enclosure-fire-dynamics-c07

7©2000byCRCPressLLCHeatTransferinCompartmentFiresTheabilitytonumericallyestimatehowmuchheatistransferredbetweenafire,thefiregases,thefuelbed,andthesurfacesinanenclosureisessentialforanyfirehazardassessment.Theenergybalanceisverymuchaffectedbyheatbeingtransferredfromtheflamesandthehotgasestotheenclosuresurfacesandoutthroughtheenclosureopenings.Theheattransferredfromthesesourcestowardafuelpackagewilltoaconsiderableextentcontroltherateatwhichfuelevaporatesandheatisreleased.Thischapterbrieflydiscussesconvectionheattransferasappliedtoenclosurefires,butmostofthetextisdedicatedtoradiativeheattransferinenclosures.Itispresumedthatthestudentalreadyhasabackgroundinthefundamentalsofheattransfer.CONTENTS7.1Terminology7.2Introduction7.2.1Background7.2.2ModesofHeatTransfer7.2.3Measurements7.3ConvectiveHeatTransferinFire7.3.1SpecificConvectiveStudies:FirePlumeHeatTransfertoCeilings7.4RadiativeHeatTransferinFire7.4.1TwoApproximateMethodsforCalculatingRadiationfromFlametoTarget7.4.2BasicPrinciplesofRadiativeTransfer7.5EnclosureApplications7.5.1ElectricalCircuitAnalogy7.5.2FirstExample:HeatFluxtoaSensoratCeilingLevel7.5.3SecondExample:HeatFluxtoaSensoratFloorLevel7.6SummaryReferencesProblemsandSuggestedAnswers7.1TERMINOLOGYAbsorptivity—Thefractionoftheradiationenergyincidentonasurfacethatisabsorbedbythesurface,giventhesymbolα.Configurationfactor,viewfactor,shapefactor—Theconfigurationfactorisapurelygeo-metricquantity.Itgivesthefractionoftheradiationleavingonesurfacethatstrikesanothersurfacedirectly.Inotherwords,itgivesthefractionofhemisphericalsurfaceareaseenbyadifferentialelementwhenlookingatanotherdifferentialelementonthehemisphere.Emissivity—Thefractionoftheradiationenergyemittedinrelationtothemaximumpossibleemissionfromasurface,giventhesymbolε.Extinctioncoefficientandabsorptioncoefficient—Theextinctioncoefficientisameasureofhowtheintensityofabeamofradiationpassingthroughamediachangeswithlength;©2000byCRCPressLLCitisgiventhesymbolκ.Theextinctioncoefficientisgenerallyasumoftwoparts:theabsorptioncoefficientandthescatteringcoefficient.Inourapplicationsscatteringisneg-ligible,andtheextinctioncoefficientrepresentsonlyabsorption.Here,theextinctioncoefficientandtheabsorptioncoefficientaresynonymous.Graygasandgraybodyassumption—Assumingthattheradiativepropertiesofagasorasurfaceareindependentofwavelength.Thissimplifiestheradiationtransferequationenormously.Forenclosurefireradiativeexchangesgraygasandgraybodyassumptionsaregenerallysatisfactory.Meanbeamlength—Ameasureofthelengththatabeamofradiationtravels,throughamedia,giventhesymbolL.Thismeasure,togetherwiththeabsorptioncoefficient,canbeusedtoestimatetheradiationintensityemittedbyabodyofgasorflames.7.2INTRODUCTIONThissectionprovidesabriefbackground,discussesthedifferentmodesofheattransfer,andintroducesthetechniquesusedtomeasuretemperaturesandheattransfer.7.2.1BACKGROUNDItispresumedthatthestudentalreadyhasabackgroundinthefundamentalsofheattransfer.Hence,inthischapterwedonotincludethebasicdevelopment,whichwouldnecessitateabookinitself.Instead,weincludesomebasicsmorerelevanttocompartmentfires.Thisshouldreinforceprinciplesandshowtheirimportance.Standardtextsonheattransfershouldbeconsultedtoexpandonourpresentation.Inthischapterwealsopresentashortdiscussionaboutthetwodifferentmodesofheattransfer,conductionandradiation.Conductionofheatbetweenamovingfluidandasolidboundaryissometimestakentobethethirdmodeandistermedconvection.Thischapterdoesnotdiscussconductionwithinasolid;thereareexcellenttextbooksavailableinthatfieldwithmethodsdirectlyapplicabletotheproblemoffiresinenclosures.Thechapterbrieflydiscussesconvectiveheattransfer,sincethishassomespecialapplicationsinenclosurefires.Convectiveheattransfercanbethedominatingmechanismfortheheatingupofsmalldevicessuchasdetectorsandtemperaturemeasuringdevices.Thismodeofheattransferisalsoimportantforheattransferfromaflameorhotgasesimpingingonasurface.Duetothehightemperaturesofflamesandfiregases,radiativeheattransferisveryoftenthedominatingmechanismfortransferringheatinenclosurefires.Theradiativetransferequationisinitsmostcompleteformanintegro-differentialequation,anditssolutionevenforaone-dimen-sional,planar,graymediumisfartoocomplexforengineeringcalculations.Infiresthemultidi-mensionalcombustionsystemconsistsofhighlynonisothermalandnonhomogeneousmediumwherespectralvariationoftheradiativepropertiesofthemediumshouldbeaccountedfor.Itisthereforenecessarytointroducesomesimplifyingassumptionsandstrikeacompromisebetweenaccuracyandcomputationaleffort.Thelatterpartofthischapterthereforeconcentratesonsimplifiedengineeringmethodsforestimatingtheradiativepropertiesofthemedium,allowingtheradiatingintensityemittedtobecalculated.Oncethisisdone,methodsareavailabletocalculateconfigurationfactorssothattheenergyreceivedbyadistantobjectcanbeestimated.7.2.2MODESOFHEATTRANSFERFundamentally,thereareonlytwomechanismsofheattransfer.Heatisenergytransmittedduetoatemperaturedifference.Itcanoccurduetoconductionandradiationwhere•conductionisamolecularenergytransport•radiationisanelectromagneticenergytransferarisingfr