Transient Conduction through vapourisation protocol

various production techniques

2. Transient Heat Conduction in Infinite solids
•Weconsiderthevariationoftemperaturewithtimeandpositioninone-dimensionalproblemssuchas
thoseassociatedwithalargeplanewall,alongcylinder,andasphere.
•Aplatewhosethicknessissmallrelativetotheotherdimensionscanbemodeledasaninfinitelylargeplate,
exceptveryneartheouteredges.Buttheedgeeffectsonlargebodiesareusuallynegligible,andthusalarge
planewallsuchasthewallofahousecanbemodeledasaninfinitelylargewallforheattransferpurposes.
Similarly,alongcylinderwhosediameterissmallrelativetoitslengthcanbeanalyzedasaninfinitelylong
cylinder.

3. Consideraplanewallofthickness2LinitiallyatauniformtemperatureofTi.Attimet=0,thewallisimmersedin
afluidattemperatureT∞andissubjectedtoconvectionheattransferfrombothsideswithaconvection
coefficientofh.Theheightandthewidthofthewallarelargerelativetoitsthickness,andthusheatconduction
inthewallcanbeapproximatedtobeone-dimensional.Also,thereisthermalsymmetryaboutthemidplane
passingthroughx=0,andthusthetemperaturedistributionmustbesymmetricalaboutthemidplane.Therefore,
thevalueoftemperatureatany−xvaluein−L≤x≤0atanytimetmustbeequaltothevalueat+xin0≤x≤Lat
thesametime.Thismeanswecanformulateandsolvetheheatconductionprobleminthepositivehalfdomain0
≤x≤L,andthenapplythesolutiontotheotherhalf.

8. Theheatconductionequationincylindricalorsphericalcoordinatescanbenondimensionalizedina
similarway.Notethatnondimensionalizationreducesthenumberofindependentvariablesand
parametersfrom8to3—fromx,L,t,k,α,h,Ti,andT∞toX,Bi,andFo

9. The Heisler Charts for Transient Heat Flow
Theanalyticalexpressionsfortemperaturedistributionandtheheatfluxincaseofaninfiniteplate,averylong
cylinderandaspherehavinguniforminitialtemperatureandsuddenlyexposedtoanenvironmentatadifferent
temperaturehavealreadybeenpresentedintheformofaninfiniteseries.
HeislershowedthatforvaluesofFouriernumberFo>0.2,theinfiniteseriessolutioncanbeapproximatedwitha
fairaccuracy(anerrorwithin1%)bythefirsttermoftheseries.Theapproximatedexpressionsfortemperature
distributionsandheatfluxwerethenplottedgraphicallywhichareknownasHeislercharts.

32. Transient Heat Conduction in Semi-Infinite solids
•Asemi-infinitesolidisanidealizedbodythathasasingleplanesurfaceandextendstoinfinityinall
directions.
•Thisidealizedbodyisusedtoindicatethatthetemperaturechangeinthepartofthebodyinwhichweare
interested(theregionclosetothesurface)isduetothethermalconditionsonasinglesurface.
•Theearth,forexample,canbeconsideredtobeasemi-infinitemediumindeterminingthevariationof
temperaturenearitssurface.Also,athickwallcanbemodeledasasemi-infinitemediumifallweare
interestedinisthevariationoftemperatureintheregionnearoneofthesurfaces,andtheothersurfaceis
toofarawaytohaveanyimpactontheregionofinterestduringthetimeofobservation.Thetemperature
inthecoreregionofthewallremainsunchangedinthiscase.

33. •Forshortperiodsoftime,mostbodiescanbemodeledassemi-infinitesolidssinceheatdoesnothave
sufficienttimetopenetratedeepintothebody,andthethicknessofthebodydoesnotenterintotheheat
transferanalysis.Asteelpieceofanyshape,forexample,canbetreatedasasemi-infinitesolidwhenitis
quenchedrapidlytohardenitssurface.Abodywhosesurfaceisheatedbyalaserpulsecanbetreatedthe
sameway.
•Considerasemi-infinitesolidwithconstantthermophysicalproperties,nointernalheatgeneration,uniform
thermalconditionsonitsexposedsurface,andinitiallyauniformtemperatureofTithroughout.
•Heatconductioninasemi-infinitesolidisgovernedbythethermalconditionsimposedontheexposed
surface,andthusthesolutiondependsstronglyontheboundaryconditionatx=0.
•WhenthesurfacetemperatureischangedtoTsatt=0andheldconstantatthatvalueatalltimes,the
formulationoftheproblemcanbeexpressedas

38. The temperature in the soil is affected by the thermal conditions at one surface only, and thus the soil can
be considered to be a semi-infinite medium.
The temperature of the soil surrounding the pipes will be 0°C after three months in the case of minimum
burial depth.