Contents PrefaceIX Part 1General Aspects1 Chapter 1Thermodynamic
Optimization3 M.M. Awad and Y.S. Muzychka Chapter 2Analytical
Solutionof Dynamic Response of Heat Exchanger53 D. Gvozdenac
Chapter 3Self-Heat Recuperation: Theory and Applications79 Yasuki
Kansha, Akira Kishimoto, Muhammad Azizand Atsushi Tsutsumi Chapter
4Development of High EfficiencyTwo-Phase Thermosyphons for Heat
Recovery97 Ignacio Carvajal-Mariscal, Florencio Sanchez-Silvaand
Georgiy Polupan Chapter 5Impact of a Medium Flow Maldistributionon
a Cross-Flow Heat Exchanger Performance117 Tomasz Bury Chapter
6Control of LNG Pyrolysis and Applicationto Regenerative Cooling
Rocket Engine143 R. Minato, K. Higashino, M. Sugioka and Y.
Sasayama Chapter 7Numerical Analysis of the StructuralStability of
Heat Exchangers The FEM Approach165 Agnieszka A. Chudzik Part
2Micro-Channels and Compact Heat Exchangers187 Chapter
8Microchannel Simulation189 Mohammad Hassan Saidi, Omid Asgari and
Hadis Hemati VIContents Chapter 9Compact Heat Exchange ReformerUsed
for High Temperature Fuel Cell Systems221 Huisheng Zhang, Shilie
Weng and Ming Su Chapter 10Single-Phase Heat Transfer and FluidFlow
Phenomena of Microchannel Heat Exchangers249 Thanhtrung Dang,
Jyh-tong Teng, Jiann-cherng Chu, Tingting Xu,Suyi Huang, Shiping
Jin and Jieqing Zheng Chapter 11Heat Exchangers for Thermoelectric
Devices289 David Astrain and lvaro Martnez Part 3Helical Coils and
Finned Surfaces309 Chapter 12Helically Coiled Heat Exchangers311 J.
S. Jayakumar Chapter 13Fin-Tube Heat Exchanger Optimization343
Piotr Wais Chapter 14Thermal Design of Cooling and Dehumidifying
Coils367 M. Khamis Mansour and M. Hassab Part 4Plate Heat
Exchangers395 Chapter 15The Characteristics of Brazed Plate
HeatExchangers with Different Chevron Angles397 M. Subbiah Part
5Energy Storage Heat Pumps Geothermal Energy425 Chapter 16PCM-Air
Heat Exchangers: Slab Geometry427 Pablo Dolado, Ana Lzaro, Jos Mara
Marnand Beln Zalba Chapter 17Ground-Source Heat Pumps and Energy
Saving459 Mohamad Kharseh Chapter 18The Soultz-sous-Forts Enhanced
GeothermalSystem: A Granitic Basement Usedas a Heat Exchanger to
Produce Electricity477 Batrice A. Ledsert and Ronan L. Hbert Part
6Fouling of Heat Exchangers505 Chapter 19Fouling and Fouling
Mitigationon Heat Exchanger Surfaces507 S. N. Kazi ContentsVII
Chapter 20Fouling in Plate Heat Exchangers:Some Practical
Experience533 Ali Bani Kananeh and Julian Peschel Chapter
21Self-Cleaning Fluidised Bed Heat Exchangers for Severely Fouling
Liquids and Their Impact on Process Design551 Dick G. Klaren and
Eric F. Boer de Preface
Asmotiveforceofprocesses,heatmustbetransferredfromonefluidtoother,task
thatisperformedbymeansofheatexchangers.Fromthispointofview,heat
exchangersrepresentanimportantelementofthermalfacilitiesthathassubstantially
contributed to technical development of the society. Today it is
impossible to imagine any branch of process engineering and energy
technology without involvement of heat exchangers. Advanced models
of these apparatus were proposed in the middle of the 18th century,
while theoretical backgrounds have been completed a century
later.Correspondingtopracticalimportanceofheatexchangers,innumerablestudiesand
treatisesaredevotedtoprocessestakingplaceinthesedevicesandtheirconstructive
shaping. The actual development trend in this field is guided by
the ideas of reduction of
thermaltransportresistancesandtheraiseofenergyconversionefficiency.Theseideas
havealsoguidedtheconceptionofthepresentbook.Itisacollectionofcontributions
prepared by the specialists. It consists of 21 Chapter that are
arranged in 6 Sections:Section 1: General Aspects,Section 2:
Micro-Channels and Compact Heat Exchangers,Section 3: Plate Heat
Exchangers,Section 4: Helical Coils and Finned Surfaces,Section 5:
Energy Storage, Heat Pumps and Geothermal Energy, Section 6:
Fouling of Heat Exchangers. Section 1 - General Aspects
Thispartcomprises7Chaptersdealingmainlywiththequestionsoffluidflowand
heattransferinheatexchangers.Chapter1byAwadandMuzychkaaddressesthe
entropygenerationarisingfromheattransferandfluidflowandprovidesabasisfor
thermodynamicoptimisationofheatexchangers.GvozdenacgivesinChapter2a
detailedanalysisofconvectiveheattransferinheatexchangersatdifferentflow
arrangements under transient conditions. Kansha et al. present in
Chapter 3 a self-heat recuperation technology for transport of
latent and sensible heat of the process streams without heat
addition and introduce a theoretical analysis of this technology.
Carvajal-Mariscal et al. recommend in Chapter 4 combinations of
process parameters that give
highefficiencyoftwo-phasethermosyphons.Thesedevicesareusedfortransportof
highheatflowratesfromheatsourcetoheatsinkbyconnectingtheevaporatorand
XPreface the condenser. The heat flow rate is reduced, if the
elements of the heat exchangers are not evenly supplied with the
fluid. Bury examined the issue in Chapter 5 and reports
anaveragedeteriorationfactorof15%foracross-flowheatexchanger.InChapter6,
Minatoetal.dealwiththeLNGpyrolysisinconnectionwithregenerativecoolingof
rocket engines. The processes occurring are exceedingly complex,
not only because of high process temperatures, which usually cause
large temperature gradients. Thermal
stressesthusinducedmayimpairthestructuralstabilityofconstructions,asis
exemplified by A. Chudzik in Chapter 7 for a shell-and-tube heat
exchanger.Section 2 - Micro-Channels and Compact Heat Exchangers
Section2clustersthecontributionsdealingwiththeprocessesoccurringinmicro-channelsandapparatuscomposedofsuchelements.Byusingmicro-channels,one
pursues the idea of shortening the heat transfer paths, thereby
trying to copy solutions evolved in the nature. In Chapter 8,
Asgari analyses numerically the heat transfer in a
heatexchanger,consistingofanumberofrectangularmicro-channels,connectedin
parallel,atlowRenumberswithfullydevelopedflow.Theappliedheatfluxisor-thogonal
and uniform on the bottom plane of the apparatus. Zhang et al., in
Chapter 9, simulate dynamically a compact heat exchange reformer
for high temperature fuel cell
systemsundercatalyticconditions.Themodellingtechniqueissuitedforquickand
realtimecalculations.Withsinglephaseflow,Dangetal.showinChapter10the
hydraulicdiameterofthemicrochanneltobethechiefparametergoverningthe
thermo-fluidcharacteristicoftheapparatus.Bothexperimentalandnumericaltreat-mentsconfirmadvantagesofcounter-currentfluidflowarrangement.Thecontribu-tioninChapter11dealswiththethermoelectricdevices,whichareusedeitherto
generateelectricpotentialinatemperaturegradient(Seebeckeffect)ortogeneratea
temperaturedifferencebymeansofelectriccurrent(Peltiereffect).Astrainand
Martnez analysed there the efficiency of the device, mainly
focussing on heat transfer.
Thethermalperformancesofheattransfermodulesaredemonstratedtodecisively
affect the efficiency of the whole system. Section 3 - Plate Heat
Exchangers
Section3comprisesthecontributionsdealingwiththeheatexchangersconsistingof
helical coils and finned surfaces. Helical coils provide the
simplest construction of heat
exchangerswhilefiningofsurfacesshouldcompensateforthelowheattransfer.In
Chapter 12 Jayakumar presents a detailed analysis of hydrodynamic
and heat transfer of single-phase and two-phase water flow in
helical pipes, for various coil parameters and boundary conditions.
Basing on the results, correlations for the average and local
Nusseltnumbersweredeveloped.WaispursuesinChapter13thepossibilitiesof
finding the fin shape that should maximize the heat transfer and
reduce the fin mass.
Theresultsofnumericalexperimentsareusedfordevelopingofheattransfer
correlations. Chapter 14 by Khamis Mansour deals with the thermal
design of cooling
anddehumidifyingcoils.Theusedrow-by-rowcalculationmethodprovidesabetter
reliability than the common averaging method. This is of particular
importance when local data are required as in case of air
dehumidifiers.PrefaceXI Section 4 - Helical Coils and Finned
Surfaces
Plateheatexchangersconsistofanumberofplatesassembledinparallelnexttoone
another thus forming flow channels such that each plate separates
hot from cold fluid
stream.Platesareprovidedwithmacrostructuresandtheneighbouringplatestouch
each other on the crests of the structures. The channels are
gasketed or brazed on the
circumference.InChapter15Muthuramanpresentsresultsoftheexperimental
condensationstudiesofR410Ainbrazedplateheatexchangersforvariousplate
structures and provides correlations for heat transfer and pressure
drop.Section 5 - Energy Storage, Heat Pumps and Geothermal Energy
Part5bundlesthecontributionsdealingwiththestorageandconversionofthermal
energy, focussing on alternative energy sources and clean energy.
Thermal radiation of the Sun counts to the cleanest energies; being
availably mainly seasonally, its storage is
becomingincreasinglyimportant.Ifstoredasinternalenergyofasubstance,the
substanceshouldundergoanendothermicphasetransitionduringstoringwhile
exothermicwhenreleasingtheheat.Chapter16byDoladoetal.dealswiththeheat
exchangerscomprisingphasechangematerials,illustratingtheprocessesmainlyin
formoftemperaturehistorydiagrams.Thermalenergystoredinthegroundmaybe
utilizedbymeansofheatpumps.Chapter17byKharsehillustratesanexamplewith
surface geothermal energy, while Ledsert and Hbert give in Chapter
18 an overview on the exploitation of deep geothermal energy. The
high temperature of energy source in later case allows
transformation of geothermal energy in other energy forms. Section
6 - Fouling of Heat Exchangers
Dissolvedsolidsubstancesandimpuritiescontainedinprocessstreamsinteractwith
theheattransfersurfaces,attractivelyorrepulsively.Incaseofattraction,the
concentrationofthedissolvedmayreachthesolubilityboundaryandinitiate
crystallisation. Starting from this initial state, a solid layer
grows on the surface during
operation;itdiminishesthethermalcapacityofheatexchanger,ifitsthermal
conductivity is low. This is referred to as fouling.The
contribution devoted to fouling
ofheatexchangersaregroupedinthisPart.Chapter19byKaziaddressesgeneral
questionsoffouling,therebyanalysingitsimpactsonheattransfer.Somepractical
insightsintofoulinginplateheatexchangersareprovidedinChapter20byBani
KananehandPeschel,whileinChapter21KlarenanddeBoerreportontheself-cleaning
fluidised bed heat exchangers. Prof. Dr. Ing. Jovan Mitrovic
Thermodynamics and Thermal Process Engineering Germany Part 1
General Aspects 1 Thermodynamic Optimization* M.M. Awad1 and Y.S.
Muzychka2 1Mechanical Power Engineering Department,Faculty of
Engineering, Mansoura University,2Faculty of Engineering and
Applied Science, St. John's, NL,Memorial University of
Newfoundland,1Egypt 2Canada 1.
IntroductionSecondlawanalysisinthedesignofthermalandchemicalprocesseshasreceived
considerable attention since 1970s. For example, Gaggioli and Petit
(1977) reviewed the first and second laws of thermodynamics as an
introduction to an explanation of the thesis that energy analyses
of plants, components, and processes should be made by application
of the second law that deals with the availability of energy or the
potential energy. They illustrated
theirmethodologysuggestedbyapplyingittoananalysisoftheKoppers-Totzek
gasification system. Optimization of heat exchangers based on
second-law rather than first-law considerations ensures that the
most efficient use of available energy is being made.Second-law
analysis has affected the design methodology of different heat and
mass transfer systems to minimize the entropy generation rate, and
so to maximize system available work.
Manyresearchersconsideredtheseprocessesintermsofoneoftwoentities:exergy
(availableenergy)andirreversibility(entropyproduction).Forinstance,McClintock(1951)
described irreversibility analysis of heat exchangers, designed to
transfer a specified amount of heat between the fluid streams. He
gave explicit equations for the local optimum design
offluidpassagesforeithersideofaheatexchanger.Totheknowledgeofauthors,
McClintock(1951)wasthefirstresearcherwhoemployedtheirreversibilityconceptfor
estimating and minimizing the usable energy wasted in heat
exchangers design. Bejan (1977) introduced the concept of designing
heat exchangers for specified irreversibility rather than
specifiedamountofheattransferred.Manyauthorsusedthistechniqueinthefieldof
cryogenicengineering(BejanandSmith(1974,1976),Bejan(1975),andHilalandBoom
(1976)).
Oneofthefirstexaminationsofentropygenerationinconvectiveheattransferwas
conductedbyBejan(1979)foranumberoffundamentalapplications.Muchoftheearly
*ThepartofthischapterwaspresentedbyY.S.Muzychkainfall2005asPartIIIduringtheshort
course: Adrian Bejan, Sylvie Lorente, and Yuri Muzychka,Constructal
Design ofPorous andComplex
FlowStructures,MemorialUniversityofNewfoundland,FacultyofEngineeringandAppliedScience,
St. John's, NL, Canada, September 21-23, 2005. Heat Exchangers
Basics Design Applications 4
workiswelldocumentedinhisbooks(Bejan,1982aand1996a).Sincethepublicationof
(Bejan,1996a),entropygenerationininternalstructurehasbeenexaminedbynumerous
researchers.Inthissection,wewillexaminethesestudiesthatincludetheoptimizationof
heat exchangers, and enhancement of internal flows. Also, we will
proceed to develop some of the basic principles and examine
selected results from the published literature. 1.1 Optimization of
heat exchangers
Inthepastthirtyfiveyears,muchworkrelatingtoheatexchangerdesignbasedonthe
second law of thermodynamics was presented by researchers (Bejan,
1988). Heat exchangers
haveoftenbeensubjectedtothermodynamicoptimization(orentropygeneration
minimization)inisolation,i.e.,removedfromthelargerinstallation,whichusesthem.
Examplesincludetheparallelflow,counterflow,crossflow,andphase-changeheat
exchanger optimizations. We will talk in details about this in this
section.
Bejan(1977)presentedaheatexchangerdesignmethodforfixedorforminimum
irreversibility (number of entropy generation units, Ns). The
researcher obtained the number
ofentropygenerationunits(Ns)bydividingentropygenerationratebythesmallestheat
capacityrateofthefluids.ThevalueofNscanrangebetween0-.Theheatexchanger
would have a better performance if the entropy generation was at
its minimum (Ns0). This dimensionless number can clearly express
how a heat exchanger performance is close to an ideal heat
exchanger in terms of thermal losses. He showed that entropy
generation in a heat exchanger is due to heat transfer through
temperature gradient and fluid friction. In contrast with
traditional design procedures, the amount of heat transferred
between streams and the
pumpingpowerforeverysidebecameoutputsoftheNsdesignapproach.Also,he
proposedamethodologyfordesigningheatexchangersbasedonentropygeneration
minimization.Toillustratetheuseofhismethod,thepaperdevelopedthedesignof
regenerativeheatexchangerswithminimumheattransfersurfaceandwithfixed
irreversibility Ns.
Thethermaldesignofcounterflowheatexchangersforgas-to-gasapplicationsisbasedon
the thermodynamic irreversibility rate or useful power no longer
available as a result of heat
exchangerfrictionalpressuredropsandstream-to-streamtemperaturedifferences.The
irreversibility(entropyproduction)conceptestablishesadirectrelationshipbetweenthe
heatexchangerdesignparametersandtheusefulpowerwastedduetoheatexchanger
nonideality.Bejan(1978)demonstratedtheuseofirreversibilityasacriterionforevaluationofthe
efficiencyofaheatexchanger.Theresearcherminimizedthewastedenergyusingthe
optimumdesignoffluidpassagesinaheatexchanger.Hestudiedtheinterrelationship
between the losses caused by heat transfer across the
stream-to-stream due to differences in temperatures and losses
caused by fluid friction. He obtained the following relation for
the entropy generation rate per unit length as follows: . . .2 201
1gen dS dq dq m dP T m dP TT T dx T dx dx T dx dxT TT T A A | | |
|= + ~ + > ||A A | | | |\ . \ .+ + ||\ . \ .(1) Thermodynamic
Optimization 5 The first term in expression (1) is the entropy
production contribution due to fluid friction in
thefluidduct.Thesecondterminexpression(1)representsthecontributionduetoheat
transfer across the wall-fluid temperature difference. These two
contributions were strongly interrelatedthroughthegeometric
characteristicsoftheheatexchanger.Itshouldbenoted that the use of
density () instead of the inverse of specific volume (v) in the
first term on the
righthandside.Also,thedenominatorofthesecondtermontherighthandsidewas
simplified by assuming that the local temperature difference (AT)
was negligible compared with the local absolute temperature (T).
Heat transfer losses could be reduced by increasing
theheattransferarea,butinthiscasepressuredropsinthechannelsincreased.Bothheat
transfer losses and frictional pressure drops in channels
determined the irreversibility level of heat
exchanger.AremarkablefeatureofEq.(1)andofmanylikeitforothersimpledevicesisthata
proposeddesignchange(forinstance,makingthepassagenarrower)induceschangesof
opposite signs in the two terms of the expression. Then, an optimal
trade-off exists between the fluid friction irreversibility and the
heat transfer irreversibility contributions, an optimal
designforwhichtheoverallmeasureofexergydestructionisminimum,whilethesystem
continuestoserveitsspecifiedfunction.Inordertoillustratethistrade-off,usethe
definitionoffrictionfactor(f),Stantonnumber(St),massflux(G),Reynoldsnumber(Re),
and hydraulic diameter (dh): 22hd dPfdx G | |= |\ .(2) 1pdqStdx p
TcG=A(3) .mGA= (4) RehGd= (5) 4hAdp= (6) In Eq. (3), the quantity
(dq/dx)/(pAT) is better known as the average heat transfer
coefficient. The entropy generation rate, Eq. (1) becomes 3. .2. 2
2224genhhpdS dq m f ddx dx TdAT mcSt| |= + |\ .(7)
Whereheattransferrateperunitlengthandmassflowratearefixed.Thegeometric
configurationoftheexchangerpassagehastwodegreesoffreedom,theperimeter(p)and
the cross-sectional area (A), or any other pair of independent
parameters, like (Re; dh) or (G; Heat Exchangers Basics Design
Applications 6 dh). If the passage is a straight pipe with circular
cross-section, p and A are related through
thepipeinnerdiameterdthatistheonlydegreeoffreedomleftinthedesignprocess.
Writing 2, /4,hd d A d and p d t t = = = (8) Equation (7) becomes
3. .22 2 2 532 genhdS dq m f ddx dx TkNu Td t t | |= + |\ .(9)
Where Re = 4 m/td. The Nusselt number (Nu) definition, and the
relation betweenNu, St, Re, and the Prandtl number (Pr = v/o)
.Re.Pr ..av hh dNu St St Pek= = = (10) Introducing two classical
correlations for fully developed turbulent pipe flow (Bejan, 1993),
0.8 0.4 40.023Re Pr ( 0.7 Pr 160 : Re 10 ) Nu = ( ( ) (11) -0.2 4
60.046 Re (10 Re 10 ) f = ( ( (12)
andcombiningthemwithEq.(9),yieldsanexpressionforexergydestruction,which
dependsonlyonRe.DifferentiatingtheexergydestructionwithrespecttotheReynolds
number(Re)andequalingtheresultwithzero,wefindthattheentropygenerationrateis
minimized when the Reynolds number (or pipe diameter) reaches the
optimal value (Bejan, 1982a) -0.071 0.358optRe2.023Pr B = (13)
Equation(13)showshowtoselecttheoptimalpipesizeforminimalirreversibility.
ParameterBisaheatandfluidflowdutyparameterthataccountsfortheconstraintsof
heat transfer rate per unit length, and mass flow rate: .5/2 1/2(
)dq pB mdx kT | |= |\ .(14) Additional results may be obtained for
non-circular ducts using the appropriate expressions for the
geometry A and p, and appropriate models for heat transfer and
friction coefficients.
TheReynoldsnumber(Re)effectontheexergydestructioncanbeexpressedinrelative
terms as . 0.8 4.8.min/ Re Re0.856 0.144Re Re( / )genopt optgendS
dxdS dx| | | | || = + ||\ . \ .(15) Thermodynamic Optimization 7
wheretheratioontheleft-handsideisknownastheentropygenerationnumber(Ns),
(Bejan,1982a).InthedenominatorofthelefthandsideofEq.(15),theminimumexergy
destructioniscalculatedattheoptimumReynoldsnumber(Reopt).Also,Re/Reopt=dopt/d
becausethemassflowrateisfixed.UsingEq.(15),itisclearthattherateofentropy
generationincreasessharplyoneithersideoftheoptimum.Thelefthandsideofthe
optimum represents the region in which the overall entropy
generation rate is dominated by heat transfer effects. The right
hand side of the optimum represents the region in which the
overallentropygenerationrateisdominatedbyfluidfrictioneffects.Thelefthandsideof
Eq. (15) is used to monitor the approach of any design relative to
the best design that can be
conceivedsubjecttothesameconstraints.Bejan(1982a,1988)usedthisperformance
criterionextensivelyintheengineeringliterature.Also,Mironovaetal.(1994)recognized
this performance criterion in the physics literature.
Bejan(1978)alsomadeaproposaltousethenumberofentropyproductionunits(Ns)asa
basicyardstickindescribingtheheatexchangerperformance.Thisdimensionlessnumber
was defined as the entropy production rate or irreversibility rate
present in a heat exchanger channel. When Ns 0, this implied an
almost ideal heat exchanger channel. According to his
study,itwasenoughtoincreasetheeffectivenessbyusingdesigncriterionslikethe
minimizationofdifferencewalltemperatureormaximizationoftheratioofheattransfer
coefficient to fluid pumping power. Bejan (1979) illustrated the
second law aspects of heat transfer by forced convection in terms
offourfundamentalflowconfigurations:pipeflow,boundarylayeroverflatplate,single
cylinderincross-flow,andflowintheentranceregionofaflatrectangularduct.The
researcher analyzed in detail the interplay between irreversibility
due to heat transfer along finite temperature gradients and, on the
other hand, irreversibility due to viscous effects. He presented
the spatial distribution of irreversibility, entropy generation
profiles or maps, and
thoseflowfeaturesactingasstrongsourcesofirreversibility.Heshowedhowtheflow
geometricparametersmightbeselectedtominimizetheirreversibilityassociatedwitha
specific convective heat transfer process.
Bejan(1980)usedthesecondlawofthermodynamicsasabasisforevaluatingthe
irreversibility(entropygeneration)associatedwithsimpleheattransferprocesses.Inthe
first part of his paper, he analyzed the irreversibility production
from the local level, at one point in a convective heat transfer
arrangement. In the second part of his paper, he devoted
toalimitedreviewofsecondlawanalysisappliedtoclassicengineeringcomponentsfor
heatexchange.Inthiscategory,thepaperincludedtopicslikeheattransferaugmentation
techniques,heatexchangerdesign,andthermalinsulationsystems.Theresearcher
presentedanalyticalmethodsforevaluatingandminimizingtheirreversibilityassociated
with textbook-type components of heat transfer equipment. Also, he
obtained an expression for the entropy generation rate in a
balanced counterflow heat exchanger with zero pressure drop
irreversibility as follows: 1 22 121 1ln(1 )sT TNTU NTUT TNNTU| | |
|+ + ||\ . \ .=+(16) Heat Exchangers Basics Design Applications 8
UsingEq.(16),Ns =0atbothc=0(oratNTU=0)andc=1(oratNTU=),andhadits
maximum value at c = 0.5 (or at NTU = 1). The maximum Ns increases
as soon as T1/T2 goes above or below 1: 1 2,max2 11 1ln2 4sT TNT T
( | |= + + (| ( \ . (17)
NsincreaseswiththeabsolutetemperatureratioT2/T1.WhenNs>1,theirreversibility
decreasessharplyasc1.OntheleftsideofthemaximumNs 0 represented
poorer quality. Thermodynamic Optimization 9
Also,hedescribedtherelativeimportanceofthetwoirreversibilitymechanismsusingthe
irreversibility distribution ratio (|) that was defined as:
.,.,fluid - flow irreversibility heat transfer irreversibilitygen
Pgen TSS|AA= = (19) For example, the irreversibility distribution
ratio (|) varies along with the V-shaped curve of
entropygenerationnumber(Ns),orrelativeentropygenerationrateinasmoothpipewith
heat transfer (Bejan, 1980), increasing in the direction of large
Reynolds numbers (small pipe diameters because the mass flow rate
is fixed) in which the overall entropy generation rate is
dominatedbyfluidfrictioneffects.Attheoptimum(correspondingtoNs=1),the
irreversibilitydistributionratio(|)assumesthevalue|opt=0.168.Thismeansthatthe
optimaltrade-offbetweentheirreversibilityduetoheattransfereffectsandthe
irreversibilityduetofluidfrictioneffectsdoesnotcoincidewiththedesignwherethe
irreversibility mechanisms are in perfect balance, even though
setting| = 1 is a fairly good way of locating the
optimum.Substituting Eq. (19) into Eq. (18) yields . ., (1 ) gen
gen T S S | A = + (20) In addition, augmentation entropy generation
number (Ns,a) was given by .,,.,gen asagen oSNS= (21)
Thisdefinitionrepresentstheratiooftheaugmentedtobasechannelentropygeneration
rates.Underparticularflowconditionsand/orconstraints,Ns,a
= == = = =(2) Heat Exchangers Basics Design Applications
56Theseconditionsassumethatonlyfluid1inletconditionisperturbed.Thestepchangeof
inlettemperatureoffluid1iscertainlythemostimportantfromphysicalpointofview.
Other inlet temperature changes can be analyzed using described
mathematical model and procedures for their analytical solution.In
equations 1 and 2, the convention of index 1 referring to weaker
fluid flow and index 2 to stronger fluid flow is introduced. Fluid
undergoing higher temperature changes because of
smallervalueofthethermalcapacity pW mc =
iscalledweaker?Theotherflowisthen
strongeranditislesschangedintheheatexchanger.Theproductofmassflowrateand
isobaricspecificheatoffluidistheindicatoroffluidsflowstrengthandrepresentsits
essentialcharacteristic.Therefore,itisnecessarytomakestrictdistinctionbetweenweaker
andstrongerflow.Onlytheweakerfluidflowcanchangethestateformaximum
temperaturedifference.Therefore, ( )' 'max 1 2minpQ mc T T =
.Thisisvalidinsteadystate
conditionsalthoughflowdesignationconventionisalsoapplicabletounsteadystate
analysis. Generally, the heat exchangers effectiveness is defined
in the relation of actually exchanged
heatandmaximumpossibleoneanditisthemeasureofthermodynamicqualityofthe
device.Inthisway,theeffectivenessofallheatexchangerscanbeanumbertakenfroma
closed interval[0, 1] c
=Anotherconventionisusefulforfurtheranalysis.Ifweakerandstrongerfluidflowsare
designatedwithindices1and2,respectively,thenstandardizedrelationbetweenheat
capacities of fluids is: 12(0 1)WWe e = s s (3) The value0 e always
designates that the stronger fluid flow tends to isothermal change
intheheatexchangersince( )2pmc .WithfinalQ,implying '' '2 20 T T
,thismeans
thattheflow2changesthephase(condensationorevaporation).Onthecontrary,1
e =refers to well balanced flows, i.e. the temperatures from inlet
to outlet change equally.
Inordertodefinedimensionlesstemperatures,itisappropriatetochoosereference
temperature Tr and a characteristic temperature difference T* - Tr
so that: *( , )( , ) ( 1, 2, )i rirTXt TXt i wT Tu= =(4)
Itissuitablethatreferencetemperaturesareminimumandmaximumones,i.e.T*andTr,
respectively. If the weaker flow is designated with index 1 and if
* '1T T =and '2 rT T =then, the weaker flow enters the heat
exchanger with '11 u = and the stronger flow with '20 u =
.Forthepurposeofsimplifyingthemathematicalmodelthedimensionlessdistanceand
dimensionless time are introduced: *,X tx NTU zL t= = (5)
Analytical Solution of Dynamic Response of Heat Exchangers 57 The
number of heat transfer units is: 1 21 2 1( ) ( ) 1( ) ( )hA
hANTUhA hA W= +(6) and time parameter *1 2( ) ( )w wc MthA hA=+(7)
Further, the relation for the product of heat transfer coefficient
and heat transfer area of each fluid and the sum of these products
is as follows: 11 2 11 2( ), 1( ) ( )hAK K KhA hA= = +(8) Finally,
complex dimensionless parameter is: 1( 1, 2)iiw w i iWC L ic M K U=
= (9)
Itisinverselyproportionaltothefluidspeedinheatexchangerflowchannels.Thehigh
fluid velocity with other unchanged values in the equation (9)
means that0iC and that fluid dwell time in the heat exchanger is
short. As the fluid velocity decreases, the value of parameters Ci
increases and the time of fluid dwell time in the core of the heat
exchanger is prolonged. Fluid velocity in heat exchangers is:( , 1,
2)iii imU fluid velocity iF = =(10) Now, the system of equations
(1) can be written in the following form : 1 1 2 2wwK Kzuu u uc+ =
+ c 1 11 2 1 wC Kz xu uu uc c + = c c 2 1 22 2 wKCz xu uu uec c + =
c c(11) The initial and inlet conditions (Eqs. 2) become: 121 20
0(0, )1 0(0, ) 0( , 0) ( , 0) ( , 0) 0wfor zzfor zzx x xuuu u u<
= >== = =(12) Heat Exchangers Basics Design Applications
58Theequation(11)and(12)definetransientresponseofparallelflowheatexchangerwith
finitewallcapacitance.Mathematicalmodelisvalidforthecasewhen 1 2W W
s and temperature of fluid 1 is perturbed (unit step change).
Outlet temperatures of both fluids in steady state ( z ) are: "1"2(
, ) 1( , )NTUNTUu cu e c = = (13) wherec
iseffectivenessofheatexchanger.Effectivenessofparallelheatexchangerisas
follows: | | 1 exp (1 )0 11NTUforec ee += < s+(14) For the case0
e =the effectiveness is( ) 1 exp NTU c = (15) and is valid for all
types of heat
exchangers.Forthecasewhenstrongerfluid(fluid2)isperturbed,theinletconditionofthe
mathematical problem is changed and is as follows: 121 2(0, ) 00
0(0, )1 0( , 0) ( , 0) ( , 0) 0wzfor zzfor zx x xuuu u u=< =
>= = =(16) In this case, outlet temperatures in the conditions
of steady state are equal: "1"2( , )( , ) 1NTUNTUu e cu c = = (17)
Inthisway,resolvingofthismathematicalproblemfortwoinletconditionsincludesall
possible cases of fluid flow strength, i.e. 1 2 1 2W W and W W s
> . Only the case 1 2W W sis
analyzedinthispaperbecauseoflimitedspace.However,thepresentedprocedurefor
resolvingmathematicalmodelforalltypesofheatexchangersgivesopportunitiestoget
easily to the solution in case when1 2W W > . 2.2 Counter
flowInthesamewayasinthecaseofparallelflowheatexchanger,itispossibletosetup
mathematicalmodelofcounterflowheatexchanger(Fig.2).Theessentialdifference
between these two heat exchangers is in inlet conditions.
Analytical Solution of Dynamic Response of Heat Exchangers 59 h1,
A1h2, A2 21X L 0F2F1x NTU 0' '1 1m , T' '2 2m , T dX Fig. 2.
Schematic Description of Counter Flow Heat Exchanger
Proceduresimilartotheaboveforparallelflowdeliversthefollowingmathematical
formulation for the transient behavior of counter flow heat
exchanger: 1 1 2 2wwK Kzuu u uc+ = + c 1 11 2 1 wC Kz xu uu uc c +
= c c 2 1 22 2 wKCz xu uu uec c = c c(18) The initial and inlet
conditions are: 121 20 0(0, )1 0( , ) 0( , 0) ( , 0) ( , 0) 0wfor
zzfor zNTUzx x xuuu u u< = >== = =(19) If the system of
equations (11) and (18) is compared, it can be observed that the
difference is
onlyinthesignbeforethesecondmemberontherightsideofthethirdequation.Ifwe
compareequations(12)and(19)(inletandinitialconditions),thedifferenceisonlyinthe
secondequation.However,theseseeminglysmalldifferencesmakesubstantialdifferences
in the solution of the problem which will be shown later on. Outlet
temperatures of both fluids in steady state ( z ) are as in the
case of parallel flow
heatexchangerbuttheeffectivenessisincaseofcounterflowheatexchangerdesignedas
follows: | || |1 exp (1 )0 11 exp (1 )NTUforNTUec ee e = s <
(20) and 11 NTUforNTUc e = =+(21) Heat Exchangers Basics Design
Applications 60When stronger fluid (fluid 2) is perturbed, the
inlet condition of the mathematical problem is changed and is as
follows: 121 2(0, ) 00 0( , )1 0( , 0) ( , 0) ( , 0) 0wzfor
zNTUzfor zx x xuuu u u=< = >= = =(22) The problem formulated
in this way is valid for W1 W2. For the case W1 W2, the problem is
very similar and because of that it will not be elaborated in
details. 2.3 Cross flow (both fluids unmixed) The drawing of cross
flow heat exchanger which is used for mathematical analysis is
shown in Fig. 3. It contains the necessary system of designation
and coordinates which will be used in this paper. The fluid 1 flows
in the X direction and the fluid 2 in the Y direction. The fluid
flows are not mixed perpendicularly to their
flow.Basedontheseassumptionsandbyapplyingenergyequationstobothfluids,three
simultaneouspartialdifferentialequationscanbeobtainedinthecoordinatesystemas
shown in Fig. 3. ( ) ( ) ( ) ( )1 21 2www w wTMc h A T T h A T Ttc=
c ( ) ( )1 11 1 1111p o wT Tm c X h A T TX U t| | c c+ = |c c\ . (
) ( )2 22 2 2221p o wT Tm c Y h A T TY U t| | c c+ = |c c\ .(23)
Independentvariablesinspaceandtime(X,Yandt)varyfrom0tothelengthofheat
exchangersXoandYo,i.efrom0to
.Bycomparingthesystemofequations(1),itcanbe
noticedthatthereisthepresenceofthespacecoordinate(Y)andtheexistenceoftwo
dimensions of heat exchangers (Xo and Yo).=e y NTU= x NTU Fig. 3.
Schematic Description of Cross Flow Heat Exchanger. Analytical
Solution of Dynamic Response of Heat Exchangers 61 Initial and
inlet conditions of analyzed problem are as follows: 1*0(0, , )0T
for tT YtT for t < = > 2( , 0, ) T X t T const = = 1 2( , ,
0) ( , , 0) ( , , 0)wT X Y T X Y T X Y T const = = = = (24) By
introducing new dimensionless variable: *, ,o oX Y tx NTU x NTU zX
Y t= = = (25) the set of equations (23) is as follows: 1 1 2 2wwK
Kzuu u uc+ = + c 1 11 2 1 wC Kz xu uu uc c + = c c 2 22 1 2 wC Kz
yu uu uc c + = c c(26) and initial and inlet conditions (Eq. 24)
as: 10 0(0, , )1 0for zyzfor zu< = > 2( , 0, ) 0 x z u = 1 2(
, , 0) ( , , 0) ( , , 0) 0wxy xy xy u u u = = = (27)
Outlettemperaturesofbothfluidsinsteadystate( z
)aredefinedbyEq.(13)butthe effectiveness in the case of cross flow
heat exchanger is defined as follows (Bali, 1978): | |( ) ( ) (
)/20 121 exp (1 )12 2 2nnnNTUI NTU I NTU I NTUc eee e e e ee== + (
+ ( (28) and | | ( ) ( )0 11 exp 2 2 2 1 NTU I NTU I NTU for c e =
+ ( = (29) In Eqs. (28 and 29), the( )nI is modified Bessel
function. Heat Exchangers Basics Design Applications
62Forthecasewhenstrongerfluid(fluid2)isperturbed,theinletconditionofthe
mathematical problem is changed and it is as follows: 1( , 0, ) 0 x
z u = 20 0(0, , )1 0for zyzfor zu< = > 1 2( , , 0) ( , , 0) (
, , 0) 0wxy xy xy u u u = = = (30)
Asopposedtoparallelandcounterflowheatexchangerswhereoutletfluidtemperatures
areconstantoverthewholelengthofoutletedges,itisnotthecaseforcrossflowheat
exchangers.Then,outlettemperaturefromtheheatexchangerisobtainedasmean
temperature at the outlet edge of the heat
exchanger.Specialcasesofcrossflowheatexchangerswhenoneorbothfluidflowsaremixed
throughout will not be elaborated in this
paper.IntheSectionthatfollows,definedmathematicalproblemsfordeterminingtemperature
fieldsandoutlettemperatureswillberesolvedforthreebasictypes:parallel,counterand
cross flow heat exchangers. 3. General solution The set of three
partial differential equations for all types of heat exchanger are
linear (Eqs.
11,18and26).ThesesystemscanbesolvedbyusingmultifoldLaplacetransform.Inthe
caseofparallelandcounterflowheatexchangers,itisdouble-foldandinthecaseofcross
flow it is three-fold Laplace transform.3.1 Parallel flow By
applying this transform over the equations (11) and initial and
inlet condition (Eq.16), the following algebraic equations are
obtained: 1 1 2 21wK Kpu uu + =+ 112 21 1 1wC psK K pu u| | ++ = +
|\ . 221 1( 1)wC psK Ke eu u| | ++ = |\ . (31) From this set of
equations, the outlet and wall temperatures are as follows: + +u =
+ + ++ +e1 22 1w1 212 11K KK s C p 1 1K Kpp 1KK s C p 1s C p 1(32)
Analytical Solution of Dynamic Response of Heat Exchangers 63 212 1
2 111 1wKK s C p K s C p puu = + + + + +(33) 2111wKs C puue=+ +(34)
Afterperformingsomemathematicaltransformationsandbyusingsomewellknown
relations: ( )101 111nnnx x+== + ;( )0nnm n mmna b a bm=| |+ = |\
.(35) the temperatures can be expressed in the following form which
is convenient for developing the inverse Laplace transform: 1111 12
012 2111 212 1 1 01 11 22 2 1 11 1( 1)11 1 1( 1)1nwn nnm n mnn mn m
n mKKK p pCs pK KnK KKm K Kp pC Cs p s pK K K Kuee e++ +=+ = =+ + |
|= + | +\ . | |+ + |\ .| | | | | | |||\ . \ . \ . +| | | | + + + +
||\ . \ . (36) 1111 212 011 12 2111 22 1 1 01 21 22 2 1 11 1 1 11(
1)11 1 1( 1)1nn nnm n mnn mn m n mKCp K p pCs ps pK KK KnK Km K Kp
pC Cs p s pK K K Kuee e++ +=+ = =+ + | |= + + | +\ . | |+ ++ + |\
.| | | | | | |||\ . \ . \ . +| | | | + + + + ||\ . \ . (37) 1 11
222 1 0 01 1 11 22 2 1 11 1 1( 1)1m n mnn mn m n mnK Km K Kp pC Cs
p s pK K K Keue e+ += =+ + +| | | | | | = |||\ . \ . \ . +| | | | +
+ + + ||\ . \ . (38) Heat Exchangers Basics Design Applications
64From the techniques of Laplace transformation (convolution and
translation theorems)and
usingtheLaplacetransformsofspecialfunctionsFn(x,c)andIn,m(x,c,d),definedinthe
Appendix, one can obtain the inverse Laplace transformation of Eqs.
36-38, and the transient temperature distributions for the parallel
flow heat exchanger: 11 12 1 1, 12 2 2 0111 222 1 1 01 21 1, 12 1 2
101( , ) , , 0, 11, , ( ) , 0,nw n nnm n mnn mxm n m nK Cxz K F x I
z xK K KnK KKm K KC CF x u F u I z x u uK K K Kuee e++ +=+ = =+ +|
| | | | |= + |||\ . \ . \ .| | | | | | + |||\ . \ . \ .| | | | | |
+ |||\ . \ . \ . }1 du ( ( ( (39) 11 12 211 12 1, 12 2 2 0111 22 1
1 02 1, 12 101( , ) ,1, , 0, 11, ,nn nnm n mnn mxm n m nCxz z x F
xK KK CF x I z xK K KnK Km K KCF x u F u I zK Ku kee++ +=+ = =+ +|
| | |= + ||\ . \ .| | | | | |+ + |||\ . \ . \ .| | | | | | + |||\ .
\ . \ .| | | | ||\ . \ . }1 22 1( ) , 0, 1Cx u u duK Ke ( | | + (|
( \ . (40) 1 11 222 1 0 01 21 1 1, 12 1 2 10( , )1, , ( ) , 0, 1m n
mnn mxm n m nnK Kxzm K KC CF x u F u I z x u uK K K Keue e+ += =+ +
+| | | | | | = |||\ . \ . \ . ( | | | | | | + (||| ( \ . \ . \ .
}(41) Outlet temperatures of both fluids are obtained for x =
NTU.In the practical use of solutions, the computation of integrals
in this paper is done through
collocationatnineChebishevspoints:0.0000000000;0.1679061842;0.5287617831;
0.6010186554; 0.9115893077, for the given integration
interval.Special case = 0 In this case, 2( , ) 0 xz u =resulting in
reduced Eq. (31): 11 12 2 211( 1)wKp C Kp s pK K Ku = | |+ + + |\
.(42) After some mathematical manipulations, using already
mentioned techniques, this equation can be transformed into:
Analytical Solution of Dynamic Response of Heat Exchangers 65 11212
0112 211( 1)nwnnnKKKCp p s pK Ku++=+| |= |\ . | | + + + |\ .(43)
The inverse two-fold Laplace transform of Eq. 43 gives: 11 12 1
1,12 2 2 01( , ) , , 1, 1nw n nnK C xxz K F x I zK K Ku++ +=| | | |
| | = |||\ . \ . \ .(44) and Eq. 32 gives: 11 1 11 1 2 1,12 2 2 2 2
01 1( , ) , , , 1, 1nn nnC x K C xxz z F x F x I zK K K K Ku k++
+=| | | | | | | | | | = + |||||\ . \ . \ . \ . \ . (45) This
solution is valid for all types of heat exchangers with = 0. 3.2
Counter flow
Averysimilarprocedurecanbeappliedforresolvingthemathematicalmodelofcounter
flowheatexchanger.Thesetofalgebraicequationsobtainedaftertwo-foldLaplace
transform of Eqs. (18) and initial and inlet conditions (Eq (19))
is as follows: 1 1 2 2( 1)wp K K u u u + = + (46) 112 2 21 1 1wCs
pK K K pu u| |+ + = + |\ . (47) ( )22 21 1 110,wCs p pK K Ke eu u
u| | = |\ . (48) The procedure will be explained in more details
here since this case is much more complex than the previous one. By
introducing designations: 12 1 22 21( , ) 1Csp K s C p K s pK Ko|
|= + + = + + |\ .,(49) 1 1 221 1( , ) 1K K Csp s C p s pK Ke e|e e|
| = + + = |\ .,(50) 1 2( , ) 1( , ) ( , )K KA sp psp sp o |= +
,(51) the both fluids and wall temperatures of the counter flow
heat exchanger are as follows: Heat Exchangers Basics Design
Applications 66 ( )1 2 1 220,wK K K Kpp A Au uo e | = (52) ( )2 1 2
1 21 220,K K K K Kpp A p Au uo e o | o = + (53) ( )1 2 1 22 21 0,K
K K Kpp A Au uo | e | || | = + | \ . (54) It is very simple to
prove that: 1 210 01 1 1( 1)nm n mn m n mn mnK Km A p o |+ = =| |=
|+ \ . ,(55)
andthatinverseLaplacetransformationsofthefunctions1/m+1(s,p)and1/m+1(s,p)
(m=1,2,3,) with respect to the complex parameter s are: 1 111 12 2
21 1 1, exps x mm mCL F x x pK K K o ++ +| | | | = `|| )\ . \
.,(56) 11 1 2111 1 11( 1) , expmms x mmCL F x x pK K Ke e e|+ + ++
| | | | | | = `||| \ . \ . \ . ).(57) The essential problem in
resolving dynamic behavior of the counter flow heat exchanger is in
the use of other inlet conditions (Eq. 19).
IftheEq.54iscollocatedintox=NTUthen,INLETtemperatureofthefluid2isobtained
which is according to given inlet conditions 2( , ) 0 NTUz u = ,
therefore: ( )1 1 1 1 2 1 2220,s NTU s NTUK K K K KL p Lp A Aue | o
| e | | | + = | ` ` \ . ) )(58)
ThisisFredholmsintegralequationofthesecondorder.Theproblemisreducedtoits
solving.The collocation method is used for solving this equation.
Perhaps, it is the simplest one. The trial function is: ( ) ( )2
210, 0, 1 exp( ) exp( )!= (= ( ( k NCPkkzz z a zku u (59)
Inequations(58)andfurtheron, 2(0, ) u
isthesteady-statefluid2outlettemperaturefor
thecounterflowheatexchanger.ItcanbecalculatedbyusingthesecondofEq.13and
effectiveness of counter flow heat exchanger (Eqs. 20 and 21). It
follows that: Analytical Solution of Dynamic Response of Heat
Exchangers 67 | || |211(0, )1 exp (1 )0 11 exp (1
)NTUforNTUNTUforNTUeuee ee e=+ = s < (60) Laplace transform of
trial function (Eq. 59) is: ( ) ( )92 2111 10, 0,( 1) ( 1)kkkp ap p
pu u+= (= (+ + ( (61)
Thetrialfunctionchoseninthiswaysatisfiescompletelytheequation(58)inpointsz=0
and z . Within the interval 0 < z < , it is necessary to
determine collocation points and coefficients ak (k = 1, 2, 3, ...
, NCP). Here, the NCP is the number of collocation points. The
accuracyinwhichtheoutlettemperaturesoffluid2versustimearedetermineddepends
directlyonNCP.Inthismodelofheatexchanger,therearemanyinfluentialfactorsand
determinationofthenumberofcollocationpointsforthegivenaccuracyofoutlet
temperatureissimplestthroughpracticaltestingofthesolution.Fortheheatexchangers
parameters appearing in practice, it can be said that NCP varying
from 5 to 7 is sufficient for the accuracy of four significant
figures and for z 15.Substituting the equation (61) in the equation
(58) and collocating resulting equation in the
NCPpoint,asetoflinearalgebraicequationsisobtainedandtheirsolvinggenerates
unknownconstantsak.Thesetofalgebraicsolutionscanalsobewritteninthefollowing
form : 1NCPk k Rka= A = A(62) Substituting the equation (61) in
(58) and using Eqs. (55), (56) and (57), it is obtained: ( ) ( ) (
)( )122 1 2 21 011 222 1 2 1 101 222 1(0, ) ( ), 1 ( 1) , 0 ( ),
11( 1) , , 0( ) ,nnk k n n knm n mNTUnn mm n mn mn kKF z r F NTU F
z rKnK KF u F NTU um K K KC CF z r uK Keuee++ + + += + += =+ + | |
A = | \ . | | | | | | | | ||||\ . \ . \ . \ .| | + |\ . }11 exp ( ,
1, 2,... ) u du kr NCPKe ( | | = ( `| ( \ . )(63) ( ) ( )( )122 1,1
2 2,11 011 222 1 2 1 10(0, ) ( ( ), 1, 1) ( 1) , 0 ( ), 1, 11( 1) ,
, 0 ...nnR n nnm n mNTUnn mm n mn mKI z r F NTU I z rKnK KF u F NTU
um K K Keue++ += + += = | | A = | \ . | | | | | | | | ||||\ . \ . \
. \ . } Heat Exchangers Basics Design Applications 68( )1 22,12 1
11 11 1 21 12 1 2 0 001 21,12 1... ( ) , 1, 1 exp1( 1) , , 0( ) ,
1, 1nm n mNTUnn mm n mn mnC CI z r u u duK K KnK KF u F NTU um K K
KC CI z r uK Ke eee++ + ++ += =+ ( | | | | + (|| ( \ . \ . | | | |
| | | | ||||\ . \ . \ . \ . | | + |\ . }1exp u duKe( | | ( `| ( \ .
) (64)
Theequations(63)and(64)definemembersinthesetofalgebraicequations(62).For
determining constants ak, it is possible to use any of the well
known
methods.Thetemperaturedistributionofbothfluidsandtheseparatingwallcanbecalculatedby
usingEqs.(52-54)andbysubstitutingtheLaplacetransformoffluid2outlettemperature
givenbyEq.(59).Constantsakarenowknownandarevalidforallvaluesofzwithinthe
close interval where the collocation is performed.Temperatures of
fluid and wall are as follows: 11 12 211 12 1,12 2 2 0111 22 1 1 02
1,2 101( , ) ,1, , 1, 1( 1)1, ,nn nnn mmnn mn mxm n m nCxz z x F xK
KK CF x I z xK K KnK Km K KF u F x u IK Ku kee++ +=+ = =+ +| | | |=
+ ||\ . \ .| | | | | | + |||\ . \ . \ .| | | | | | |||\ . \ . \ .|
| | | ||\ . \ . }1 212 11 11 2 1 22 1 0 01 21 1 2,12 1 2 10( ) , 1,
1(0, )( 1)1, , ( ) , 1, 1m n mnn mn mxm n m nC Cz u x u duK KnK Km
K KC CF u F x u I z u x uK K K Keu eee e+ + += =+ + +| |( | ( | \
.| | | | | | |||\ . \ . \ . ( | | | | | | (||| ( \ . \ . \ . }91
222 1 1( ) , 1k n kkC Ca F z u x u duK Ke+ += ( | | (| ( \ . (65)
11 12 1 1,12 2 2 0111 22 1 1 01 21 1,12 1 2 101( , ) , , 1, 1( 1)1,
, ( )nw n nnm n mnn mn mxm n m nK Cxz K F x I z xK K KnK Km K KC CF
u F x u I z u x uK K K Kuee e++ +=+ = =+ +| | | | | |= +|||\ . \ .
\ . | | | | | | |||\ . \ . \ .| | | | ||\ . \ . }, 1, 1 ... du | |
( | `( | \ . ) Analytical Solution of Dynamic Response of Heat
Exchangers 69 11 1 2 21 2,11 1 1 01 22 1 221 2 1 1 1 12... ( 1) , ,
1, 11, 1 ( 1)1,nnn nnm n mK nn mk n kk n mm n mK K CF x I z xK K
KnC K Ka F z xm K K KF u FKe e eee ee+++ +=+ ++ += = = + | | | | |
| + ||| \ . \ . \ . ( | | | | | | | | + + (||||( \ . \ . \ . \ . |
| |\ . 1 21 2,11 2 101 222 1 1, ( ) , 1, 1( ) , 1xnKk n kkC Cx u I
z u x uK K KC Ca F z u x u duK Ke ee++ +=( | | | | ( || ( \ . \ . (
| | (`| (\ . )}(66) 1 11 1 222 1 0 01 21 1 1,12 1 2 1022 1 1,11 1(
, ) ( 1)1, , ( ) , 1, 1(0, ) , , 1,m n mnn mn mxm n m nnK Kxzm K KC
CF u F x u I z u x u duK K K KCF x I z xK Keue ee eu+ + += =+ + +|
| | | | | = |||\ . \ . \ . | | | |( + `||( \ . \ . )| | + |\ .
}9221 1122 21 1 092 22,1 21 1 1122 1 11 , 1(0, ) ( 1) ,, 1, 1 ,
1(0, ) ( 1)k n kknnnnn k n kknn mn mCa F z xKKF xK KC CI z x a F z
xK KKKee eue eu+ +=++=+ + +== = ( | | | | + (|| ( \ . \ . | | | |
||\ . \ . ( | | | | + + (|| ( \ . \ . | 1211 22 2,12 1 2 1091 222 1
11, , ( ) , 1, 1( ) , 1m n mxm n m nk n kknKm KC CF u F x u I z u x
uK K K KC Ca F z u x u duK Kee ee + + ++ +=| | | | | |||\ . \ . \
.( | | | | | | ( ||| ( \ . \ . \ . ( | | (`| ( \ . )}(67) 3.3 Cross
flow
Theequations(25)arelinearper1(x,y,z),w(x,y,z),and2(x,y,z).Ifthree-foldLaplace
transform of above equations is taken in relation to x, y and z
with complex parameters s, q,
andp,respectively,andifinletandinitialconditionsareused(equation15),asetof
algebraic equations is generated : 1 1 2 2( 1)wp K K u u u + = +
(68) ( )22 1 11wKK s C ppqu u + + = + (69) Heat Exchangers Basics
Design Applications 70( )1 2 21wK q C p u u + + = (70) Solving the
set of algebraic set (equations (16)-(18)) is as follows: ( )1 22
11 22 1 1 2111 1wK Kpq K s C pK KpK s C p K q C pu + +=+ + + +
+(71) ( ) ( )212 1 2 11 1wKK s C p pq K s C puu = ++ + + +(72) (
)21 21wK q C puu = + +(73)
Afterperformingcertainmathematicaltransformationsasdoneinpreviouscases,the
algebraic equation (71) can be expressed in the following form: ( )
( ) ( )1 11 21 10 02 1 1 21 1 1m n m nwn m n mn mnK Kmp p K s C p q
K q C pu+ + + + = =| | = | + + + + + \ . (74)
whichisverysuitableforinverseLaplacetransformsbymeansoffunctions( ,
)nF x c and ,( , , )n mI x cddefined in the Annex. However, for the
case n = m in the equation (74) and later on, the twofold sum will
be separated into two (single and double) sums so that: ( ) ( )( )
( ) ( )11 21 102 11 1 11 21 11 02 1 1 21 11 1 1nwn nnm n m nn m n
mn mK Kp p q K s C pnK Kmp p K s C p q K q C pu+ + +=+ + + + = == +
+ + +| | | + + + + + \ . (75)
Theinsertionoftheequation(74)inequations(72)and(73)generatesthefollowing
algebraic equations: ( )( ) ( )( ) ( ) ( )12 1 211 22 1 02 11 1 11
21 21 02 1 1 211 11 1 1nn nnm n m nn m n mn mK K Kp q K s C pp p q
K s C pnK Kmp p K s C p q K q C pu+ + +=+ + + + = == + + + + + + +|
| | + + + + + \ . (76) ( ) ( ) ( )1 11 221 1 10 02 1 1 21 1 1m n m
nn m n mn mnK Kmp p K s C p q K q C pu+ + + + += =| | = | + + + + +
\ . (77) Now it is possible to get the inverse Laplace transform
equation (75)-(77), so that: Analytical Solution of Dynamic
Response of Heat Exchangers 71 111 1 1,1 12 2 0111 2 12 1 0/1,1 1
21 2 1 10( , , ) ,1 ,1,1,1,1 ,1,1nw n nnnm n mmn my Kn m nx xx yz K
F I z CK KnxK K Fm Kv x v dvF I z C CK K K Ku++ += + += = +| | | |=
+ ||\ . \ .| | | | ||\ . \ .| | | | ||\ . \ .}(78) 11 1 12 211 2
1,1 12 2 0111 2 22 1 0/1,1 1 21 2 1 10( , , ) ,1,1 ,1,1,1,1 ,1,1nn
nnnm n mmn my Kn m nx xx yz z C FK Kx xK F I z CK KnxK K Fm Kv x v
dvF I z C CK K K Ku k++ += + += = +| | | |= + ||\ . \ .| | | | +
||\ . \ .| | | | ||\ . \ .| | | | ||\ . \ .}(79) 112 1 2 12 0 0/1
1,1 1 21 2 1 10( , , ) ,1,1 ,1,1nm n mmn my Kn m nnxx yz K K Fm Kv
x v dvF I z C CK K K Ku+ += =+ +| | | |= ||\ . \ .| | | | ||\ . \
.}(80)
Theequations(78)-(80)areanalyticalexpressionsfortemperaturefieldsoffluids1and2
and separating wall of cross heat exchanger dependant on time. At
the beginning, the inlet
temperatureoffluid1isinstantlyraisedfrom0to1,andflowvelocitiesofbothfluidsare
constant.
Outlettemperaturesofbothfluidsareobtainedbyintegratingtemperaturesalongoutlet
edges of the heat exchanger. This is how outlet temperatures become
equal; "1 101( ) ( , , )bz ayz dybu u = } (81) "2 201( ) ( , , )az
xbz dxau u = } ,(82) where a = NTU and b = NTU.
Substitutingequations(79)and(80)inequations(81)and(82)generatesaccurateexplicit
expressions for mean outlet temperatures: Heat Exchangers Basics
Design Applications 72 1"1 1 12 211 2 1,1 12 2 0121 2 22 1 0/1,1 1
21 1 2 10( ) , 1, 1 , 1, 11, 1, 1 , 1, 1nn nnnm n mmn mb Kn m na az
z C FK Ka aK F I z CK KnaK K Fm b Kb v v a vF I z C CK K K Ku k++
+= + += = +| | | |= + ||\ . \ .| | | | + ||\ . \ .| | | | ||\ . \
.| | | | ||\ . \ . }1dvK(83) 1 2" 12 1 20 0/ /1 1 1,1 1 22 1 2 1 2
10 01( ), 1 , 1 , 1, 1nm n mn my K a Km n m nnz K Km au v u v du
dvF F I z C CK K K K K Ku+ = =+ + +| |= |\ .| | | | | | |||\ . \ .
\ . } }(84) Above solutions are also valid for the case of
indefinite fluid velocities (C1 = C2 = 0).4. Calculation results
Themainpurposeofthispaperistoprovideexactanalyticalsolutionsbywhich
performancesofparallel,counterandcrossflowheatexchangerscanbecalculatedand
compared.Manyparametersareinvolvedintemperaturedistributionsofbothfluidsand
thewalland,therefore,itisnotpossibletopresentquantitativeinfluencesofallthese
parameters in this paper. However, there is enough space to give
particular results showing main characteristics of solutions.
Programmingofequationsexpressingtemperaturefieldsandoutlettemperaturesfor
consideredtypesofheatexchangerscanbeverytiresome.Therefore,thewebsite
www.peec.uns.ac.rspresentsprogramsinMSEXCELforcalculations.Programscanbe
modified and improved as required.The example of a heat exchanger
where NTU = 1, = 0.5, K1 = 0.25 (K2 = 1 K1 = 0.75), C1 =
4.0andC2=0.5willbediscussedbelow.Thetemperaturedistributionsofbothfluidsand
thewallofPARALLELflowheatexchangerareplottedversusdimensionlessheat
exchanger length (distance x) for z = 2 and 4 in Figure 4.The
occurrence of heating up of separating wall and fluid 1 by fluid 2
is typical for parallel
flowheatexchanger.Thiscanhappenatthebeginningofanon-steadystateprocesswhen
thevelocityofthefluid2flowishigherthanthevelocityoffluid1.Thiswillbeexplained
somewhat later when comparing outlet temperatures for all three
types of heat exchangers.
TheFigure5showstemperaturedistributionfortheCOUNTERflowheatexchanger.The
parametersofthisheatexchangerarethesameasfortheparallelone.Differencesof
temperature distribution between parallel and counter flow heat
exchangers are evident. Analytical Solution of Dynamic Response of
Heat Exchangers 73 Fig. 4. Temperature Distribution of Both Fluids
and the Wall of Parallel Flow Heat Exchanger for z = 2 and 4. Heat
Exchangers Basics Design Applications 74Fluid 1WallFluid 2z =
2Dimensionless Distance, xDimensionless Temperature,1, 2and
w0.00.10.20.30.40.50.60.70.80.91.00.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.8 0.9 1.0Fluid 1WallFluid 2z = 4Dimensionless Distance,
xDimensionless Temperature,1, 2and w0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.8 0.9 1.00.00.10.20.30.40.50.60.70.80.91.0 Fig. 5. Temperature
Distribution of Both fluids and the Wall of Counter Flow Heat
Exchanger for z = 2 and 4. As an example of the use of presented
solutions for cross flow heat exchanger,temperature fields for both
fluids and separating wall are given for the same case (NTU = 1, =
0.5, K1 =
0.25,C1=4,andC2=0.5).Temperaturefieldsofbothfluidsandthewallareshownfor
dimensionless lengths of heat exchangers at dimensionless time z =
6 (Figure 6). At the time
z=6,thefrontofbothfluidshasleftboundariesoftheheatexchanger.Alongtheoutlet
Analytical Solution of Dynamic Response of Heat Exchangers 75
fluidedge,walltemperaturehasbeensignificantlyraisedbutwalltemperaturealongthe
outletedgeofthefluid1isverymodest.Theperturbationofthefluid1hasjustleftthe
outlet edge of the heat exchanger. For the fluid 2, the
perturbation has moved far away from the outlet edge. Since the the
perturbation front of the fluid 1 has just left the outlet edge of
the heat exchanger, wall temperature at this edge are low. The same
conclusion is also valid for fluid 2 temperature. However, it
should be noted that the strength of the fluid 2 flow is two times
higher that the strength of the fluid 1.iu Fig. 6. Temperature
Fields of Both Fluids and The wall of CROSS Flow Heat Exchanger for
z = 2 and 4.
Fig.7showsoutlettemperaturesofbothfluidflowsforallthreetypesofheatexchangers.
ThesizeofthesethreeheatexchangersisNTU=1.0and=0.5.Thecharacteristicsof
transient heat are also equal for all three types of heat
exchangers and they are defined by K1
=0.25,i.e.,K2=1-K1=0.75.Thevelocityoffluidflow1(C1=4.0,i.e.,1 11 /
U C )isless thanthevelocityoftheflow2(C2=0.5,i.e.,2 21 / U C
).Thismeansthatthefluid1flows
longerthroughtheflowchannelsthanfluid2.Intheanalyzedcase,theratiooffluid
velocities is U1/U2 = 0.04167. For the fluid 2, the time from z=0
to 1 is necessary to pass the
wholelengthoftheheatexchangeratitssideoftheseparatingwall.Thetimez=5.33is
required for the fluid 1.The change curve of outlet temperature of
fluid 2 is continuous for all three cases (Fig. 7). It is logical
that the highest outlet temperature is achieved in the counter flow
heat exchanger for which the effectiveness (steady-state) is also
the highest for the same values of NTU and . It is followed by the
cross flow and then by the parallel flow heat exchanger as the
worst amongthethree.Inallcases,thefinaloutlettemperature( ) z
isequalto 1 ( , , ) NTU flow arrangement c e =
.Also,intransientregime,differencesregardingthe quality of
exchangers are
retained.Itisoppositeforthefluid1.Thelowesttemperatureisobtainedforthecounterflowheat
exchangerandthehighestfortheparallelone.Finaloutlettemperaturesareequal
Heat Exchangers Basics Design Applications 76( , , ) NTU flow
arrangement e c e =
.Itislogicalthattheoutlettemperatureofthefluid1isa discontinued
function. After the step unit increase of the temperature of the
fluid 1 at z = 0, the temperature of the fluid 1 falls due to
heating of the wall of the heat exchanger and then
heatingofthefluid2.However,inthecaseoftheparallelflowheatexchanger,inthe
beginningafterperturbation,theoutlettemperatureofthefluid1growsevenbeforethe
perturbationreachestheoutletoftheexchanger.Thismeansthatatonetimeofthenon-steadystatepartoftheprocess,thefluid2heatsuptheflowofthefluid1,aswellasthe
wall instead of vice versa. Namely, ahead of the front, there is
the fluid flow 2 heated up by the fluid flow 1. Since the velocity
of the fluid flow 2 is higher than the velocity of the fluid
flow1therefore,itheatsuplaternon-perturbedpartoftheflow1whichisaheadofthe
movingfrontoftheperturbation.Byallmeans,thisindicatesthatbeforetheoccurrenceof
theperturbationallnon-dimensionlesstemperaturesareequaltozero(initialcondition).
Afterthetimez=5.33,theperturbationofthefluid1hasreachedtheoutletedgeofthe
exchangerwhichisregisteredbythestepchangeoftheoutlettemperature.Incaseofthe
cross and counter flow heat exchangers, there is not heating up of
the fluid flow 1 ahead of theperturbationfront(Fig.7).
Thefluidflow1coolsdown inthebeginningbyheatingup the wall of the
heat exchanger and the part of the fluid flow 2 in case of the
cross flow heat exchanger and the whole fluid flow 1 in the case of
counter flow but, it cannot happen that the fluid flow 2 gets ahead
of the perturbation front and causes a reversal process of the heat
transfer which is possible in case of the parallel flow heat
exchanger.
Fig. 7. Outlet Temperature of Both Fluids for Parallel, Counter
and Cross Flow Heat Exchangers. Analytical Solution of Dynamic
Response of Heat Exchangers 77 5. Conclusion A method providing
exact analytical solutions for transient response of parallel,
counter and
crossflowheatexchangerswithfinitewallcapacitanceispresented.Solutionsarevalidin
thecasewherevelocitiesaredifferentorequal.Thesesolutionsprocedureprovides
necessary basis for the study of parameters estimated, model
discriminations and control of all analyzed heat exchangers.
Generallyspeaking,theanalyticalmethodissuperiortonumericaltechniquesbecausethe
finalsolutionalsopreservesphysicalessenceoftheproblem.Testingofsolutionsgivenin
thispaperindicatesthattheycanbeusedinpracticeefficientlywhendesigningand
managing processes with heat exchangers. 6. Appendix Functions( ,
)nF x c and ,( , , )n mI x cd
andtheirLaplacetransformsaregivenasdescribed below (x 0,, cd <
< , and n, m = 1, 2, 3,....). For x < 0, both functions are
equal to zero. ( )( )( )11( , ) exp1 !nnnxF x c c xns c= +(A.1) ( )
( ),111( , , ) ( , , )jn m n m jn mjm jI x cd d F x cdjs c s c d+
+=+ | |= |+ + \ .(A.2) Some additional details about these
functions can be found in an earlier paper (Gvozdenac, 1986). 7.
Nomenclature A1, A2total heat transfer area on sides 1 and 2 of a
heat exchanger, respectively, [m2] F1, F2cross-section area of flow
passages 1 and 2, respectively, [m2] cpisobaric specific heat of
fluid, [J/(kg K)] cwspecific heat of core material, [J/(kg K)]
hheat transfer coefficient between fluid and the heat exchanger
wall, [W/(K m2)] Mwmass of heat exchanger core, [kg] m mass flow
rate, [kg/s] NTUnumber of heat transfer units, [-] (Eq. )
Ttemperature, [K] ttime, [s] Wthermal capacity rate of fluid, pmc =
, [W/K] Wminlesser of W1 and W2, [W/K] X, Ydistance from fluid
entrances, [m] Ufluid velocity, [m/s] density, [kg/m3] unit step
function dimensionless temperature x, y, zdimensionless independent
variables, (Eqs. ) Heat Exchangers Basics Design Applications
78Subscripts: 1fluid 1 2fluid 2 wwall 8.
AcknowledgmentThisworkwasperformedasapartoftheresearchsupportedbyProvincialSecretariatfor
Science and Technological Development of Autonomous Province of
Vojvodina. 9. References
Profos,P.(1943).DieBehandlungvonRegelproblemenvermittelsdesFrequenzgangesdes
Regelkreises, Dissertation, Zurich, 1943 Tahkahashi, Y. (1951).
Automatic control of heat exchanger, Bull. JSME, 54, pp 426-431
Kays,W.M.&London,A.L.(1984).Compactheatexchangers(3rded),NewYork,McGraw-Hill
Liapis, A. I. & McAvoy, T. J. (1981). Transient solutions for a
class of hyperbolic counter-current distributed heat and mass
transfer systems, Trans. IChemE, 59, pp 89-94
Li,Ch.H.(1986).Exacttransientsolutionsofparallel-currenttransferprocesses,ASMEJ.Heat
Transfer, 108, pp 365-369
Romie,F.E.(1985).Transientresponseofcounterflowheatexchanger,ASMEJournalofHeat
Transfer, 106, pp 620-626
Romie,F.E.(1986).Transientresponseoftheparallel-flowheatexchanger,ASMEJ.Heat
Transfer, 107, pp 727 -730
Gvozdenac,D.D.(1987).Analyticalsolutionoftransientresponseofgas-to-gasparalleland
counterflow heat exchangers, ASME J. Heat Transfer, 109, pp 848-855
Romie,E.E.(1983).Transientresponseofgas-to-gascrossflowheatexchangerswithneithergas
mixed, ASME J. Heat Transfer, 105, pp 563-570 Gvozdenac, D. D.
(1986). Analytical solution of the transient response of gas-to-gas
crossflow heat exchanger with both fluids unmixed, ASME J. Heat
Transfer, 108, pp 722-727
Spiga,G.&Spiga,M.(1987).Two-dimensionaltransientsolutionsforcrossflowheatexchangers
with neither gas mixed, ASME J. Heat Transfer, 109, pp 281-286
Spiga, M. & Spiga, G. (1988). Transient temperature fields in
crossflow heat exchangers with finite wall capacitance, ASME J.
Heat Transfer, 110, pp 49-53
Gvozdenac,D.D.(1990).Transientresponseoftheparallelflowheatexchangerwithfinitewall
capacitance, Ing. Arch., 60, pp 481 -490
Gvozdenac,D.D.(1991).Dynamicresponseofthecrossflowheatexchangerwithfinitewall
capacitance, Wrme- und Stoffbertragung, 26, pp 207-212
Roetzel,W.&Xuan,Y.(1999).DynamicBehaviorofHeatExchangers(DevelopmentsinHeat
Transfer, Volume 3, WITpress/Computational Mechanics Publications
Bali,B.S.(1978),ASimplifiedFormulaforCross-FlowHeatExchangerEffectiveness,ASME
Journal of Heat Transfer, 100, pp 746-747 3 Self-Heat
Recuperation:Theory and Applications Yasuki Kansha1, Akira
Kishimoto1,Muhammad Aziz2 and Atsushi Tsutsumi1 1Collaborative
Research Center for Energy Engineering, Institute of Industrial
Science,The University of Tokyo 2Advanced Energy Systems for
Sustainability, Solution Research Laboratory Tokyo Institute of
Technology Japan 1. Introduction
Sincethe1970s,energysavinghascontributedtovariouselementsofsocietiesaroundthe
worldforeconomicreasons.Recently,energysavingtechnologyhasattractedincreased
interest in many countries as a means to suppress global warming
and to reduce the use of
fossilfuels.Thecombustionoffossilfuelsforheatingproducesalargeamountofcarbon
dioxide(CO2),whichisthemaincontributortoglobalgreenhousegaseffects(Eastop&
Croft1990,Kemp2007).Thus,thereductionofenergyconsumptionforheatingisavery
importantissue.Todate,toreduceenergyconsumption,heatrecoverytechnologysuchas
pinch technology, which exchanges heat between the hot and cold
streams in a process, has
beenappliedtothermalprocesses(Linnhoffetal.1979,Cerdaetal.1983,Linnhoffetal.
1983, Linnhoff 1993, Linnhoff & Eastwood 1997, Ebrahim &
Kawari 2000). A simple example ofthistechnologyistheapplication ofa
feed-effluentheatexchangerinthermalprocesses, wherein heat is
exchanged between feed (cold) and effluent (hot) streams to
recirculate the
self-heatofthestream(Seideretal.2004).Toexchangetheheat,anadditionalheatsource
mayberequired,dependingontheavailabletemperaturedifferencebetweentwostreams
forheatexchange.Theadditionalheatmaybeprovidedbythecombustionoffossilfuels,
leading to exergy destruction during heat production (Som &
Datta 2008). In addition, many
energysavingtechnologiesrecentlydevelopedareonlyconsideredonthebasisofthefirst
lawofthermodynamics,i.e. energyconservation.Hence,process
designmethodsbasedon these technologies are distinguished by
cascading heat utilization. Simultaneously, many researchers have
paid attention to the analysis of process exergy and
irreversibility through consideration of the second law of
thermodynamics. However, many
oftheseinvestigationsshowonlythecalculationresultsofexergyanalysisandthe
possibilityoftheenergysavingsofsomeprocesses,andfewclearlydescribemethodsfor
reducing the energy consumption of processes (Lampinen &
Heillinen 1995, Chengqin et al
2002,Grubbstrm2007).Toreduceexergyreduction,aheatpumphasbeenappliedto
thermal processes, in which the ambient heat or the process waste
heat is generally pumped
toheattheprocessstreambyusingworkingfluidcompression.Althoughitiswell-known
thataheatpumpcanreduceenergyconsumptionandexergydestructioninaprocess,the
Heat Exchangers Basics Design Applications
80heatloadandcapacityoftheprocessstreamareoftendifferentfromthoseofthepumped
heat.Thus,anormalheatpumpstillpossiblycauseslargeexergydestructionduring
heating.Inheatrecoverytechnologies,vaporrecompressionhasbeenappliedto
evaporation,distillation,anddrying,inwhichthevaporevaporatedfromtheprocessis
compressedtoahigherpressureandthencondensed,providingaheatingeffect.The
condensationheatofthestreamisrecirculatedasthevaporizationheatintheprocessby
using vapor recompression. However, many investigators have only
focused on latent heat
andfewhavepaidattentiontosensibleheat.Asaresult,thetotalprocessheatcannotbe
recovered,indicatingthepotentialforfurtherenergysavingsinmanycases.Recently,an
energy recuperative integrated gasification power generation system
has been proposed and a design method for the system developed
(Kuchonthara & Tsutsumi 2003, Kuchonthara et al. 2005,
Kuchonthara & Tsutsumi 2006). Kansha et al. have developed
self-heat recuperation
technologybasedonexergyrecuperation(2009).Themostimportantcharacteristicsofthis
technologyarethattheentireprocessstreamheatcanberecirculatedintoaprocess
designedbythistechnologybasedonexergyrecuperation,leadingtomarkedenergy
savings for the process. In this chapter, an innovative self-heat
recuperation technology, in which not only the latent heat but also
the sensible heat of the process stream can be circulated without
heat addition,
andthetheoreticalanalysisofthistechnologyareintroduced.Then,severalindustrial
applicationcasestudiesofthistechnologyarepresentedandcomparedwiththeir
conventional counterparts. 2. Self-heat recuperation technology
Self-heatrecuperationtechnology(Kanshaetal.2009)facilitatesrecirculationofnotonly
latent heat but also sensible heat in a process, and helps to
reduce the energy consumption of the process by using compressors
and self-heat exchangers based on exergy recuperation.
Inthistechnology,i)aprocessunitisdividedonthebasisoffunctionstobalancethe
heatingandcoolingloadsbyperformingenthalpyandexergyanalysisandii)thecooling
loadisrecuperatedbycompressorsandexchangedwiththeheatingload.Asaresult,the
heat of the process stream is perfectly circulated without heat
addition, and thus the energy
consumptionfortheprocesscanbegreatlyreduced.Inthissection,first,thetheoryofthe
self-heatrecuperationtechnologyandthedesignmethodologyforself-heatrecuperative
processesareintroducedforabasicthermalprocess,andthenself-heatrecuperative
processes applied to separation processes are introduced. 2.1
Self-heat recuperative thermal process Exergy loss in conventional
thermal processes such as a fired heater normally occurs during
heattransferbetweenthereactionheatproducedbyfuelcombustionandtheheatofthe
processstream,leadingtolargeenergyconsumptionintheprocess.Toreducetheenergy
consumptionintheprocessthroughheatrecovery,heatingandcoolingfunctionsare
generallyintegratedforheatexchangebetweenfeedandeffluenttointroduceheat
circulation.Asysteminwhichsuchintegrationisadoptediscalledaself-heatexchange
system. To maximize the self-heat exchange load, a heat circulation
module for the heating and cooling functions of the process unit
has been proposed, as shown in Figure 1 (Kansha et al. 2009).
Self-Heat Recuperation: Theory and Applications 81
Figure1(a)showsathermalprocessforgasstreamswithheatcirculationusingself-heat
recuperationtechnology.Inthisprocess,thefeedstreamisheatedwithaheatexchanger
(12)fromastandardtemperature,T1,toasettemperature,T2.Theeffluentstreamfrom
the following process is pressurized with a compressor to
recuperate the heat of the effluent
stream(34)andthetemperatureofthestreamexitingthecompressorisraisedtoT2
throughadiabaticcompression.Stream4iscooledwithaheatexchangerforself-heat
exchange (45). The effluent stream is then decompressed with an
expander to recover part
oftheworkofthecompressor.Thisleadstoperfectinternalheatcirculationthroughself-heat
recuperation. The effluent stream is finally cooled to T1 with a
cooler (67). Note that
thetotalheatingdutyisequaltotheinternalself-heatexchangeloadwithoutanyexternal
heating load, as shown in Fig. 1 (b). Thus, the net energy required
of this process is equal to the cooling duty in the cooler (67). To
be exact, the heat capacity of the feed stream is not
equaltothatoftheeffluentstream.However,theeffectofpressuretotheheatcapacityis
small. Thus, two composite curves in Fig. 1 (b) seem to be in
parallel. In addition, the exergy
destructionoccursonlyduringtheheattransferintheheatexchanger.Theamountofthis
exergy destruction is illustrated by the gray area in Fig. 1 (b).
Inthecaseofidealadiabaticcompressionandexpansion,theinputworkprovidedtothe
compressorperformsaheatpumpingroleinwhichtheeffluenttemperaturecanachieve
perfectinternalheatcirculationwithoutexergydestruction.Therefore,self-heat
recuperationcandramaticallyreduceenergyconsumption.Figure1(c)showsathermal
processforvapor/liquidstreamswithheatcirculationusingtheself-heatrecuperation
technology.Inthisprocess,thefeedstreamisheatedwithaheatexchanger(12)froma
standard temperature, T1, to a set temperature, T2. The effluent
stream from the subsequent
processispressurizedbyacompressor(34).Thelatentheatcanthenbeexchanged
between feed and effluent streams because the boiling temperature
of the effluent stream is raised to Tb by compression. Thus, the
effluent stream is cooled through the heat exchanger
forself-heatexchange(45)whilerecuperatingitsheat.Theeffluentstreamisthen
depressurizedbyavalve(56)andfinallycooledtoT1withacooler(67).Thisleadsto
perfectinternalheatcirculationbyself-heatrecuperation,similartotheabovegasstream
case. Note that the total heating duty is equal to the internal
self-heat exchange load without an external heating load, as shown
in Fig. 1 (d). It is clear that the vapor and liquid sensible
heatofthefeedstreamcanbeexchangedwiththesensibleheatofthecorresponding
effluentstreamandthevaporizationheatofthefeedstreamisexchangedwiththe
condensation heat of the effluent stream. Similar to the thermal
process for gas streams with
heatcirculationusingself-heatrecuperationtechnologymentionedabove,thenetenergy
requiredofthisprocessisequaltothecoolingdutyinthecooler(67)andtheexergy
destructionoccursonlyduringheattransferintheheatexchangerandtheamountofthis
exergy destruction is indicated by the gray area in Fig. 1 (d). As
well as the gas stream, the effect of pressure to the heat capacity
is small. Thus, two composite curves in Fig. 1 (b) are
closedtobeinparallel.Asaresult,theenergyrequiredbytheheatcirculationmoduleis
reduced to 1/221/2 of the original by the self-heat exchange system
in gas streams and/or vapor/liquid streams.To use the proposed
self-heat recuperative thermal process in the reaction section of
hydro-desulfurizationinthepetrochemicalindustryasanindustrialapplication,Matsudaetal.
(2010)reportedthattheadvancedprocessrequires1/5oftheenergyrequiredofthe
Heat Exchangers Basics Design Applications
82conventionalprocessonthebasisofenthalpyandexaminedtheconsiderablereductionof
theexergydestructionsinthisprocess.Theotherrelatedindustrialapplicationsofthe
proposedself-heatrecuperativethermalprocessarethepreheatingsectionsofthefeed
streams for reaction to satisfy the required physical conditions.
Fig. 1. Self-heat recuperative thermal process a) process flow of
gas streams, b) temperature-entropy diagram of gas streams, c)
process flow of vapor/liquid streams, d) temperature-entropy
diagram of vapor/liquid streams. 2.2 Self-heat recuperative
separation processes Expanding the self-heat recuperative thermal
process to separation processes (Kansha et al.
2010a),asystemincludingnotonlytheseparationprocessitselfbutalsothe
preheating/cooling section, can be divided on the basis of
functions, namely the separation
moduleandtheheatcirculationmodule,inwhichtheheatingandcoolingloadsare
balanced, as shown in Fig. 2. To simplify the process for
explanation, Fig. 2 shows a case that has one feed and two
effluents. In this figure, the enthalpy of inlet stream (feed) is
equal to
thesumoftheoutletstreams(effluents)enthalpiesineachmodule,givinganenthalpy
Self-Heat Recuperation: Theory and Applications 83 difference
between inlet and outlet streams of zero. The cooling load in each
module is then
recuperatedbycompressorsandexchangedwiththeheatingloadusingself-heat
recuperationtechnology.Asaresult,theheatoftheprocessstream(self-heat)isperfectly
circulatedwithoutheatadditionineachmodule,resultinginperfectinternalheat
circulation over the entire separation process. Fig. 2. Conceptual
figure for self-heat recuperative separation processes. 2.2.1
Self-heat recuperative distillation process
Althoughdistillationcolumnshavebeenwidelyusedinseparationprocessesbasedon
vapor/liquid equilibria in petroleum refineries and chemical
plants, the distillation process
consumesamassiveamountofenergyrequiredforthelatentheatofthephasechange,
resulting in the emission of a large amount of CO2. To prevent the
emission of CO2 through
useofself-heatrecuperationtechnology(Kanshaetal.2010b),adistillationprocesscanbe
dividedintotwosections,namelythepreheatinganddistillationsections,onthebasisof
functionsthatbalancetheheatingandcoolingloadbyperformingenthalpyandexergy
analysis,andtheself-heatrecuperationtechnologyisappliedtothesetwosections.Inthe
preheating section, one of the streams from the distillation
section is a vapor stream and the stream to the distillation
section has a vaporliquid phase that balances the enthalpy of the
feed streams and that of the effluent streams in the section. In
balancing the enthalpy of the feed and effluent streams in the heat
circulation module, the enthalpy of the streams in the
distillationmoduleisautomaticallybalanced.Thus,thereboilerdutyisequaltothe
condenserdutyofthedistillationcolumn.Therefore,thevaporandliquidsensibleheatof
thefeedstreamscanbeexchangedwiththesensibleheatofthecorrespondingeffluent
streams,andthevaporizationheatcanbeexchangedwiththecondensationheatineach
module. Figure 3 (a) shows the structure of a self-heat
recuperative distillation process consisting of two standardized
modules, namely, the heat circulation module and the distillation
module.
Notethatineachmodule,thesumoftheenthalpyofthefeedstreamsandthatofthe
effluent streams are equal. The feed stream in this integrated
process module is represented
bystream1.Thisstreamisheatedtoitsboilingpointbythetwostreamsindependently
recuperatingheatfromthedistillate(12)andbottoms(13)bytheheatexchanger(12).A
distillationcolumnseparatesthedistillate(3)andbottoms(9)fromstream2.Thedistillate
(3) is divided into two streams (4, 12). Stream 4 is compressed
adiabatically by a compressor
andcooleddownbytheheatexchanger(2).Thepressureandtemperatureofstream6are
adjustedbyavalveandacooler(678),andstream8isthenfedintothedistillation
Heat Exchangers Basics Design Applications 84column as a reflux
stream. Simultaneously, the bottoms (9) is divided into two streams
(10,
13).Stream10isheatedbytheheatexchangerandfedtothedistillationcolumn(1011).
Streams12and13aretheeffluentstreamsfromthedistillationmoduleandreturntothe
heat circulation module. In addition, the cooling duty of the
cooler in the distillation module is equal to the compression work
of the compressor in the distillation module because of the
enthalpy balance in the distillation module.
Theeffluentstream(12)fromthedistillationmoduleiscompressedadiabaticallybya
compressor(1214).Streams13and14aresuccessivelycooledbyaheatexchanger.The
pressure of stream 17 is adjusted to standard pressure by a valve
(1718), and the effluents
arefinallycooledtostandardtemperaturebycoolers(1516,1819).Thesumofthe
cooling duties of the coolers is equal to the compression work of
the compressor in the heat circulation module. Streams 16 and 19
are the products.
Figure3(b)showsthetemperatureandheatdiagramfortheself-heatrecuperative
distillation process. In this figure, each number corresponds to
the stream numbers in Fig. 3
(a),andTstdandTbarethestandardtemperatureandtheboilingtemperatureofthefeed
stream,respectively.Boththesensibleheatandthelatentheatofthefeedstreamare
subsequentlyexchangedwiththesensibleandlatentheatofeffluentsinheatexchanger1.
Thevaporizationheatofthebottomsfromthedistillationcolumnisexchangedwiththe
condensationheatofthedistillatefromthedistillationcolumninthedistillationmodule.
The heat of streams 4 and 12 is recuperated by the compressors and
exchanged with the heat in the module. It can be seen that all the
self-heat is exchanged. As a result, the exergy loss of the heat
exchangers can be minimized and the energy required by the
distillation process is
reducedto1/61/8ofthatrequiredbytheconventional,heat-exchangeddistillation
process.Toexaminetheenergyrequired,thetemperaturedifferenceofheatexchangers
betweencoldandhotstreamsisanimportantparameter.Infact,toincreasethis,theheat
transfersurfaceareacanbedecreased.Toachieveindustrialself-heatrecuperative
distillationprocesses,furtherinvestigationoftheminimumtemperaturedifferenceinthe
heat exchangers is required, especially the difference of the heat
types of the streams in the heat exchanger (e.g. sensible heat and
latent heat).
Asindustrialapplicationsofthisself-heatrecuperativedistillationprocesses,Kanshaetal.
(2010c) examined the energy saving efficiency of an integrated
bioethanoldistillation process
usinganazeotropicdistillationmethodascomparedwiththeconventionalazeotropic
distillation processes. In this paper, the energy required for the
proposed integrated processes using self-heat recuperative
distillation was only 1/8 of the conventional process, leading to a
dramatic reduction in the production cost of bioethanol. They also
applied it to the cryogenic
airseparationprocessandexaminedtheenergyrequiredcomparedwiththeconventional
cryogenic air separation for an industrial feasibility study
(Kansha et al. 2011a). In that paper, the conventional cryogenic
air separation was well integrated on the basis of the heat
required to decrease the temperature to near -200 C, especially,
and they pointed out that a cryogenic air separation is a kind of
multi-effect distillation column. However, there was potential for
a
40%energyreductionbyusingself-heatrecuperativedistillation.Furthermore,theauthors
appliedittoawell-knownandrecentlydevelopedenergysavingdistillationprocess,an
internally heat integrated distillation column (HIDiC). In HIDiC,
the distillation column can be
dividedintotwosections(therectificationsectionandthestrippingsection)andthe
condensationheatisexchangedwiththevaporizationheatbetweenthesetwosectionsusing
Self-Heat Recuperation: Theory and Applications 85
thepressuredifference.Designingthisbasedonself-heatrecuperationtechnologyshows
further energy saving (Kansha et al. 2011b). From these three
industrial case studies, self-heat
recuperationtechnologycanbeappliedtorecentlydevelopedheatrecoverydistillation
processessuchasheatintegrateddistillationprocesses,multi-effectdistillationprocessesand
HIDiCprocesses.Finally,toexaminethefeasibilityofself-heatrecuperationforindustrial
processesinthepetrochemicalindustry,Matsudaetal.(2011)applieditusingpractical
industrial dataandmodified the stream lines to enablepractical
processesand examinedthe
energyrequired,exergydestructionandeconomicalefficiency.Fromthesestudies,itcanbe
concludedthattheself-heatrecuperativedistillationprocessisverypromisingforsaving
energy. Fig. 3. Self-heat recuperative distillation process a)
process flow diagram, b) temperature-heat diagram. Heat Exchangers
Basics Design Applications 862.2.2 Self-heat recuperative drying
process
Dryingisusuallyconductedtoreducetransportationcostsbydecreasingproductweight
andsize,givinglong-termstoragestabilityandincreasingthethermalefficiencyin
thermochemicalconversionprocesses.Unfortunately,dryingisoneofthemostenergy
intensiveprocessesowingtothehighlatentheatofwaterevaporation.Theoretically,
assuminganambienttemperatureof15C,theenergyrequiredforwaterevaporation
ranges from 2.5 to 2.6 MJ per kg evaporated water, depending on the
wet bulb temperature
(Brammer&Bridgwater1999).Therearetwoimportantpointsregardingreductionof
energyconsumptionduringdrying:(i)intensificationofheatandmasstransferinsidethe
dryerand(ii)efficientheatrecoveryandenergyutilization(Strumilloetal.2006).
Concerningthelatter,severalmethodshavebeendevelopedtoimproveenergysaving
during drying, including heat recovery with and without flue gas
recirculation, heat pumps, and pinch technology. However, these
systems cannot effectively recover all the heat of the drying
medium, the evaporated water, and the dried
products.Toimprovetheenergyefficiencyindrying,Azizetal.(2011a,2011b)haverecently
developed a drying process based on self-heat recuperation
technology. In this technology,
thehotstreamisheatedbycompressiontoprovideaminimumtemperaturedifference
requiredforheatpairingandexchangewiththecoldstreamandalloftheself-heatofthe
processstreamisrecirculatedbasedonexergyrecuperation.Asaresult,alloftheheat
involvedindryingcanberecuperatedandreusedasaheatsourceforthesubsequent
dryingprocess.Thisincludesrecuperationofsensibleheatfromthegasservingasthe
drying medium, both sensible and latent heat of the evaporated
water and the sensible heat
ofthedriedproducts.Aprocessdiagramforbrowncoaldryingbasedonself-heat
recuperation technology is shown in Fig. 4 (a). A fluidized bed
dryer with an immersed heat
exchangerisselectedastheevaporatorowingtoitshighheattransfercoefficient,excellent
solidmixing,anduniformtemperaturedistribution(WanDaud,2008,Law&Mujumdar
2009).Wetbrowncoalisfedandheatedthroughapre-heater(dryer1a)toagiven
temperature.Subsequently,themaindryingstage(waterevaporation)isperformedinside
the fluidized bed dryer (dryer 2), where evaporation occurs. The
immersed heat exchangers,
whicharefilledbyacompressedmixtureofairandsteam,areimmersedinsidethe
fluidized bed, providing the heat required for water removal. The
exhausted mixture of air and steam is then compressed to achieve a
higher exergy rate before it is circulated back and utilized as the
heat source for evaporation (dryer 2) and pre-heating (dryer 1a,
dryer 1b), in
thatorder.Inaddition,thesensibleheatofthehot,driedbrowncoalisrecoveredbythe
drying medium, to further reduce drying energy consumption (dryer
1c).The heat exchange inside the fluidized bed dryer is considered
to be co-current because the
bediswellmixedandtheminimumtemperatureapproachdependsontheoutlet
temperatureofthehotstreams(compressedair-steammixture)andthetemperatureofthe
bed.Figure4(b)showsatemperature-enthalpydiagramfortheself-heatrecuperativebrown
coal drying. Almost all of the heat is recovered, leading to a
significant reduction in the total
energyconsumption.Thelargestamountofheatrecuperationoccursindryer2,which
involvestheheatexchangebetweenthecondensationheatofthecompressedair-steam
mixture and the evaporation heat of the water in the brown coal.
The heat curves of the hot Self-Heat Recuperation: Theory and
Applications 87 and cold streams, especially in dryer 2, are almost
parallel owing to the efficient heat pairing within the dryer. Fig.
4. Self-heat recuperative brown coal drying (a) process flow
diagram, (b) temperature-heat diagram.This drying process can
reduce the total energy consumption to about 75% of that required
forhotairdryingusingconventionalheatrecovery.Furthermore,astheheatrequiredfor
water evaporation is provided by the condensation of the compressed
air-steam mixture, the inlet air temperature is considerably lower,
leading to safer operation due to reduced risk of fire or
explosion. Heat Exchangers Basics Design Applications 88In
addition, the thermodynamic model of heat exchange inside the
fluidized bed is shown in Fig. 5. The compressed air-steam mixture
flows inside a heat transfer tube immersed in the fluidized bed
dryer. Thus, in-tube condensation occurs and heat is transferred to
the bed via the tube wall and is finally transferred from the bed
to the brown coal particles. Fig. 5. Model of heat transfer inside
the fluidized bed dryer. The heat transfer rate from the compressed
vapor inside the heat transfer tube to the drying sample in FBD,
qs, can be approximated as: s v s( ) q UA T T = (1)
Also,becausetheheatexchangeinsidethefluidizedbeddryerinvolvesconvectionand
conduction, the product of the overall heat transfer coefficient,
U, and surface area, A, may be approximated by equation (2). ( )c c
t t tln1 1 12RrUA A L A o t o= + +(2) The first term of the right
side of equation (2) represents the heat transfer resistance of
vapor
condensationinsidethetube.Acandocaretheinnersurfaceareaofthetubeandtheheat
transfercoefficient,respectively.Thesecondtermcorrespondstotheconductiveheat
transferthroughthetubewallhavingthethermalconductivity,innerradiusandouter
radius of t, r and R, respectively. Convective heat transfer from
the outer tube surface to the
browncoalparticlesinsidethebedisexpressedbythethirdterm,inwhichtheconvective
heat transfer coefficient and the outer surface area of the tube
are ot and At, respectively.
Theheattransfercoefficientonahorizontaltubeimmersedinsidethefluidizedbedhas
been reported by Borodulya (1989, 1991): ( )( )0.14 0.24 2320.1 s
s3tg g10.74 1 0.46CNu Ar Re PrCc c c| | | | || = + ||\ . \ .(3)
Self-Heat Recuperation: Theory and Applications 89 t stgdNuo= (4)
Theheattransfercoefficientofthecondensingvaporiscalculatedusingageneral
correlation proposed by Shah (1979): ( )( )( )0.040.76 0.8 0.40.8l
l lc0.38crit3.8 1 0.02312x x Re Prxrp po ( ( = + ( (5) 2.2.3
Self-heat recuperative CO2 absorption process Carbon capture and
storage (CCS) has attracted significant attention in the past two
decades
toreducegreenhousegasemissionsandmitigateglobalwarming.CCSconsistsofthe
separationofCO2fromindustrialandenergy-relatedsources,transportationofCO2toa
storage location and long-term isolation of CO2 from the atmosphere
(Rubin et al. 2005).It is reported that the most significant
stationary point sources of CO2 are power generation processes. In
fact, the amount of CO2 emission from power generation processes
comprises
40%ofglobalCO2emissions(Rubinetal.2005,Toftegaard,2010).Forpowergeneration,
therearethreedifferent typesforCO2 captureprocesses:
post-combustion,pre-combustion and oxy-fuel combustion (Rubin et
al. 2005). In this section, the CO2 absorption process for
post-combustion is used as a case study (Fig. 6).
Post-combustioncaptureinpowerplantsisgenerallyusedforpulverized-coal-firedpower
plants. The CO2 concentration in post-combustion is low compared
with the other two CO2 capture processes: around 10% (wet base).
The CO2 capture is generally performed through chemical absorption
with monoethanolamine (MEA).Electricity & Heat
generationCO2captureDehydration, Compression, Transportation and
StorageCoal, GasAirFlue GasCO2N2, O2 Fig. 6. Post-combustion
capture. Figure 7 shows a diagram of the conventional CO2
absorption process, which consists of an
absorber,aheatexchanger(HX)forheatrecoveryandastripper(regenerator)witha
reboiler. The flue gas and a lean CO2 concentration' amine solution
(lean amine) are fed into
theabsorber,andCO2gasisabsorbedintotheleanamine.Thisaminesolutioncontaining
absorbedCO2iscalledthe'richCO2concentration'aminesolution(richamine).Exhaust
gasesaredischargedfromthetopoftheabsorber.Therichamineisfedintothestripper
through the HX and then lean amine is regenerated and the CO2 gas
is stripped by heating
inthereboilerofthestripper.IntheconventionalabsorptionprocessusingMEA,theheat
(4.1GJ/t-CO2)issuppliedbythereboilerinthestripper.Theratioofthisheatfor
regeneration and vaporization is 1:1. From Fig. 7, it can be
understood that a part of sensible heat is recovered from lean
amine using the HX. However, the heat of vaporization cannot
berecoveredfromheatofsteamcondensationforstrippinginthereboilerbecauseofthe
Heat Exchangers Basics Design Applications
90temperaturedifferencebetweenthecondenserandthereboiler.Thus,CO2captureisthe
mostcostlyandhighenergyconsumptionprocessofpowergeneration,leadingtohigher
CO2emissions.Infact,
itisreportedthatthisprocessdropsthenetefficiencyofthepower plant by
about 10% (Damen 2006, Davison 2007). Fig. 7. Conventional CO2
absorption process.
Ifallprocessheat(sensibleheat,latentandreactionheat)canberecirculatedintothe
process,theenergyrequiredforCO2capturecanbegreatlyreduced.Toachieveperfect
internalheatcirculation,aself-heatrecuperationtechnologywasappliedtotheCO2
absorptionprocessandaself-heatrecuperativeCO2absorptionprocesswasproposed,as
showninFig.8(a)(Kishimotoetal.2011).Inthisprocess,theaforementionedself-heat
recuperative distillation module in 2.2.1 can be applied to the
stripping section (A) in Fig. 8
(a).AmixtureofCO2andsteamisdischargedfromthetopofstripperandcompressed
adiabaticallybyacompressortorecuperatethesteamcondensationheat.Thisrecuperated
heatisexchangedwiththeheatofvaporizationforstrippinginthereboiler,leadingtoa
reduction in the energy consumption for
stripping.InthesectionBinFig.8(a),theaforementionedheatcirculationmodulein2.2.1canbe
applied, and furthermore the heat of the exothermic reaction
generated at low temperature
intheabsorberistransportedandreusedasreactionheatforsolutionregenerationathigh
temperatureusingareactionheattransformer(RHT).ThisRHTisatypeofclosed-cycle
compression system with a volatile fluid as the working fluid and
consists of an evaporator
toreceiveheatfromtheheatofexothermicreactionintheabsorber,acompressorwith
drivingenergy,acondensertosupplyheattothestripperasheatoftheendothermic
reaction,andanexpansionvalve.Theheatoftheexothermicabsorptionreactionatthe
evaporatorintheabsorberistransportedtotheendothermicdesorptionreactioninthe
condenser of the stripper by the RHT. Therefore, both the heat of
the exothermic absorption
reactionintheabsorberandtheheatofsteamcondensationfromthecondenserinthe
Self-Heat Recuperation: Theory and Applications 91
stripperarerecuperatedandreusedasthereactionheatforsolutionregenerationandthe
vaporization heat for CO2 stripping in the reboiler of the
stripper.Asaresult,theproposedself-heatrecuperativeCO2absorptionprocesscanrecirculatethe
entire process heat into the process and reduce the total energy
consumption to about 1/3 of the conventional process. Fig. 8.
Self-heat recuperative CO2 absorption process, (a) process flow
diagram, (b) temperature-heat diagram. Heat Exchangers Basics
Design Applications 923. Conclusion In this chapter, a newly
developed self-heat recuperation technology, in which not only the
latentheatbutalsothesensibleheatoftheprocessstreamcanbecirculatedwithoutheat
addition, and the theoretical analysis