Thermal Diffusivity>If thethermal conductivity (k)is a constant and uniform in all directions atanydistance0akaTa2TaT(2.4)R0x2axaxaxax>Then,theheatdiffusionequationEq.(2.3)canbeexpressedasa2Ta2Ta2T1aT(2.5)ax2+ay2+az2=αatwherethethermaldiffusivity(a)isdefinedask(2.6)apCpThethermaldiffusivitymeasurestheoverall effectivenessofheatconductioninchanging object'stemperature orhowfasttoheatup theobjectFire ScienceDrXinyanHuang,PolyU
Fire Science Dr Xinyan Huang, PolyU Thermal Diffusivity 𝜶 ≡ 𝒌 𝝆𝒄𝒑 (2.6) where the thermal diffusivity (α) is defined as The thermal diffusivity measures the overall effectiveness of heat conduction in changing object’s temperature or how fast to heat up the object. 𝜕 𝜕𝑥 𝑘 𝜕𝑇 𝜕𝑥 = 𝜕𝑘 𝜕𝑥 𝜕𝑇 𝜕𝑥 + 𝑘 𝜕 2𝑇 𝜕𝑥 2 (2.4) ➢ If the thermal conductivity (𝒌) is a constant and uniform in all directions at any distance 𝜕 2𝑇 𝜕𝑥 2 + 𝜕 2𝑇 𝜕𝑦 2 + 𝜕 2𝑇 𝜕𝑧 2 = 1 𝛼 𝜕𝑇 𝜕𝑡 (2.5) ➢ Then, the heat diffusion equation Eq.(2.3) can be expressed as 0
Biot(Bi)NumberUndersteady-stateconditions,thesurfaceenergybalancecanbeexpressedwithNewton'sLawofcoolingasLeondAconvTssKAT.2-(Ts,1 - Ts,2) = hA(Ts,2 - Too)(2.7)Bi<<l1Bi~T$.2wherekisthethermalconductivityofthesolidBi>>Ts3To,hL/kAhL出Ts,1 - Ts,2BiLTs,2A-To1/hASteady-statetemperaturehLconductionresistancedistribution inaplanewall with(2.8)Bi三ksurfaceconvectionconvectionresistance.Binumberisusedto judge if temperature inside solidis uniform ornot.Bi<o.1meansthetemperatureinsidesolidisrelativeuniform(thermallythin)DrXinyanHuang.PolyUFireScience
Fire Science Dr Xinyan Huang, PolyU Biot (Bi) Number • Bi number is used to judge if temperature inside solid is uniform or not. • Bi < 0.1 means the temperature inside solid is relative uniform (thermally thin) Under steady-state conditions, the surface energy balance can be expressed with Newton’s Law of cooling as 𝑘𝐴 𝐿 𝑇𝑠,1 − 𝑇𝑠,2 = ℎ𝐴 𝑇𝑠,2 − 𝑇∞ (2.7) 𝐵𝑖 = 𝑇𝑠,1 − 𝑇𝑠,2 𝑇𝑠,2 − 𝑇∞ = 𝐿/𝑘𝐴 1/ℎ𝐴 = ℎ𝐿 𝑘 𝐵𝑖 ≡ ℎ𝐿 𝑘 ≡ conduction resistance convection resistance (2.8) where k is the thermal conductivity of the solid. Steady-state temperature distribution in a plane wall with surface convection
THEHONGKONGPOLYTECHNICUNIVERSITY香港理工大ConductionConvectionContentsRadiationHeatconduction and diffusionXMasstransfer&moleculardiffusionconvectionHeat convectionRadiationradiationhotairconductioncoolairDrXinyanHuang.PolyUFire Science
Fire Science Dr Xinyan Huang, PolyU Contents ❖ Heat conduction and diffusion ❖ Mass transfer & molecular diffusion ❖ Heat convection ❖ Radiation
Gas MixingMasstransferisthenetmovementofmassfromonelocationtoanother:Heattransferisthenetmovementofheat (thermalenergy)fromonelocationtoanotherMasstransferandheattransfercanoccuratthesametimeFireScienceDrXinyanHuang,PolyU
Fire Science Dr Xinyan Huang, PolyU Gas Mixing • Mass transfer is the net movement of mass from one location to another • Heat transfer is the net movement of heat (thermal energy) from one location to another • Mass transfer and heat transfer can occur at the same time
WhatisMass Transfer?Masstransferisthenetmovementofmassfromonelocationtoanotherinsolid,liquid,gasDiffusionistheprocessofmasstransferofindividualmoleculebecauseoftherandommolecularmotion(Brownianmotion)andassociatedwithdriving force such as concentration gradientMassandheattransfersimultaneouslyoccurinmanyprocesses,suchasevaporation,drying,anddistillationDrXinyanHuang.PolyUFireScience
Fire Science Dr Xinyan Huang, PolyU What is Mass Transfer? • Mass transfer is the net movement of mass from one location to another in solid, liquid, gas. • Diffusion is the process of mass transfer of individual molecule because of the random molecular motion (Brownian motion) and associated with driving force such as concentration gradient. • Mass and heat transfer simultaneously occur in many processes, such as evaporation, drying, and distillation