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过程工程学报 2013
SimilaritySolutioninChemicalEngineeringGuidedbyDimensionalAnalysisKeywords: chemicalengineeringmathematics,similaritysolution,dimensionalanalysis,variabletransformation,masstransfer Abstract: Similaritysolutionisaclassicaltopicinchemicalengineering,frequentlyencounteredinanalysisofflowandtransportphenomenainsemi-infinitedomains.Inthisarticle,dimensionalanalysisisappliedtoresolvesystematicallytheconditionsfortheexistenceofsimilaritysolutionsandformulateabasicproceduretogetsuchsolutions.Withseveralclassicexamples,themethodforfindingthesuitablecombinationofindependentvariablesfromoriginalonesisdemonstrated,sothattheoriginalpartialdifferentialequationcanbetransformedintoasimplerordinarydifferentialequation,throughwhichthedesiredsimilaritysolutionisfinallyachieved.In-depthanalysisofone-dimensionaldiffusion/reactionproblemsbydimensionalanalysisresultsinsomenewinsights.Theelaborationissignificantfordeepinsightofsimilaritysolutionanditsapplicationinchemicalengineering.
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