香港理工大学：《火灾科学与城市安全》课程教学课件（讲稿）Review of Heat and Mass Transfer

THEHONGKONGDEPARTMENTOFPOLYTECHNICUNIVERSITYBUILDINGSERVICESENGINEERING香港理工大屋宇设储工程翠系BSE533:FireDynamicsLecture 2: Review of Heat and Mass TransferXinyan Huang, Ph.D.AssistantProfessorBuilding Services EngineeringResearchCentreforFireEngineering,PolyUxy.huang@polyu.edu.hkFireScienceDrXinyanHuang.PolyU

Fire Science Dr Xinyan Huang, PolyU Xinyan Huang, Ph.D. Assistant Professor Building Services Engineering Research Centre for Fire Engineering, PolyU xy.huang@polyu.edu.hk BSE533: Fire Dynamics Lecture 2: Review of Heat and Mass Transfer

Course ScheduleWeekDateTopicRemarks211MarchIntrotoFirePhenomena318 MarchReviewofHeatTransfer425 MarchBurningandFirePlume51 AprilIntrotoCombustioninFire68AprilHW1dueIgnitionPhenomena715AprilFireSpread822 AprilRoomFireLab report due929 AprilFire Modelling106MayHW2dueWildland Fire1113MayFire SafetyEngineering1220 MayCourseprojectGrouppresentationEach day:2-unitLecture Session+1-unitQ&ASession2DrXinyanHuang.PolyUFire Science

Fire Science 2 Dr Xinyan Huang, PolyU Week Date Topic Remarks 2 11 March Intro to Fire Phenomena 3 18 March Review of Heat Transfer 4 25 March Burning and Fire Plume 5 1 April Intro to Combustion in Fire 6 8 April Ignition Phenomena HW 1 due 7 15 April Fire Spread 8 22 April Room Fire Lab report due 9 29 April Fire Modelling 10 6 May Wildland Fire HW 2 due 11 13 May Fire Safety Engineering 12 20 May Course project Group presentation Each day: 2-unit Lecture Session + 1-unit Q&A Session

What is heat transfer?ConductionConvectionRadiationFireScienceDrXinyanHuang,PolyU

Fire Science Dr Xinyan Huang, PolyU What is heat transfer?

THEHONGKONGPOLYTECHNICUNIVERSITY香港理工大ConductionConvectionContentsRadiation*HeatconductionanddiffusionMasstransfer&moleculardiffusionXconvection*HeatconvectionRadiationradiationhotairconductioncoolairDrXinyanHuang.PolyUFire Science

Fire Science Dr Xinyan Huang, PolyU Contents ❖ Heat conduction and diffusion ❖ Mass transfer & molecular diffusion ❖ Heat convection ❖ Radiation

Heat(Thermal Energy)TransportationHotFireScienceDrXinyanHuang.PolyU

Fire Science Dr Xinyan Huang, PolyU Heat (Thermal Energy) Transportation

HeatConductioninSolidGLASS RODMETAL RODpuehpuehFormostsolids,thermalenergyistransferredthroughthevibrationandcollisionofmoleculesand atoms.Formetals,thermalenergyisalsospreadthroughfreeelectrondiffusion.Onceheated,electrons gainkinetic energyand movefaster.They collidewith atoms inthe coolerparts ofmetal and transfertheirkinetic energy.DrXinyan Huang.PolyUFireScience

Fire Science Dr Xinyan Huang, PolyU Heat Conduction in Solid • For most solids, thermal energy is transferred through the vibration and collision of molecules and atoms. • For metals, thermal energy is also spread through free electron diffusion. • Once heated, electrons gain kinetic energy and move faster. They collide with atoms in the cooler parts of metal and transfer their kinetic energy

History of Heat ConductionBaronJean-BaptisteFourierwasaProfessoratEcolePolytechnique,Paris,andhewasthescientificadvisertoNapoleon Bonaparte's expedition to Egypt (design weapons)Best knownforwriting TheAnalytic Theory of Heat (1822)1.Formulated the principleforheat conduction,Fourier's law.2.Formulatedtheheatdiffusionequation3.PutforwardthefoundationsofFourierseriesBaronJean-BaptisteFourier4.(1768-1830)StarteddimensionalanalysisFrenchmathematicianandphysicistDrXinyanHuang.PolyUFire Science

Fire Science Dr Xinyan Huang, PolyU History of Heat Conduction Best known for writing The Analytic Theory of Heat (1822) 1. Formulated the principle for heat conduction, Fourier’s law. 2. Formulated the heat diffusion equation. 3. Put forward the foundations of Fourier series. 4. Started dimensional analysis. Baron Jean-Baptiste Fourier was a Professor at École Polytechnique, Paris, and he was the scientific adviser to Napoleon Bonaparte’s expedition to Egypt (design weapons). wikipedia Baron Jean-Baptiste Fourier (1768-1830) French mathematician and physicist

Fourier'sLaw>Fourier'slawisthephenomenologicalForthesteady-state1-DheattransferoCoC5050dTqcondqcondheat40A40dxr=03030temATTh-Te20k-tanα(2.1)20kAxL01000Profile0kisthethermalconductivity.isan1importantthermalpropertyofthemateria20xMinussign()isnecessarybecauseheatisalwaystransferredindirectionofdecreasingtemperatureDrXinyanHuang.PolyUFireScience

Fire Science Dr Xinyan Huang, PolyU Fourier’s Law 𝑞ሶ𝑐𝑜𝑛𝑑 ′′ = 𝑞ሶ𝑐𝑜𝑛𝑑 𝐴 = −𝑘 ቤ 𝑑𝑇 𝑑𝑥 𝑥=0 = 𝑘 ∆𝑇 ∆𝑥 = 𝑘 𝑇ℎ − 𝑇𝑐 𝐿 = 𝑘 ∙ tan𝛼 (2.1) ➢ For the steady-state 1-D heat transfer 𝑻 𝑻𝒄 𝑻𝒉 𝑳 𝒙 𝜶 ➢ Fourier’s law is the phenomenological ▪ 𝑘 is the thermal conductivity, is an important thermal property of the material ▪ Minus sign (-) is necessary because heat is always transferred in direction of decreasing temperature

Conductivity(kora)-MaterialPropertydT(2.1)qcondZincSilverdxPUREMETALSNickelAluminumALLOYSPlasticsIceOxidesMetalsaregoodconductors,suchaslron,silverNONMETALLICSOLIDSaluminum,steel,copper (>10W/m-K)FibersFoamsINSULATIONSYSTEMSPlastic,wood,rubber,andglassaregoodOilsWaterMercuryinsulators(0.2W/m-K)LIQUIDSCarbonHydrogendioxideAirisagood insulator (0.1W/m-K)GASESLiquid(~1W/m-K)0.11100.011001000Thermalconductivity (W/m-K)dT+ Note that fluid (gas and liquid) can flow to created convection to enhance heat transfer, i.e., increasingdxFire ScienceDrXinyanHuang.PolyU

Fire Science Dr Xinyan Huang, PolyU Conductivity (k or 𝝀) – Material Property • Metals are good conductors, such as Iron, silver, aluminum, steel, copper (>10 W/m-K). • Plastic, wood, rubber, and glass are good insulators (0.2 W/m-K). • Air is a good insulator (0.1 W/m-K). • Liquid (~ 1 W/m-K) 𝑞ሶ𝑐𝑜𝑛𝑑 ′′ = −𝑘 ቤ 𝑑𝑇 𝑑𝑥 𝑥=0 (2.1) ❖ Note that fluid (gas and liquid) can flow to created convection to enhance heat transfer, i.e., increasing 𝒅𝑻 𝒅𝒙

Fourier'sLawin3Ddy + dy>Heatfluxisavector(magnitude+direction)az+ dzInreality,theheatfluxshouldbe3DphenomenonaT+dxqcond,x=Ks1015018ky(2.2)qcond =-kVT =3qcond,y='oqcond,z>Foratransientheat-transfer process,theheat diffusion equation isaaTaaT)0aTaT(2.3)V(kVT)K1kkpCpazataxaxayayaz》Heatconduction=thermaldiffusionFireScienceDrXinyanHuang.PolyU

Fire Science Dr Xinyan Huang, PolyU Fourier’s Law in 3D 𝑞ሶ𝑐𝑜𝑛𝑑 ′′ = −𝑘∇𝑇 = 𝑞ሶ𝑐𝑜𝑛𝑑,𝑥 ′′ = −𝑘𝑥 𝜕𝑇 𝜕𝑥 𝑞ሶ𝑐𝑜𝑛𝑑,𝑦 ′′ = −𝑘𝑦 𝜕𝑇 𝜕𝑦 𝑞ሶ𝑐𝑜𝑛𝑑,𝑧 ′′ = −𝑘𝑧 𝜕𝑇 𝜕𝑧 (2.2) ➢ Heat flux is a vector (magnitude + direction) ➢ In reality, the heat flux should be 3D phenomenon ➢ For a transient heat-transfer process, the heat diffusion equation is ∇ 𝑘∇𝑇 = 𝜕 𝜕𝑥 𝑘𝑥 𝜕𝑇 𝜕𝑥 + 𝜕 𝜕𝑦 𝑘𝑦 𝜕𝑇 𝜕𝑦 + 𝜕 𝜕𝑧 𝑘𝑧 𝜕𝑇 𝜕𝑧 = 𝜌𝑐𝑝 𝜕𝑇 𝜕𝑡 (2.3) ➢ Heat conduction ≡ thermal diffusion