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