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Experimental Fluid Mechanics Forfurthervolumes: http://www.springer.com/series/3837 . L.P. Yarin The Pi-Theorem Applications to Fluid Mechanics and Heat and Mass Transfer L.P.Yarin Technion-IsraelInstituteofTechnology Dept.ofMechanicalEngineering TechnionCity 32000Haifa Israel ISBN978-3-642-19564-8 e-ISBN978-3-642-19565-5 DOI10.1007/978-3-642-19565-5 SpringerHeidelbergDordrechtLondonNewYork LibraryofCongressControlNumber:2011944650 #Springer-VerlagBerlinHeidelberg2012 Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting, reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9, 1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violations areliabletoprosecutionundertheGermanCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnot imply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotec- tivelawsandregulationsandthereforefreeforgeneraluse. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) To the blessed memory of my parents Professor Peter Yarin and Mrs. Leah Aranovich . Preface ThebookisdevotedtotheBuckinghamPi-theoremanditsapplicationstovarious phenomenainnatureandengineering.Theaccentismadeonproblemscharacter- istic of heat and mass transfer in solid bodies, as well as in laminar and turbulent flows of liquids and gases. Such choice is not accidental. It is dictated by the requirementsofmoderntechnologyandencompassesavastmajorityofimportant problemsrelatedwithdragandheattransferexperiencedbysolidbodiesmovingin viscous fluids. These problems involve the evaluation of temperature fields in media with constant and temperature-dependent thermal diffusivity, heat and mass transfer in boundary layers, pipe and jet flows, as well as thermal processes occurring in reactive media. In all these cases a uniform approach to the corresponding complex thermohydrodynamical problems is used. It is based on the direct application of the Pi-theorem to the analysis of two types of problems: thosewhichadmitarigorousmathematicalformulation,aswellasthoseforwhich such formulation is unavailable. For the former problems our attention will be focusedontheestablishmentofself-similaritywhichreducesthegoverningpartial differentialequationstotheordinaryonesbymeansofthePi-theorem,whereasfor the latter problems the Pi-theorem will be used to reveal a set of the governing dimensionlessgroups.Toacertaindegreethechoiceoftheproblemsissubjective. However, it allows the evaluation of the range of possible applications of the Pi-theorem and the peculiarities characteristic of the complex thermohydrodyna- micalprocessesincontinuousmedia. Thebookconsistsofninechapters.Theydealwiththebasicsofthedimensional analysis,theapplicationofthePi-theoremtofindself-similaritiesandreducepartial differentialequationstotheordinaryones.Then,suchinterrelatedtopicsasthedrag force,laminarflowsinchannels,pipesandjetsarecoveredindetail.Thediscussion alsoinvolveskindredheatandmasstransferinnatural,forcedandmixedconvec- tionandinsituationswithphasechangeandchemicalreactions.Someproblemsof turbulencetheoryarealsocoveredintheframeworkofthePi-theorem.Inaddition tothein-depthexpositionofthebasictheoryandthegenericproblems,anumberof worked examples of problems related to the application of the Pi-theorem to different hydrodynamic,heatandmasstransferquestionsarepresentedintheend ofeachchapter.Theycanbeinteresttotheengineeringandphysicsstudents. vii viii Preface Thebookisintendedtoscientistsandengineersinterestedinhydrodynamicand heat and mass transfer problems. It could also be useful to graduate students studyingmechanical,civilandchemicalengineering,aswellasappliedphysics. L.P.Yarin Acknowledgment IamespeciallygratefulanddeeplyindebtedtomysonProfessorAlexanderYarin for some special consultations related to the applications of the dimensional analysis to thermohydrodynamics problems, many insightful suggestions and dis- cussions,aswellasmultiplecommentsonthecontentsofthebook. Iam deeplyobligated tomydaughterMrs.ElenaYarinandmygranddaughter MissInnaYarin.Withouttheirhelpthisbookwouldnothavematerialized. ix .