years of teaching,

we have endeavored to demonstrate interrelationships between the component and 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 systemdesign experience

sys-Considering the fact that heat exchangers constitute a multibillion-dollar industry inthe 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 anintroductory 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 tocover in one semester is up to the instructor, depending on his or her desire to focus onspecific exchanger types and specific topics in each chapter The prerequisites for thiscourse are first undergraduate courses in fluid mechanics, thermodynamics, and heattransfer It is expected that the student is familiar with the basics of forced convectionand the basic concepts of the heat transfer coefficient, heat exchanger effectiveness, andmean temperature difference

Starting with a detailed classification of a variety of heat exchangers in Chapter 1, anoverview of heat exchanger design methodology is provided in Chapter 2 The basicthermal design theory for recuperators is presented in Chapter 3, advanced design theoryfor recuperators in Chapter 4, and thermal design theory for regenerators in Chapter 5.Pressure drop analysis is presented in Chapter 6 The methods and sources for obtainingheat transfer and flow friction characteristics of exchanger surfaces are presented inChapter 7 Surface geometrical properties needed for heat exchanger design are covered

in Chapter 8 The thermal and hydraulic designs of extended-surface (compactand noncompact plate-fin and tube-fin), plate, and shell-and-tube exchangers are out-lined in Chapter 9 Guidelines for selecting the exchanger core construction and surfacegeometry are presented in Chapter 10 Chapter 11 is devoted to thermodynamic analysisfor heat exchanger design and includes basic studies of temperature distributions in heatexchangers, a heuristic approach to an assessment of heat exchanger effectiveness, andadvanced topics important for modeling, analysis, and optimization of heat exchangers

as components All topics covered up to this point are related to thermal–hydraulicdesign of heat exchangers in steady-state or periodic-flow operation Operationalproblems for compact and other heat exchangers are covered in Chapters 12 and 13.They include the problems caused by flow maldistribution and by fouling and corrosion.Solved examples from industrial experience and classroom practice are presentedthroughout the book to illustrate important concepts and applications Numerous reviewquestions and problems are also provided at the end of each chapter If students cananswer the review questions and solve the problems correctly, they can be sure of theirgrasp of the basic concepts and material presented in the text It is hoped that readers will

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

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

intellec-Material presented in Chapters 11 through 13 is significantly more interdisciplinarythan the rest of the book and is presented here in a modified methodological approach InChapter 11 in particular, analytical modeling is used extensively Readers will participateactively through a set of examples and problems that extend the breadth and depth of thematerial given in the main body of the text A number of examples and problems inChapter 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 diverseapproach to terminology, less routine treatment of established conventions, and a morecreative approach to some unresolved dilemmas

Because of the breadth of the subject, the coverage includes various design aspects andproblems for indirect-contact two-fluid heat exchangers with primarily single-phasefluids on each side Heat exchangers with condensing and evaporating fluids on oneside can also be analyzed using the design methods presented as long as the thermalresistance 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-phaseand multiphase heat exchangers (such as condensers and vaporizers), direct-contactheat exchangers (such as humidifiers, dehumidifiers, cooling towers), and multifluidand multistream heat exchangers Coverage of mechanical design, exchanger fabricationmethods, and manufacturing techniques is also deemed beyond the scope of thebook

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 analysisfollowing World War II In the last thirty or so years, a significant number of bookshave been published on heat exchangers These are summarized in the GeneralReferences 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 ofNew York at Buffalo and the University of Novi Sad, Yugoslavia Over the past fifteenyears or more, the notes of the first author have been used for teaching purposes at anumber of institutions, including the University of Miami by Professor S Kakac¸,Rensselaer Polytechnic Institute by Professors A E Bergles and R N Smith,Rochester Institute of Technology by Professor S G Kandlikar, Rice University byProfessor Y Bayazitogˇlu, University of Tennessee Space Center by Dr R Schultz,University of Texas at Arlington by Professor A Haji-Sheikh, University ofCincinnati by Professor R M Manglik, Northeastern University by Professor YamanYener, North Carolina A&T State University by Professor Lonnie Sharpe, Auburn

University by Dr Peter Jones, Southern Methodist University by Dr Donald Price,University of Tennessee by Professor Edward Keshock, and Gonzaga University byProfessor A Aziz In addition, these course notes have been used occasionally at anumber of other U.S and foreign institutions The notes of the second author havealso been used for a number of undergraduate and graduate courses at MarquetteUniversity 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 MotorsCorporation), for their varied support activities over an extended period of time Thesecond author acknowledges with appreciation many years of support by his colleaguesand friends on the faculty of the School of Engineering, University of Novi Sad, andmore recently at Marquette University and the University of Kentucky We are alsothankful for the support provided by the College of Engineering, University ofKentucky, for preparation of the first five and final three chapters of the book A specialword of appreciation is in order for the diligence and care exercised by Messrs Dale Halland Mack Mosley in preparing the manuscript and drawings through Chapter 5.The first author is grateful to Professor A L London of Stanford University forteaching him the ABCs of heat exchangers and for providing constant inspiration andencouragement throughout his professional career and particularly during the course ofpreparation of this book The first author would also like to thank Professors SadikKakac¸ of the University of Miami and Ralph Webb of the Pennsylvania State Universityfor their support, encouragement, and involvement in many professional activitiesrelated to heat exchangers The second author is grateful to his colleague and friendProfessor 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 authorhave had with Dr R Gregory of the University of Kentucky regarding not only whatone 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 andencouragement of Dr Frederick Edeskuty of Los Alamos National Laboratory, andProfessor Richard Gaggioli of Marquette University were immensely important to thesecond author in an effort to exercise his academic experience on both sides of theAtlantic Ocean We appreciate Professor P V Kadaba of the Georgia Institute ofTechnology and James Seebald of ABB Alstom Air Preheater for reviewing the completemanuscript and providing constructive suggestions, and Dr M S Bhatti of DelphiHarrison Thermal Systems for reviewing Chapters 1 through 6 and Dr T Skiepko ofBialystok Technical University for reviewing Chapter 5 and providing constructivesuggestions 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, andour children, Nilay and Nirav Shah and Visˇnja and Aleksandar Sekulic´, during thecourse 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

Ramesh K ShahDusˇan P Sekulic´

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

side of a direct transfer type exchanger (recuperator), total heat transfersurface area of all matrices of a regenerator,{m2, ft2

of an exchanger, m2, ft2

Aeff effective surface area on one side of an extended surface exchanger [defined by

Eq (4.167)], m2, ft2

Af fin or extended surface area on one side of the exchanger, m2, ft2

Afr frontal or face area on one side of an exchanger, m2, ft2

Afr;t window area occupied by tubes, m2, ft2

Afr;w gross (total) window area, m2, ft2

hot fluid side of an exchanger, m2, ft2

Ak fin cross-sectional area for heat conduction in Section 4.3 (Ak;o is Akat the

fin base), m2, ft2

subscripts c, h, and t, if present, denote cold side, hot side, and total (hotþcold) for a regenerator] in Section 5.4, m2, ft2

dimensionless

transfer surface area on tube outside in a tubular exchanger in Chapter 13only, 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

Ao;sb shell-to-baffle leakage flow area, m2, ft2

Ao;tb tube-to-baffle leakage flow area, 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 tion), m2, ft2

{

B parameter for a thin fin with end leakage allowed, he=mkf, dimensionless

regenerator analysis, dimensionless

or b2(b on fluid 1 or 2 side)], m, ft

dimensionless

yearly basis), c/m2(c/ft2)



1=2gcÞ, dimensionless

Cr heat capacity rate of a regenerator, MwcwN or Mwcw=Pt[see Eq (5.7) for the

hot- and cold-side matrix heat capacity rates Cr;hand Cr;c], W/K, Btu/hr-8FC*r total matrix heat capacity rate ratio, Cr=Cmin, C*r;h¼ Cr;h=Ch, C*r;c¼ Cr;c=Cc,

dimensionless



Cr total matrix wall heat capacitance, Mwcwor CrPt [see Eq (5.6) for hot- and

cold-side matrix heat capacitances Cr;hand Cr;c], W s=K, Btu/8F



C

C*r ratio of Crto Cmin, dimensionless



Cw total wall heat capacitance for a recuperator, Mwcw, W s=K, Btu/8F



Cw* ratio of Cw to Cmin, dimensionless

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

{ J ¼ joule ¼ newton  meter ¼ watt  second; newton ¼ N ¼ kg  m=s 2 :

Dh;w hydraulic diameter of the window section, m, ft

Dotl diameter of the outer tube limit (see Fig 8.9), m, ft

finned tube after tube expansion, if any, m, ft

dimensionless

m=2gcÞ, p gcDh=ð2LG2Þ, dimensionless

Chapter 7,p=ð4G2Nr=2gcÞ, Eu/4, dimensionless

G fluid mass velocity based on the minimum free area,m=A_m o(replace Aoby Ao;c

for the crossflow section of a tube bundle in a shell-and-tube heat ger), kg=m2 s, lbm/hr-ft2

Gzx local Graetz number,mc_m p=kx, dimensionless

dimensionless in SI units, gc¼ 32:174 lbm-ft/lbf-sec2

_H

wall heat flux; also constant peripheral wall temperature; boundarycondition valid only for the circular tube, parallel plates, and concentricannular ducts when symmetrically heated

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

constant peripheral wall temperature

constant peripheral wall heat flux

hr-ft2-8F

he heat transfer coefficient at the fin tip, W=m2 K, Btu/hr-ft2

-8F

_IIirr irreversibility rate (defined in Table 11.3), W, Btu/hr

InðÞ modified Bessel function of the first kind and nth order

units, J¼ 778:163 lbf-ft/Btu

Delaware method [see Eq (9.50)]; i¼ c for baffle cut and spacing; i ¼ ‘ forbaffle leakage effects, including both shell-to-baffle and tube-to-baffle leak-age; i¼ b for the bundle bypass flow (C and F streams); i ¼ s for variablebaffle spacing in the inlet and outlet sections; i¼ r for adverse temperaturegradient buildup in laminar flow, dimensionless

j Colburn factor, St Pr2/3,ðh=GcpÞPr2=3, dimensionless

m=2gcÞ; subscripts: b for a circular bend, s for

a miter bend, and v for a screwed valve in Chapter 6, and br for branches inChapter 12, dimensionless

the definition), dimensionless

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

‘ 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 forindividually finned tubes,‘ with this meaning used only in the fin analysisand 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

between interruptions, m, ft

‘* flow length between interruptions,‘ef=ðDh Re  PrÞ, dimensionless

‘c* baffle cut,‘c=Ds, dimensionless

of differently sized/shaped passages in passage-to-passage nonuniformity,used in Chapter 12

crossflow stream in a shell-and-tube exchanger

lanes in a shell-and-tube exchanger

Nr;ccþ Nr;cw

section (between baffle tips)

a segmental baffled shell-and-tube heat exchanger

Nt 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;c number of tubes at the tube bundle centerline cross section

through (3.64)], it represents the total number of transfer units in a multipassunit, dimensionless

UA=C1; similarly, NTU2¼ UA=C2, dimensionless

NTUc number of exchanger heat transfer units based on Cc, UA=Cc, dimensionlessNTUh number of exchanger heat transfer units based on Ch, UA=Ch, dimensionless

(5.48)], dimensionless

nc number of cells of a regenerator matrix per unit of frontal area, 1/m2, 1/ft2

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

dimensionless

(3.97)], dimensionless

Afr, m, ft

of matrix in the cold-gas stream, used in Chapter 5, s, sec

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

Pt total period between the start of two successive heating (or cooling) periods in

a regenerator, used in Chapter 5, Pt¼ Phþ Pcþ Pr Phþ Pc, s, sec

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

{ Pa ¼ Pascal ¼ N=m 2 ¼ kg=m  s 2

; N ¼ newton ¼ kg  m=s 2

; psf ¼ lbf=ft 3

; psi ¼ lbf=in 3 :

p porosity of a matrix, a ratio of void volume to total volume of a matrix, rh,

Eq (6.28)], Pa, psf (psi)

m=2gcÞ, dimensionless

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

two baffles, Pa, psf (psi)

(crossflow zone) between baffle tips, Pa, psf (psi)

Eq (12.36)], Pa, psf (psi)

pw;i fluid static pressure drop associated with an ideal window section, Pa, psf (psi)

heat ‘‘duty,’’ W, Btu/hr

q normalized heat transfer rate, q=½ð _mmcpÞðT2;i
T1;iÞ, dimensionless

q00 heat flux, heat transfer rate per unit surface area, q=A, W/m2

, Btu/hr-ft2

exchanger as expressed by Eq (3.42), and also that through the fin base asexpressed by Eq (4.130), W, Btu/hr

resistance in a two-fluid exchanger,Rh¼ 1=ðhAÞh¼ hot-side film resistance(between the fluid and the wall),Rc¼ cold-side film resistance, Rf ¼ foulingresistance, and Rw¼ wall thermal resistance [definitions found after Eq.(3.24)], K/W, hr-8F/Btu

^RR unit thermal resistance, ^RR ¼ RA ¼ 1=U, ^RRh¼ 1=ðohÞh, ^Rw¼ 1=ðohÞc,

^RRw¼
w=Aw, m2 K=W, hr-ft28F/Btu

R* ratio of thermal resistances on the Cminto Cmaxside, 1=ðohAÞ*; it is also the

same as the ratio of hot to cold reduced periods,h=c, Chapter 5, sionless

R* total thermal resistance (wall, fouling, and convective) on the enhanced (or

plain with subscript p) ‘‘outside’’ surface side normalized with respect to thethermal resistance½1=ðhAi; pÞ of ‘‘inside’’ plain tube/surface (see Table 10.5for explicit formulas), dimensionless

~

m2 K=W, hr-ft2-8F/Btu

bundle bypass flow effects (C stream), i¼ ‘ for baffle leakage effects (A and

E streams), i¼ s for unequal inlet/outlet baffle spacing effects, less

umdo= , dimensionless

dimensionless

(approach or core upstream) velocity,u1do= , dimensionless

rf fouling factor or fouling resistance rf ¼ ^RRf ¼ 1=hf ¼
f=kf, m2 K=W, hr-ft2

8F/Btu

-rh hydraulic radius, AoL=A or Dh=4, m, ft

S* normalized entropy generation rate, _Sirr=C2or _Sirr=Cmax, dimensionless

Chapter 11, dimensionless

and (7.158) and in Chapter 11 where it is defined on an absolute temperaturescale,8C, 8F

axially and peripherally

8F

8F

Ts steam temperature,8C, 8F

boundary layer on the wall,8C, 8F

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

dimensionless

Tc* ¼ ðTc
Tc;iÞ=ðTh;i
Tc:iÞ, dimensionless

Th* ¼ ðTh
Tc;iÞ=ðTh;i
Tc:iÞ, dimensionless

Tw* ¼ ðTw
Tc;iÞ=ðTh;i
Tc;iÞ, dimensionless

Tc temperature rise of the cold fluid in the exchanger, Tc;o
Tc;i,8C, 8F

Th temperature drop of the hot fluid in the exchanger, Th;i
Th;o,8C, 8F

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

m represents mean value when local U is variable (see Table 4.2 for thedefinitions of other U ’s), W=m2 K, Btu/hr-ft2

-8F

exchanger unless specified, m/s, ft/sec

the gapðXt
doÞ; evaluated at or near the shell centerline for a plate-baffledshell-and-tube exchanger, m/s, ft/sec

ucr 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

u friction velocity,ðwgc=Þ1=2, m/s, ft/sec

transfer surface area, Vcdefined similarly for the cold fluid side, m3, ft3

_V

V volumetric flow rate, _V¼ _mm= ¼ umAo, m3/s, ft3/sec

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‘=do, dimensionless

Xt* ratio of the transverse pitch to the tube diameter in a circular tube bank, Xt=do,

dimensionless

regenerator, or along fluid 2 flow direction in other exchangers, m, ft

exchanger, m, ft

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

volume of an exchanger, A=V, m2

/m3, ft2/ft3

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

dimensionless

plate length (  908) (see Fig 1.18c or 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 fluidside, A=AfrL, packing density for a regenerator, m2=m3, ft2=ft3

unbalance factor, ðc=
cÞ=ðh=
hÞ or Cc=Ch in Chapter 5 [see Eq (5.92)],dimensionless

specific heat ratio, cp=cv, dimensionless

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

dimensionless

‘ laminar (viscous) sublayer thickness in a turbulent boundary layer, m, ft

otl shell-to-tube outer limit diameter clearance, Do
Dotl, m, ft

difference for the stream analysis method [defined by Eq (4.170)], sionless

dimen-
sb shell-to-baffle diametral clearance, Ds
Dbaffle, m, ft

tb tube-to-baffle hole diametral clearance, d1
do, m, ft

represents an overall exchanger effectiveness for a multipass unit, sionless

dimen-"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 on both fluid

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

method [see Eq (9.51)]; i¼ ‘ for tube-to-baffle and baffle-to-shell leakage;

i¼ b for bypass flow; i ¼ s for inlet and outlet sections, dimensionless

j¼ c and h for cold- and hot-gas flow periods, dimensionless

exchanger [see Eqs (4.158) and (4.160) for the definition], dimensionlessðohAÞ* convection conductance ratio [defined by Eq (4.8)], dimensionless

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

 ¼ 1
¼ ðT
T1;iÞ=ðT2;i
T1;iÞ in Chapter 11 only, dimensionless

0¼ T0
T1at the fin base,8C, 8F

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

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

r disk sector angle covered by the radial seals in a rotary regenerator, rad, deg

dimensionless

are on absolute temperature scale, dimensionless

ðT
TwÞ=ðTe
TwÞ, dimensionless

(4.32) and (4.33)] dimensionless

T isothermal compressibility, 1/Pa, ft2/lbf

dimensionless

 ¼ kwAk;t=CminL,c¼ kwAk;c=CcLc,h¼ kwAw;h=ChLh, dimensionless

/s, ft2/sec

Chapter 13; dwell time, residence time, or transit time of a fluid particle in aheat exchanger in Chapter 5, s, sec

d;min dwell time of the Cminfluid, s, sec

c*,h* time variable for the cold and hot fluids [defined by Eq (5.26)], dimensionless

i fractional distribution of the ith shaped passage, dimensionless

Tm=ðTh;i
Tc;iÞ, dimensionless

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

Subscripts

constant peripheral wall temperature

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

1 Classification of Heat Exchangers

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

or reject heat, or sterilize, pasteurize, fractionate, distill, concentrate, crystallize, or trol a process fluid In a few heat exchangers, the fluids exchanging heat are in directcontact In most heat exchangers, heat transfer between fluids takes place through aseparating 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 as direct transfer type, or simply recuperators In con-trast, exchangers in which there is intermittent heat exchange between the hot and coldfluids—via thermal energy storage and release through the exchanger surface or matrix—are referred to as indirect transfer type, or simply regenerators Such exchangers usuallyhave fluid leakage from one fluid stream to the other, due to pressure differences andmatrix rotation/valve switching Common examples of heat exchangers are shell-and-tube exchangers, automobile radiators, condensers, evaporators, air preheaters, andcooling towers If no phase change occurs in any of the fluids in the exchanger, it issometimes referred to as a sensible heat exchanger There could be internal thermalenergy 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 inboilers, fired heaters, and fluidized-bed exchangers Mechanical devices may be used insome exchangers such as in scraped surface exchangers, agitated vessels, and stirred tankreactors Heat transfer in the separating wall of a recuperator generally takes place by

con-1

Fundamentals of Heat Exchanger Design Ramesh K Shah and Dušan P Sekulic

Copyright © 2003 John Wiley & Sons, Inc.

conduction However, in a heat pipe heat exchanger, the heat pipe not only acts as aseparating 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 areimmiscible, the separating wall may be eliminated, and the interface between the fluidsreplaces a heat transfer surface, as in a direct-contact heat exchanger.

FIGURE 1.1 Classification of heat exchangers (Shah, 1981).

A heat exchanger consists of heat transfer elements such as a core or matrix containingthe 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 scrapedsurface heat exchanger

The heat transfer surface is a surface of the exchanger core that is in direct contactwith fluids and through which heat is transferred by conduction That portion of thesurface that is in direct contact with both the hot and cold fluids and transfers heatbetween them is referred to as the primary or direct surface To increase the heat transferarea, appendages may be intimately connected to the primary surface to provide anextended, secondary, or indirect surface These extended surface elements are referred

to as fins Thus, heat is conducted through the fin and convected (and/or radiated) fromthe fin (through the surface area) to the surrounding fluid, or vice versa, depending onwhether the fin is being cooled or heated As a result, the addition of fins to the primarysurface reduces the thermal resistance on that side and thereby increases the total heattransfer from the surface for the same temperature difference Fins may form flowpassages for the individual fluids but do not separate the two (or more) fluids of theexchanger 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, andmanufacturing industries, they also serve as key components of many industrial productsavailable 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 transfermechanisms Conventional heat exchangers are further classified according to construc-tion type and flow arrangements Another arbitrary classification can be made, based onthe 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, anddesign techniques generally differ All these classifications are summarized in Fig 1.1 anddiscussed further in this chapter Heat exchangers can also be classified according to theprocess function, as outlined in Fig 1.2 However, they are not discussed here and thereader may refer to Shah and Mueller (1988) Additional ways to classify heat exchangersare 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 contact types

direct-1.2.1 Indirect-Contact Heat Exchangers

In an indirect-contact heat exchanger, the fluid streams remain separate and the heattransfers continuously through an impervious dividing wall or into and out of a wall in atransient manner Thus, ideally, there is no direct contact between thermally interactingfluids This type of heat exchanger, also referred to as a surface heat exchanger, can befurther classified into direct-transfer type, storage type, and fluidized-bed exchangers

1.2.1.1 Direct-Transfer Type Exchangers In this type, heat transfers continuouslyfrom the hot fluid to the cold fluid through a dividing wall Although a simultaneousflow of two (or more) fluids is required in the exchanger, there is no direct mixing of thetwo (or more) fluids because each fluid flows in separate fluid passages In general, thereare no moving parts in most such heat exchangers This type of exchanger is designated

as a recuperative heat exchanger or simply as a recuperator.{Some examples of transfer type heat exchangers are tubular, plate-type, and extended surface exchangers.Note that the term recuperator is not commonly used in the process industry for shell-

direct-FIGURE 1.2 (a) Classification according to process function; (b) classification of condensers; (c) classification of liquid-to-vapor phase-change exchangers.

{ In vehicular gas turbines, a stationary heat exchanger is usually referred to as a recuperator, and a rotating heat exchanger as a regenerator However, in industrial gas turbines, by long tradition and in a thermodynamic sense, a stationary heat exchanger is generally referred to as a regenerator Hence, a gas turbine regenerator could be either

a recuperator or a regenerator in a strict sense, depending on the construction In power plants, a heat exchanger is

and-tube and plate heat exchangers, although they are also considered as recuperators.Recuperators are further subclassified as prime surface exchangers and extended-surfaceexchangers Prime surface exchangers do not employ fins or extended surfaces on anyfluid side Plain tubular exchangers, shell-and-tube exchangers with plain tubes, andplate 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 natively through the same flow passages, and hence heat transfer is intermittent Theheat transfer surface (or flow passages) is generally cellular in structure and is referred to

alter-as a matrix (see Fig 1.43), or it is a permeable (porous) solid material, referred to alter-as apacked bed.When hot gas flows over the heat transfer surface (through flow passages),

FIGURE 1.2 (d) classification of chemical evaporators according to (i) the type of construction, and (ii) how energy is supplied (Shah and Mueller, 1988); (e) classification of reboilers.

the thermal energy from the hot gas is stored in the matrix wall, and thus the hot gas isbeing cooled during the matrix heating period As cold gas flows through the samepassages later (i.e., during the matrix cooling period), the matrix wall gives up thermalenergy, which is absorbed by the cold fluid Thus, heat is not transferred continuouslythrough the wall as in a direct-transfer type exchanger (recuperator), but the corre-sponding thermal energy is alternately stored and released by the matrix wall Thisstorage type heat exchanger is also referred to as a regenerative heat exchanger, orsimply as a regenerator.{ To operate continuously and within a desired temperaturerange, the gases, headers, or matrices are switched periodically (i.e., rotated), so thatthe same passage is occupied periodically by hot and cold gases, as described further inSection 1.5.4 The actual time that hot gas takes to flow through a cold regeneratormatrix is called the hot period or hot blow, and the time that cold gas flows through thehot regenerator matrix is called the cold period or cold blow For successful operation, it

is not necessary to have hot- and cold-gas flow periods of equal duration There is someunavoidable carryover of a small fraction of the fluid trapped in the passage to the otherfluid stream just after switching of the fluids; this is referred to as carryover leakage Inaddition, if the hot and cold fluids are at different pressures, there will be leakage fromthe high-pressure fluid to the low-pressure fluid past the radial, peripheral, and axialseals, or across the valves This leakage is referred to as pressure leakage Since theseleaks are unavoidable, regenerators are used exclusively in gas-to-gas heat (and mass)transfer applications with sensible heat transfer; in some applications, regenerators maytransfer moisture from humid air to dry air up to about 5%

For heat transfer analysis of regenerators, the"-NTU method of recuperators needs

to be modified to take into account the thermal energy storage capacity of the matrix Wediscuss the design theory of regenerators in detail in Chapter 5

1.2.1.3 Fluidized-Bed Heat Exchangers In a fluidized-bed heat exchanger, one side of

a two-fluid exchanger is immersed in a bed of finely divided solid material, such as atube bundle immersed in a bed of sand or coal particles, as shown in Fig 1.3 If theupward fluid velocity on the bed side is low, the solid particles will remain fixed inposition in the bed and the fluid will flow through the interstices of the bed If theupward fluid velocity is high, the solid particles will be carried away with the fluid At a

‘‘proper’’ value of the fluid velocity, the upward drag force is slightly higher than theweight of the bed particles As a result, the solid particles will float with an increase inbed volume, and the bed behaves as a liquid This characteristic of the bed is referred to

as a fluidized condition Under this condition, the fluid pressure drop through the bedremains almost constant, independent of the flow rate, and a strong mixing of the solidparticles occurs This results in a uniform temperature for the total bed (gas and par-ticles) with an apparent thermal conductivity of the solid particles as infinity Very highheat transfer coefficients are achieved on the fluidized side compared to particle-free ordilute-phase particle gas flows Chemical reaction is common on the fluidized side inmany process applications, and combustion takes place in coal combustion fluidizedbeds The common applications of the fluidized-bed heat exchanger are drying, mixing,adsorption, reactor engineering, coal combustion, and waste heat recovery Since the

{ Regenerators are also used for storing thermal energy for later use, as in the storage of thermal energy Here the objective is how to store the maximum fraction of the input energy and minimize heat leakage However, we do not

initial temperature difference (Th;i
Tf;i){is reduced due to fluidization, the exchangereffectiveness is lower, and hence"-NTU theory for a fluidized-bed exchanger needs to bemodified (Suo, 1976) Chemical reaction and combustion further complicate the design

of these exchangers but are beyond the scope of this book

1.2.2 Direct-Contact Heat Exchangers

In a direct-contact exchanger, two fluid streams come into direct contact, exchange heat,and are then separated Common applications of a direct-contact exchanger involve masstransfer in addition to heat transfer, such as in evaporative cooling and rectification;applications involving only sensible heat transfer are rare The enthalpy of phase change

in such an exchanger generally represents a significant portion of the total energy fer The phase change generally enhances the heat transfer rate Compared to indirect-contact recuperators and regenerators, in direct-contact heat exchangers, (1) very highheat transfer rates are achievable, (2) the exchanger construction is relatively inexpensive,and (3) the fouling problem is generally nonexistent, due to the absence of a heat transfersurface (wall) between the two fluids However, the applications are limited to those caseswhere a direct contact of two fluid streams is permissible The design theory for these

FIGURE 1.3 Fluidized-bed heat exchanger.

{T , inlet temperature of the hot fluid to the fluidized bed; T , temperature of the fluidized bed itself at the inlet.

exchangers is beyond the scope of this book and is not covered These exchangers may befurther classified as follows.

1.2.2.1 Immiscible Fluid Exchangers In this type, two immiscible fluid streams arebrought into direct contact These fluids may be single-phase fluids, or they may involvecondensation or vaporization Condensation of organic vapors and oil vapors withwater or air are typical examples

1.2.2.2 Gas–Liquid Exchangers In this type, one fluid is a gas (more commonly, air)and the other a low-pressure liquid (more commonly, water) and are readily separableafter the energy exchange In either cooling of liquid (water) or humidification of gas(air) applications, liquid partially evaporates and the vapor is carried away with the gas

In these exchangers, more than 90% of the energy transfer is by virtue of mass transfer(due to the evaporation of the liquid), and convective heat transfer is a minor mechan-ism A ‘‘wet’’ (water) cooling tower with forced- or natural-draft airflow is the mostcommon application Other applications are the air-conditioning spray chamber, spraydrier, spray tower, and spray pond

1.2.2.3 Liquid–Vapor Exchangers In this type, typically steam is partially or fullycondensed using cooling water, or water is heated with waste steam through directcontact in the exchanger Noncondensables and residual steam and hot water are theoutlet streams Common examples are desuperheaters and open feedwater heaters (alsoknown as deaeraters) in power plants

1.3 CLASSIFICATION ACCORDING TO NUMBER OF FLUIDS

Most processes of heating, cooling, heat recovery, and heat rejection involve transfer ofheat between two fluids Hence, two-fluid heat exchangers are the most common Three-fluid heat exchangers are widely used in cryogenics and some chemical processes (e.g., airseparation systems, a helium–air separation unit, purification and liquefaction of hydro-gen, ammonia gas synthesis) Heat exchangers with as many as 12 fluid streams have beenused in some chemical process applications The design theory of three- and multifluidheat exchangers is algebraically very complex and is not covered in this book.Exclusively, only the design theory for two-fluid exchangers and some associatedproblems are presented in this book

1.4 CLASSIFICATION ACCORDING TO SURFACE COMPACTNESS

Compared to shell-and-tube exchangers, compact heat exchangers are characterized by alarge heat transfer surface area per unit volume of the exchanger, resulting in reducedspace, weight, support structure and footprint, energy requirements and cost, as well asimproved process design and plant layout and processing conditions, together with lowfluid inventory

A gas-to-fluid exchanger is referred to as a compact heat exchanger if it incorporates

a heat transfer surface having a surface area density greater than about 700 m2/m3

(213 ft2/ft3){or a hydraulic diameter Dh 6 mm (1

4in.) for operating in a gas stream and

400 m2/m3(122 ft2/ft3) or higher for operating in a liquid or phase-change stream Alaminar flow heat exchanger (also referred to as a meso heat exchanger) has a surfacearea density greater than about 3000 m2/m3(914 ft2/ft3) or 100mm  Dh 1 mm Theterm micro heat exchanger is used if the surface area density is greater than about15,000 m2/m3 (4570 ft2/ft3) or 1mm  Dh 100 mm A liquid/two-phase fluid heatexchanger is referred to as a compact heat exchanger if the surface area density on anyone fluid side is greater than about 400 m2/m3 In contrast, a typical process industry shell-and-tube exchanger has a surface area density of less than 100 m2/m3on one fluid side withplain tubes, and two to three times greater than that with high-fin-density low-finnedtubing A typical plate heat exchanger has about twice the average heat transfer coefficient

hon one fluid side or the average overall heat transfer coefficient U than that for a and-tube exchanger for water/water applications A compact heat exchanger is not neces-sarily of small bulk and mass However, if it did not incorporate a surface of high-surface-area density, it would be much more bulky and massive Plate-fin, tube-fin, and rotaryregenerators are examples of compact heat exchangers for gas flow on one or both fluidsides, and gasketed, welded, brazed plate heat exchangers and printed-circuit heat exchan-gers are examples of compact heat exchangers for liquid flows Basic flow arrangements oftwo-fluid compact heat exchangers are single-pass crossflow, counterflow, and multipasscross-counterflow (see Section 1.6 for details); for noncompact heat exchangers, manyother flow arrangements are also used The aforementioned last two flow arrangements forcompact or noncompact heat exchangers can yield a very high exchanger effectivenessvalue or a very small temperature approach (see Section 3.2.3 for the definition) betweenfluid streams

shell-A spectrum of surface area density of heat exchanger surfaces is shown in Fig 1.4 Onthe bottom of the figure, two scales are shown: the heat transfer surface area density
(m2/m3) and the hydraulic diameter Dh,{ (mm), which is the tube inside or outsidediameter D (mm) for a thin-walled circular tube Different heat exchanger surfaces areshown in the rectangles When projected on the
(or Dh) scale, the short vertical sides of

a rectangle indicate the range of surface area density (or hydraulic diameter) for theparticular surface in question What is referred to as
in this figure is either
1or
2,defined as follows For plate heat exchangers, plate-fin exchangers, and regenerators,

{ The unit conversion throughout the book may not be exact; it depends on whether the number is exact or is an engineering value.

{ The hydraulic diameter is defined as 4A o =P, where A o is the minimum free-flow area on one fluid side of a heat exchanger and P is the wetted perimeter of flow passages of that side Note that the wetted perimeter can be different for heat transfer and pressure drop calculations For example, the hydraulic diameter for an annulus of a double-pipe heat exchanger for q and
p calculations is as follows.

a two-fluid exchanger is immersed in a bed of finely divided solid material, such as atube bundle immersed in a bed of sand... andplate 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,