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(/1T=.Lumped System Transient -Varying hot face flux]ALumped System AnalysisGDisadvantage: It ignores the effect of conduction lag into the object. &::=.1-D Transient Conduction Transient conduction is important when Q is large and L/k is large (i.e. low conductivity)  body does not achieve thermal equilibrium quicklyB31-D Transient ConductionC4Common Boundary ConditionsBody initially at To; surface raised to Ts at time zero (e.g. body immersed in boiling or condensing fluid or a molten metal) One face is perfectly insulated i.e. dT/dx=0 Body heated equally on both sides then mid- plane has zero temperature gradient Can then model the slab as half slab (line of symmetry at mid plane) Constant heat flux  the surface T has little influence on the heat transferBZZMZMD5+Numerical Model of 1-D Transient Conduction@Using finite differences to approximate the temperature variation with position and time Reduces the solution of the partial differential equation to a solution of a system of algebraic equations Consider a semi-infinite slab with a constant heat flux at the hot boundary and a convective boundary at the opposite face AZAF71D Transient ConductionFSlab is sub-divided into equally spaced nodes. The temperature at each node represents the temperature of a thin slice (i) of thickness Dx An energy balance about the node is then written which in words states: Heat flow into i  Heat leaving i = Change in heat content within i over time DtQJ  ,E641D Transient Conduction Through a Semi-Infinite SlabG81D Transient ConductionCan introduce variation in k, r and Cp with position and temperature. Can simulate multi-layer walls Can vary boundary conditions (continuously or abruptly  step change) Can apply to cylindrical and spherical bodies provided T varies in 1-D.H91D Transient ConductionThe transient solution should approach the steady-state condition as time increases Provides a means of checking Also useful to check overall heat balance on the body (i.e. does heat in  heat out at boundaries equate to the total change in heat content of the body) Should repeat the solution with more nodes to check for grid dependencyNTZZHZTHX><1-D Transient Analysis - Constant Heat Flux Final DT = 210oC6=2Z@O1-D Transient Analysis - Variable heat flux- Constant Tfurnace Final DT = 85oCHP76 uG!1-D Transient Conduction AnalysisaProvides a useful and simple approximation to many practical engineering and scientific problems.Long Furnace ModelThe Long Furnace ModelPredicted Output DatadEnergy consumption/thermal efficiency Load heat flux distribution Gas and flue temperatures Surface temperatures Insulation requirements Dynamic performance  e.g. Start-up times"The Long Furnace Model AssumptionsIsothermal gas zones (well-stirred) Isothermal surface zones Grey diffuse surfaces 1-D transient conduction Convective heat transfer small Heat Balance on a ZoneRadiation Model.All surfaces are grey Gas emissivity  represented by mixed clear/grey gas model Interzone radiation exchange Monte Carlo simulation for  view factors &n*n*Q >!Gas properties  Combustion products are not grey H2O bands at 1.38mm, 1.87mm, 2.7mm& .. CO2 bands at 2.0mm, 2.7mm, 4.3mm& .. "J"  m -$Radiation in Furnaces Atmosphere radiates due to presence of: CO2 H2O Other minor constituents (CO, methane) Soot & particulates  Continuum radiationh("*(X#Monte Carlo Method$Monte Carlo Method - Shadowing& Transient LFMLink furnace model to heat transfer models for load and insulating walls Lumped parameter model  assumes infinite conduction in the load 1-D transient conduction  finite conduction Apply a time step approach6InIn  41D Transient Conduction Through a Semi-Infinite Slab' jC gB mDResults+Energy use: PROFILE 1 = 41.137 MW gross PROFILE 2 = 40.055 MW gross Saving = 1.082 MW gross Saving in SFC = 1.082 x 3600/90 = 43.28 MJ/tonne For an annual production of 200,000 tonnes Cost saving ~ 17,000 p.a. CO2 reduction ~ 450 tonnes p.a. Uniformity: PROFILE 1 DT = 138oC PROFILE 2 DT = 104oC ZZ,Z*Z  )  sESteel Surface TemperaturestFSUMMARY/Shown how heat transfer analysis of a complex system can be built up from simple elements, using basic simplifying assumptions, and simple models. 1-D analysis for conduction 1-D long furnace model Simple models enable you to vary boundary conditions and to allow for temperature dependent properties. <3j3j.{ISUMMARYA relatively simple 1-D model of the furnace and conduction has produced information that can be applied to identify and evaluate design and operational changes that can lead to reduced cost, improved quality and lower emissions. |J ` ` ̙33` 333MMM` ff3333f` f` f` 3>?" dd@,|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>> .&(    6hZ P  T Click to edit Master title style! !  0X\   RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S  0 ``  >*  0 `   @*`  HKd޽h @ ? ̙33 Default Design 008(  0 0 06 P    >*  0 0\:     @*  0 6 `P   >*  0 6T `   @* H 0 0޽h ? ̙33w '0 H(  H~ H s *Z0   r H S Z `   Z F  `  H Px" H Hvd @o  ` ZB H s *DԔ ZB  HB s *DԔ P   H <Z  M  9erontec ZB  HB s *DԔ    H <Z{P b0Copyright  Zerontec LtdH H 0޽h ? ̙33  @4$(  4r 4 S  ZP  Z r 4 S L Z Z H 4 0޽h ? ̙33  P$(  r  S HZP  Z r  S Z Z H  0޽h ? ̙33  `$(  r  S QP   r  S hR  H  0޽h ? ̙33T p44(   * 0Z\J _-Four-zone Continuous Steel Reheating Furnace..$k 0 <Z*  Objectives: To heat steel to a controlled temperature. 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"--Ix-- zH x.2 r Zerontec Ltd   . x.%2 A$(Energy Consultancy)  .&o&n &--&&- $p p zz- $z z - $  z- $  h- $  X- $  L- $  vG- $  &&& "- &,$pqsuxxusqp&Wtb&-&& &&-&&,$pqsuxxusqp&&- $p p zz-  $z z - $  z-  $  h- $  X-  $  L- $  vG-  $  &-  --& "--,$pqsuxxusqp--&&} -- $~~--&&-- $--&--x-- x@"Arial- x.2  erontec .&} -- $ --&&---- x@Times New Roman- x.2 " Copyright  . x. 2 s . x.2  Zerontec Ltd    .--"System-&TNPP & ՜.+,0h     On-screen Show Zerontec Sh 1 =Times New RomanArial WingdingsSymbol BG-MediumZapf DingbatsBG-BoldBGBoldDefault DesignMicrosoft Equation 3.0Microsoft Excel WorksheetMicrosoft Excel Chart"Simulation of Furnace Performance ObjectiveOutlineMetal ReheatingPowerPoint PresentationFurnace Design FeaturesThroughput SpecificationSteel PropertiesTransient Heating7Lumped System Analysis, or Lumped Heat Capacity MethodLumped System Analysis-Heat Transfer in a Simple Furnace EnclosureLumped System Analysis/Lumped System Transient -Varying hot face fluxLumped System Analysis1-D Transient Conduction1-D Transient ConductionCommon Boundary Conditions,Numerical Model of 1-D Transient Conduction1D Transient Conduction51D Transient Conduction Through a Semi-Infinite Slab1D Transient Conduction1D Transient Conduction=1-D Transient Analysis - Constant Heat Flux Final DT = 210oCP1-D Transient Analysis - Variable heat flux- Constant Tfurnace Final DT = 85oC"1-D Transient Conduction AnalysisLong Furnace ModelThe Long Furnace ModelPredicted Output Data#The Long Furnace Model AssumptionsHeat Balance on a ZoneRadiation ModelGas propertiesRadiation in FurnacesMonte Carlo MethodMonte Carlo Method - ShadowingTransient LFMPowerPoint Presentation51D Transient Conduction Through a Semi-Infinite SlabPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationResultsSteel Surface TemperaturesSUMMARYSUMMARYPowerPoint Presentation  Fonts UsedDesign TemplateEmbedded OLE Servers Slide Titles1(_.Dr.Robert TuckerDr.Robert Tucker  !"#$%&'()*+,-./023456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root EntrydO)Picturesg`Current UserSummaryInformation(`PowerPoint Document(1RDocumentSummaryInformation8Root EntrydO)`;IPicturesg`Current UserGSummaryInformation(`%_. Robert TuckerRobert Tucker