http://people.csail.mit.edu/jaffer/SimRoof/Convection

ConvectionFromaRectangularPlate

IntroductionSitesWeatherNetRadiativeTransferLambertianPerfromanceLimitsCoolRoofConvectionFromaRectangularPlate

AbstractIntroduction

MotivationConvectiveHeatTransferTypesofConvection

1997ASHRAEFundamentalsThermalEmissivityStillAir

2009ASHRAEFundamentalsPhysicalParametersThermodynamicandTransportPropertiesofAirCharacteristicLengthDimensionlessQuantities

NaturalConvectionVerticalPlateHorizontalPlate

T9.9InclinedPlate

DownwardConvectionUpwardConvection

NaturalConvectiveSurfaceConductanceDoubleSidedNaturalConvectionNaturalConvectionSummary

ForcedConvectionLaminarTurbulentProgressionLaminarTurbulentTransitionLaminarConvectionConvectioninaDuctSurfaceRoughnessData

SurfaceRoughnessForcedConvectioninaPipeBoundaryLayerForcedConvectionfromaRoughPlateColebrookWhiteEquationAsymptotesScaledColburnAnalogyAsymptoteForcedConvectionSummaryNaturalConvectionfromaRoughPlate

OffAxisConvectionForcedOffAxisConvectionEffectiveLengthNaturalOffAxisConvection

http://people.csail.mit.edu/jaffer/SimRoof/Convectionhttp://localhost/~jaffer/SimRoof/Introductionhttp://localhost/~jaffer/SimRoof/Siteshttp://localhost/~jaffer/SimRoof/Weatherhttp://localhost/~jaffer/SimRoof/NRThttp://localhost/~jaffer/SimRoof/PerfectLambertianhttp://localhost/~jaffer/cool/CoolRoofhttp://localhost/~jaffer/SimRoof/Convection/http://localhost/~jaffer/SimRoof/Convection/#Abstracthttp://localhost/~jaffer/SimRoof/Convection/#Introductionhttp://localhost/~jaffer/SimRoof/Convection/#Motivationhttp://localhost/~jaffer/SimRoof/Convection/#Convective Heat Transferhttp://localhost/~jaffer/SimRoof/Convection/#Types of Convectionhttp://localhost/~jaffer/SimRoof/Convection/#1997 ASHRAE Fundamentalshttp://localhost/~jaffer/SimRoof/Convection/#Thermal Emissivityhttp://localhost/~jaffer/SimRoof/Convection/#Still Airhttp://localhost/~jaffer/SimRoof/Convection/#2009 ASHRAE Fundamentalshttp://localhost/~jaffer/SimRoof/Convection/#Physical Parametershttp://localhost/~jaffer/SimRoof/Convection/#Thermodynamic and Transport Properties of Airhttp://localhost/~jaffer/SimRoof/Convection/#Characteristic Lengthhttp://localhost/~jaffer/SimRoof/Convection/#Dimensionless Quantitieshttp://localhost/~jaffer/SimRoof/Convection/#Natural Convectionhttp://localhost/~jaffer/SimRoof/Convection/#Vertical Platehttp://localhost/~jaffer/SimRoof/Convection/#Horizontal Platehttp://localhost/~jaffer/SimRoof/Convection/#T9.9http://localhost/~jaffer/SimRoof/Convection/#Inclined Platehttp://localhost/~jaffer/SimRoof/Convection/#Downwardhttp://localhost/~jaffer/SimRoof/Convection/#Upwardhttp://localhost/~jaffer/SimRoof/Convection/#Natural Convective Surface Conductancehttp://localhost/~jaffer/SimRoof/Convection/#Double-Sided Natural Convectionhttp://localhost/~jaffer/SimRoof/Convection/#Natural Convection Summaryhttp://localhost/~jaffer/SimRoof/Convection/#Forced Convectionhttp://localhost/~jaffer/SimRoof/Convection/#Laminar-Turbulent Progressionhttp://localhost/~jaffer/SimRoof/Convection/#Laminar-Turbulent Transitionhttp://localhost/~jaffer/SimRoof/Convection/#Laminar Convectionhttp://localhost/~jaffer/SimRoof/Convection/#Convection in a Ducthttp://localhost/~jaffer/SimRoof/Convection/#Surface Roughness Datahttp://localhost/~jaffer/SimRoof/Convection/#Surface Roughnesshttp://localhost/~jaffer/SimRoof/Convection/#Forced Convection in a Pipehttp://localhost/~jaffer/SimRoof/Convection/#Boundary Layerhttp://localhost/~jaffer/SimRoof/Convection/#Forced Convection from a Rough Platehttp://localhost/~jaffer/SimRoof/Convection/#Colebrook-White Equation Asymptoteshttp://localhost/~jaffer/SimRoof/Convection/#Scaled Colburn Analogy Asymptotehttp://localhost/~jaffer/SimRoof/Convection/#Forced Convection Summaryhttp://localhost/~jaffer/SimRoof/Convection/#Natural Convection from a Rough Platehttp://localhost/~jaffer/SimRoof/Convection/#Off-Axis Convectionhttp://localhost/~jaffer/SimRoof/Convection/#Forced Off-Axis Convectionhttp://localhost/~jaffer/SimRoof/Convection/#Effective Lengthhttp://localhost/~jaffer/SimRoof/Convection/#Natural Off-Axis Convection

MixedConvectionLocalMixedConvectionCorrelationsFromFieldMeasurementsVerticalPlatesVerticalPlateswithOffAxisFlowInclinedPlatesMixedConvectionSummary

ApplicationtoRoofsWindFlatRoofsPeakedRoofsRoofPerformance

ConclusionFutureWork

FlatConvexPlatesConvectionwithPhaseChangeExperiments

BibliographySolarScreenModelSolarScreenPerformanceThermalInfraredOptics(footnotesandsupplementalinformation)

Abstract

Acompletemodelforsinglephase(noncondensing)convectionfromanisothermalrectangularplateisdevelopedandtestedagainstavailablepublishedexperimentaldata.ItgeneralizesFujiiandImura[76]'snaturalconvectionmodeltothefullrangeofinclinations(90to+90)whileeliminatingtheuseoftheirofadhocformulaforthelaminarturbulentthreshold.TheforcedconvectionmodelfindsacorrelationforroughsurfaceconvectionbyapplyingtheColburnanalogytoflatplates.Throughtheuseofeffectivecharacteristiclength,thetheoryisextendedtonaturalconvectionforallorientationsofaplate,notjustthosehavingahorizontaledge,andoffaxisforced(butinplane)flows.Formixedconvectionacorrespondenceisfoundbetweenforcedconvectionandtheverticalplatemodeofnaturalconvectionwhichallowsthemtobecombinedandusedwithinthemultimodenaturalconvectionsolution.

Arelatedmodelforconvectionfromsymmetricalpeakedroofsisalsodeveloped.

Aplanfor(anapparatusand)experimentstotesttheroughsurfacecorrelationsispresented.

Introduction

Motivation

Themostimportantthermalprocessesforabuilding'sroofareinsolation,convection,andthermalradiation.Themostcomplicatedtocomputeisconvectionbecauseitdependsonsomanyvariables:airandsurfacetemperatures,humidity,wind,androofsize,shape,orientation,and(surface)roughness.

Thereareadditionalcomplications:totalheattransferisnotequaltothesumofheattransferfromashape'spartsconsideredindividuallywindusuallyvariesbothinspeedanddirection,butconvectivesurfaceconductanceisnotalinearfunctionofwindspeed.

In2011,establishedtheorywasnotsufficienttocomputeconvectionfromroofparametersandmeteorologicalmeasurements.Thisworkrectifiesthatsituation.

ConvectiveHeatTransfer

http://localhost/~jaffer/SimRoof/Convection/#Mixed Convectionhttp://localhost/~jaffer/SimRoof/Convection/#Local Mixed Convectionhttp://localhost/~jaffer/SimRoof/Convection/#Correlations From Field Measurementshttp://localhost/~jaffer/SimRoof/Convection/#Vertical Plateshttp://localhost/~jaffer/SimRoof/Convection/#Vertical Plates with Off-Axis Flowhttp://localhost/~jaffer/SimRoof/Convection/#Inclined Plateshttp://localhost/~jaffer/SimRoof/Convection/#Mixed Convection Summaryhttp://localhost/~jaffer/SimRoof/Convection/#Application to Roofshttp://localhost/~jaffer/SimRoof/Convection/#Windhttp://localhost/~jaffer/SimRoof/Convection/#Flat Roofshttp://localhost/~jaffer/SimRoof/Convection/#Peaked Roofshttp://localhost/~jaffer/SimRoof/Convection/#Roof Performancehttp://localhost/~jaffer/SimRoof/Convection/#Conclusionhttp://localhost/~jaffer/SimRoof/Convection/#Future Workhttp://localhost/~jaffer/SimRoof/Convection/#Flat Convex Plateshttp://localhost/~jaffer/SimRoof/Convection/#Convection with Phase-Changehttp://localhost/~jaffer/SimRoof/Convection/#Experimentshttp://localhost/~jaffer/SimRoof/Convection/#Bibliographyhttp://localhost/~jaffer/SimRoof/SolarScreenhttp://localhost/~jaffer/cool/SolarScreenshttp://localhost/~jaffer/SimRoof/ThermalOpticshttp://localhost/~jaffer/SimRoof/Convection/#Mixed Convection Summaryhttp://localhost/~jaffer/SimRoof/Convection/#Inclined Platehttp://localhost/~jaffer/SimRoof/Convection/#76http://localhost/~jaffer/SimRoof/Convection/#Surface Roughnesshttp://localhost/~jaffer/SimRoof/Convection/#Effective Lengthhttp://localhost/~jaffer/SimRoof/Convection/#Vertical Plateshttp://localhost/~jaffer/SimRoof/Convection/#Peaked Roofshttp://localhost/~jaffer/SimRoof/Convection/#Experimentshttp://en.wikipedia.org/wiki/Insolationhttp://en.wikipedia.org/wiki/Thermal_radiation

SaysWikipedia:

Convectiveheattransfer,oftenreferredtosimplyasconvection,isthetransferofheatfromoneplacetoanotherbythemovementoffluids.Convectionisusuallythedominantformofheattransferinliquidsandgases.

Tomodelthethermaldynamicsofroofsweareinterestedintheconvectiveflowofheattoorfromthetopsurfaceoftheroof.ForaflatplateatauniformtemperatureT,therateofheatflow(inWatts)duetoconvectionfromonesideoftheplateis:

hAT

h W/(Km2) convectivesurfaceconductanceA m2 areaofonesideofplate

T K TTenvT K platetemperatureTenv K fluidtemperature

Thecomplicationisthatthevalueofhdependsontemperatures,fluidvelocity,andthearea,shape,orientation,androughnessoftheplatesurface.Avalueofhfora1mby1mplatewillusuallybelarger(andneversmaller)thanhfora2mby2mplateunderotherwiseidenticalconditions.Thelargerplatewilltransfermoreheatbecauseithasfourtimestheareaofthesmallerplate,butnotmorethan4timestheheat.

TypesofConvection

Convectionisnatural(free),forced,ormixed.Innaturalconvection,fluidmotionisdrivenbythedifferenceintemperaturebetweentheplateandthefluid.Inforcedconvection,fluidmotionisdrivenbyanexternalforcesuchaswind.Mixedconvectionisamixtureofnaturalandforcedconvectionoccurringatlowfluidspeeds.

(Natural)upwardconvectionisproducedbyanupwardfacingplatewhichiswarmerthanthefluid,oradownwardfacingplatewhichiscolderthanthefluid.(Natural)downwardconvectionisproducedbyanupwardfacingplatewhichiscoolerthanthefluid,oradownwardfacingplatewhichiswarmerthanthefluid.

Acorrelation(approximateequationrelatingdimensionlessquantities)canmodelanisothermalsurfaceoraconstantheatfluxthroughthesurface.Thecorrelationsforthesetworegimesusuallydifferonlyincoefficientsandadditiveconstants.Thisarticleaddressesconvectionfromisothermalplates.

Aforcedconvectioncorrelationcanbeforlocalheatfloworforheatflowaveragedacrossthesurface.Section"LaminarT