Advances in Heat Transfer PDF
Preview Advances in Heat Transfer
VOLUME FORTY FOUR A DVANCES IN HEAT TRANSFER Serial Editors EPHRAIM M. SPARROW University of Minnesota, Minneapolis YOUNG I. CHO Department of Mechanical Engineering and Mechanics, Drexel University, Philadelphia, Pennsylvania JOHN P. ABRAHAM University of St. Thomas, St. Paul, Minneapolis JOHN M. GORMAN University of Minnesota, Minneapolis Founding Editors THOMAS F. IRVINE, JR. State University of New York at Stony Brook, Stony Brook, NY JAMES P. HARTNETT University of Illinois at Chicago, Chicago, IL Amsterdam(cid:129)Boston(cid:129)Heidelberg(cid:129)London NewYork(cid:129)Oxford(cid:129)Paris(cid:129)SanDiego SanFrancisco(cid:129)Singapore(cid:129)Sydney(cid:129)Tokyo AcademicPressisanimprintofElsevier AcademicPressisanimprintofElsevier 225WymanStreet,Waltham,MA02451,USA 525BStreet,Suite1900,SanDiego,CA92101-4495,USA Radarweg29,POBox211,1000AEAmsterdam,TheNetherlands TheBoulevard,LangfordLane,Kidlington,Oxford,OX51GB,UK 32,JamestownRoad,LondonNW17BY,UK Firstedition2012 Copyright(cid:1)2012ElsevierInc.Allrightsreserved Nopartofthispublicationmaybereproduced,storedinaretrievalsystemortransmittedin anyformorbyanymeanselectronic,mechanical,photocopying,recordingorotherwise withoutthepriorwrittenpermissionofthepublisher PermissionsmaybesoughtdirectlyfromElsevier’sScience&TechnologyRights DepartmentinOxford,UK:phone(þ44)(0)1865843830;fax(þ44)(0)1865853333; email:permissions@elsevier.com.Alternativelyyoucansubmityourrequestonlineby visitingtheElsevierwebsiteathttp://www.elsevier.com/locate/permissions,andselecting ObtainingpermissiontouseElseviermaterial Notice Noresponsibilityisassumedbythepublisherforanyinjuryand/ordamagetopersonsor propertyasamatterofproductsliability,negligenceorotherwise,orfromanyuseor operationofanymethods,products,instructionsorideascontainedinthematerialherein. Becauseofrapidadvancesinthemedicalsciences,inparticular,independentverificationof diagnosesanddrugdosagesshouldbemade BritishLibraryCataloguinginPublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress ISBN:978-0-12-396529-5 ISSN:0065-2717 ForinformationonallAcademicPresspublications visitourwebsiteatstore.elsevier.com PrintedandboundinUSA 12 10987654321 CONTRIBUTORS Stuart W.Churchill Department of Chemical and Biomolecular Engineering, University ofPennsylvania, Philadelphia, PA, USA Ya-Ling He KeyLaboratoryofThermal-FluidScienceandEngineeringofMOE,SchoolofEnergyand Power Engineering, Xi’an Jiaotong University,Xi’an,Shaanxi, P.R. China Bo Yu BeijingKeyLaboratoryofUrbanOilandGasDistributionTechnology,ChinaUniversity of Petroleum (Beijing), Beijing,PR China Yuwen Zhang KeyLaboratoryofThermal-FluidScienceandEngineeringofMOE,SchoolofEnergyand Power Engineering, Xi’an Jiaotong University,Xi’an,Shaanxi, P.R. China; DepartmentofMechanicalandAerospaceEngineering,UniversityofMissouri,Columbia, Missouri, USA j vii PREFACE This volume of Advances in Heat Transfer demonstrates the extraordinary breadth of this branch of engineering and applied science. The two articles thatcomprisethisvolumeconstituteastudyincontrast.Oneofthearticlesis authored by Professors Stuart Churchill and Bo Yu. This lengthy and comprehensive treatise can be regarded as Professor Churchill’s magnum opus. It sets forth an in-depth, multiyear accumulation of knowledge about a complex application of heat transfer. The focus of the work is the inter- action of chemical reactions and heat transfer. Inasmuch as chemical reac- tions invariably produce or absorb thermal energy, the information conveyed by the Yu-Churchill treatise is highly relevant. TheotherarticlethatisfeaturedinthisvolumeofAdvances,authoredby Professors He and Zhang, relates to heat transfer enhancement. It describes apassivetechniquebasedonhighlyeffectivefluidflowmanagementwhich notonlygivesrisetonotableincreasesinheattransfer,butaccomplishesthis goal without a significant pressure drop penalty. That technique, longitu- dinal vortex generation, has witnessed considerable development in recent yearssothatitisveryappropriatetobringtheavailableknowledgebaseinto a coherent report. Upon the completion of the present volume of Advances, the editorial team responsible for its contents will be expanded. Professor Young Cho willcontinuetoprovidewisecounselwhilecollaboratingwithEphSparrow andJohnGormanattheUniversityofMinnesotaandwithJohnAbrahamat the University of St. Thomas. j ix CHAPTER ONE fl Prediction of the In uence of Energetic Chemical Reactions on Forced Convective Heat Transfer Bo Yu*, and Stuart W. Churchilly *BeijingKeyLaboratoryofUrbanOilandGasDistributionTechnology,ChinaUniversityofPetroleum (Beijing),Beijing,PRChina yDepartmentofChemicalandBiomolecularEngineering,UniversityofPennsylvania,Philadelphia,PA, USA Contents 1. Introduction 3 2. PriorWork 5 2.1. UnconfinedFlowandSurface-CatalyzedReactions 5 2.2. InternalHeatTransfer 5 2.3. MassTransfer 7 2.4. AnOverviewandInterpretationofPriorInvestigations 8 3. AModelforNewNumericalSolutions 10 3.1. GeneralConsiderations 11 3.2. ThePartial-DifferentialModel 16 3.3. TheNumericalMethodology 21 3.3.1. UniformHeatFluxDensity 21 3.3.2. UniformWallTemperature 23 4. Closed-FormAnalyses 23 4.1. ChemicalConversions 24 4.1.1. IsothermalChemicalConversions 24 4.1.2. AdiabaticChemicalConversions 27 4.1.3. ChemicalConversionswithaUniformHeatFluxDensity 28 4.1.4. ChemicalConversionswithaUniformWallTemperature 29 4.1.5. RecommendedExponentsandCoefficientsinEmpiricalExpressionsforthe 29 ChemicalConversion 4.1.6. ExpressionsfortheEffectoftheTemperatureDistributionintheFluidonthe 30 ChemicalConversion 4.1.7. AnInterpretationoftheExpressionsfortheChemicalConversionforDifferent 31 Conditions 4.2. ThermalEffectsofanEnergeticReactionControlledbyaUniformHeatFlux 33 Density 4.2.1. BasicModelforHeatTransferCoefficient 33 4.2.2. InclusionofanExpressionfortheDependenceoftheReaction-Rate 36 ConstantonTemperature AdvancesinHeatTransfer,Volume44 (cid:1)2012ElsevierInc. j 1 ISSN0065-2717, Allrightsreserved. http://dx.doi.org/10.1016/B978-0-12-396529-5.00001-9 2 BoYuandStuartW.Churchill 4.2.3. TheTemperatureoftheWall 38 4.2.4. ExcursionsintheTemperatureoftheFluid 38 4.3. ThermalandChemicalEffectsofanEnergeticChemicalReaction 40 ControlledbyaUniformWallTemperature 4.3.1. BasicModelfortheHeatTransferCoefficient 41 4.3.2. AFormalSolutionfortheChemicalConversion 43 4.3.3. SerendipitousApproximations 44 4.4. SolutionsforPureConvectioninFullyDevelopedFlow 47 5. NewNumericalSolutions 49 5.1. OperationalConditionsandThermophysicalProperties 49 5.2. ImposedParametricValues 49 5.3. TestsofAccuracy 50 5.3.1. PriorResultsforPureConvection 50 5.3.2. PriorResultsforCombinedReactionandConvection 51 5.3.3. ComparisonwithExperimentalResults 51 5.3.4. TestsofInternalConsistency 52 5.3.5. OverallAssessmentofNumericallyComputedValues 52 5.4. RepresentationandInterpretationoftheNumericallyComputedValues 52 foraUniformHeatFluxDensity 5.4.1. GraphicalRepresentations 53 5.4.2. TabularRepresentations 62 5.5. RepresentationandInterpretationoftheNumericallyComputedValues 83 foraUniformWallTemperature 5.5.1. GraphicalRepresentations 83 5.5.2. TabularRepresentations 91 5.6. MathematicalandPhysicalExplanationsfortheExtremeandChaotic 103 VariationofNu x 5.6.1. AUniformHeatFluxDensityattheWall 103 5.6.2. AUniformWallTemperatureEqualtoThatattheInlet 106 5.7. SummaryofFindings 107 5.7.1. ResultsandConclusionsofDirectPracticalInterest 108 5.7.2. ResultsofIntrinsicInterest 111 5.7.3. LessonsfromthePathofInvestigation 112 5.7.4. QuestionsandAnswers 113 6. Conclusions 114 7. Apology 115 Acknowledgment 115 References 115 Abstract Althoughenergeticchemicalreactionshavebeenknownforatleast50yearstoeither enhance or attenuate both external and internal forced convective heat transfer strongly,thiseffect,letaloneitsexplanation,doesnotappeartohavebeenmentioned inanytextbookontransport,heattransfer,reactionengineering,orprocessdesign.The InfluenceofChemicalReactionsonForcedConvection 3 enhancementorattenuationofinternalforcedconvectionaredescribedandexplained herein by means of a combination of essentially exact numerical solutions and of approximate,closed-formasymptoticexpressions.Thecomplexityandtheadditional parameters introduced by the localized generation of the heat of reaction and the exponential dependence of the reaction-rate constant on temperature appear to preclude a generalized predictive or correlative equation for the enhancement and attenuation. However, the numerical solution of a realistic model on a case-by-case basisisdemonstratedtobeafeasiblealternative. 1. INTRODUCTION Thefractionalchangeintheabsolutetemperatureduetoanenergetic reaction, here calledthe thermicityand symbolized bys, wasfound to bean effectivevariableforcharacterizationofthethermochemicalbehaviorbeing examined. (The term thermicity has been utilized for other quantities in other topics, for example, in the absorption of infrared radiation and in the release of energy by a detonation, but that should not cause confusion herein.) Ifthethermicityofareactingstreamissufficientlysmall,theriseorfallin temperatureinatubularreactormaybenegligibleoratleasttolerable.Thisis oftenthecasewithliquid-phasereactionsbecauseoftherelativelyhighheat capacityofthereactingfluid,butisrarelysowithgas-phasereactionsbecause they generally have a significant thermicity. Precautions, such as heat exchange,quenching,ordilution,arethenessentialtoavoidthepossibilityof a thermal runaway or the occurrence of undesirable side-reactions in the exothermiccase,orself-quenchingintheendothermicone.Anexplosionis an extreme example of a runaway, the production of NO in a flame is an x example of an undesirable side-reaction, and thermal cracking of light hydrocarbonsisanexampleofself-quenching.Inthecaseofatubularreactor, heatexchangethroughtheoutersurfaceiscommonlyemployedtoproduce a close approach to the idealized case of isothermal reaction and thereby to avoid such unwanted behavior. Reactors/heat exchangers are ordinarily designed using one of the well-known correlating equations for the convective heat transfer coefficient. However, in the instance of even a slightly energetic chemical reaction, the heat transfer coefficient for the reactingfluidmaydifferbyanorderofmagnitudeormorefromthatforno reactionbecauseofasynergeticcouplingofthesetwoprocesses.Thiseffect has been the subject of scattered theoretical analyses and experimental investigationsgoingbackatleastto1961,butdespiteitsindustrialimportance 4 BoYuandStuartW.Churchill and intrinsic interest, it has been virtually ignored in the textbooks on transport,heattransfer,andreactionengineering,aswellasinthoseinprocess design.Presumably,itisnotaccountedforinthecomputerpackagesforthese topics. The apparent reasons for this omission include the academic schism betweenthesesubjects,thenegligibleconverseeffect,thatis,themuchlesser influence of concomitant heat exchange on the chemical conversion other thantochangethetemperature,andthepervasivepostulateofplugflowin reaction engineering, which is the equivalent of perfect radial mixing and thereby implies infinite total diffusivities for momentum, energy and molecularcomponents,andprecludesheatexchange. Oneobjectiveofalong-terminvestigation,ofwhichthecurrentworkis a part, has been to evaluate such enhancements and attenuations systemat- ically and accurately by means of numerical solution of the differential equations of conservation. A second objective has been, insofar as possible, to explain the results in qualitative terms, while a third has been to devise generalized predictive or correlative expressions for such behavior. The fourth,andperhapsthemostimportantone,hasbeentocallthisinteraction to the attention of those who teach or practice transport, heat transfer, reaction engineering, or process design. This manuscript reportson a long-term investigation ofa process thatis complicatedanduniqueintworespects:first,byvirtueofthelargenumber of variables and parameters, and second, by virtueof the interaction of two processes that are ordinarily considered to be noninteractive. The report itself follows the traditional serial path of 1) a description of prior work; 2) the development of a general mathematical model; 3) identificationoftheidealizationsthatarenecessarytosolvethatmodelin closed form, and then those that are necessary to permit its numerical solution; 4) execution of those methods of solution; 5) preparation of graphical, tabular, and algebraic (correlative) representa- tions of the solutions; 6) interpretiveanalysesofthegraphs,tabulations,andcorrelativeequations; 7) summarization, conclusions, and recommendations. This final phase of themanuscriptis,incontrasttothefirstsix,quitenontraditional,inthatit is very extended and consists of several different interpretations of the behavior. The manuscript itself is long and segmented, reflecting the several separate elements,everyoneofwhichisnecessarytoresolvetheinteractivebehavior InfluenceofChemicalReactionsonForcedConvection 5 andtodeviseameansofpredictingitforprocessdesign.Itisrecommended thatareaderwithalimitedinterestinthissubjectconsidersthepossibilityof skipping from this point to Section 5.7. Summary of Findings. Then, after skimming that section, returning to this point or proceeding to sections of particular interest, rather than studying the manuscript page by page from the beginning to the end. 2. PRIOR WORK Adetailedreviewofallearlierpriorinvestigationsoftheinteractionof anenergeticreactionwithconvectiveheattransferwasnotconsideredtobe essential to the objective of this study but the historically significant and seemingly relevant ones are noted. 2.1. Unconfined Flow and Surface-Catalyzed Reactions Theenhancementofheattransferbyanenergeticreactioninanunconfined flow was apparently first observed in the 1950s in connection with the dissociation of air during the re-entry of satellites and missiles into the atmosphere. This enhancement was generally expressed in terms of an effective thermal conductivity for the gaseous mixture (see, for example, Brokaw [1]), but that application and those extreme temperatures are beyond the scope of the current analysis, which is confined to tubular reactors and moderate temperatures. Some of the early investigations of interaction were for surface-catalyzed reactions rather than for the homo- geneous ones considered exclusively herein. The arbitrarily excluded work on interactions in unconfined flow and on surface-catalyzed reactions, which includes some recent studies, may well be worthy of a separate overview by someone more knowledgeable in those respects than the present authors. 2.2. Internal Heat Transfer In1954,SundstromandChurchill[2]undertookanexperimentalstudyof theeffectofachemicallyreactinggasonheattransferinthecontextofthe combustion of premixed propane and air, with the flame stabilized on a bluff-body centrally located inside a stainless steel tube. The rate of heat transferwasenhancedsogreatlybytheunexpectedoccurrenceofresonant (screeching) combustion that purely chemical effects were overwhelmed andundetectable.Accordingly,thepursuitofchemicaleffectswasdeferred 6 BoYuandStuartW.Churchill in favor of a study of the resonance and its effects by Zartman and Churchill [3]. The interest of one of the current authors in this synergetic interaction was, however, eventually reactivated by the work of Bernstein and Churchill [4]. They observed that a 10-fold or greater increase in the convectiveheattransfercoefficientrelativetothatpredictedbythestandard correlating equations was required to bring the predictions of a model for the stability of a thermally stabilized flame in a refractory tube into agree- mentwithexperimentalmeasurements.Theensuingsearchoftheliterature identifiedseveralrelevantstudiesoftheenhancementoftheconvectiveheat transfer by an energetic reaction that are described in the immediately ensuing paragraphs. Oneoftheearlier,ifnottheearliest,successfulinvestigationoftheeffectof anenergeticreactionontherateofheattransferbetweenthewallandthefluid stream in a tubular reactor was by Irving and Smith [5], who, in 1961, investigated analytically the reaction N O 4 2NO in turbulent flow in 2 4 2 atubewithauniformwalltemperature.Inthatinvestigation,thevalueofthe resulting heat transfer coefficient was found to be as much as 18 times that predicted by the well-known correlating equations for no reaction. Roth- enberg and Smith [6] in 1966 carried out finite-difference solutions for a variety of presumably representative conditions. They postulated a first- orderirreversiblebutnotnecessarilyequimolarreactioninlaminarflowwith invariant physical properties,including density and viscosity, and a uniform temperatureatthewallequalinvaluetothatofthefluidattheinlet.Withthat thermalboundarycondition,theheattransferisautomaticallycompliant,that is,thefluidstreamisheatedifthereactionisendothermicandcooledifitis exothermic. The computations predicted that the heat transfer coefficient basedonthemixed-meantemperaturewouldbeincreasedrelativetothatfor inertflowforbothendothermicandexothermicreactions.Inparticular,the heat transfer coefficient was increased by as much as a factor of four for astronglyendothermicreaction.Theyattributedthisenhancementprimarily totheradialdiffusionofthereactant. Brian and Reid [7] in 1962 derived a closed-form solution for the local heat transfer coefficient in turbulent flow in a tube with a uniform temperature at the wall by linearizing the energy balance and postulating thatthethermalresistancewaseffectivelyconfinedtoathinboundarylayer. Theirmodelandcalculationspredictedanenhancementfactorofasgreatas 50 for the heat transfer coefficient. Brian [8] in 1963 carried out numerical solutionsforasymptoticconditions(chemicalequilibriuminthebulkofthe
The list of books you might like
