Mass transfer, Topic : Ficks law of diffusion

Ficks law of diffusion

1. Module -7
MASS TRANSFER
By
Faculty:Mr.LALANKUMAR
AssistantProfessor
DepartmentofMechanicalEngineering
KatiharEngineeringCollegeKatihar

2. 01 Version: 1, KEC Katihar
❑What we shall learn from this chapter ?????????
❖Contents
▪Introduction
▪AnalogybetweenHeattransferandMasstransfer
▪MassDiffusion
▪SteadyMassDiffusionthroughwall
▪Transientmassdiffusion
▪Massconvection
DEPARTMENT OF MECHANICAL ENGINEERING
▪Fick’sLawofDiffusion:

3. 02 Version: 1, KEC KatiharDEPARTMENT OF MECHANICAL ENGINEERING
❖ANALOGY BETWEEN HEAT AND MASS TRANSFER
▪Therateofheatconductioninadirectionxisproportionaltothetemperature
gradientdT/dxinthatdirectionandisexpressedbyFourier’slawofheat
conductionas
▪wherekisthethermalconductivityofthemediumand
Aistheareanormaltothedirectionofheattransfer.

4. 03 Version: 1, KEC KatiharDEPARTMENT OF MECHANICAL ENGINEERING
▪TherateofmassdiffusionmdiffofachemicalspeciesAin
astationarymediuminthedirectionxisproportionalto
theconcentrationgradientdC/dxinthatdirectionandis
expressedbyFick’slawofdiffusion
where D
ABis the diffusion coefficient (or mass diffusivity)
of the species in the mixture and CA is the concentration
of the species in the mixture at that location.

5. 04 Version: 1, KEC KatiharDEPARTMENT OF MECHANICAL ENGINEERING
▪Itcanbeshownthatthedifferentialequationsforbothheatconductionandmass
diffusionareofthesameform.
❖Convection
▪TherateofheatconvectionforexternalflowwasexpressedconvenientlybyNewton’s
lawofcoolingas
•whereh
convistheheattransfercoefficient,Asisthesurfacearea,and(Ts-T)isthe
temperaturedifferenceacrossthethermalboundarylayer.
▪Therateofmassconvectioncanbeexpressedas

6. 05 Version: 1, KEC KatiharDEPARTMENT OF MECHANICAL ENGINEERING
•whereh
massisthemasstransfercoefficient,Asisthesurfacearea,and(Cs-C)isa
suitableconcentrationdifferenceacrosstheconcentrationboundarylayer.
❖MASS DIFFUSION
❑Mass Basis

7. 06 Version: 1, KEC KatiharDEPARTMENT OF MECHANICAL ENGINEERING
▪Themassandmolarconcentrationsarerelatedtoeachotherby
•whereMisthemolarmassofthemixturewhichcanbedeterminedfrom
▪Themassandmolefractionsofspeciesiofamixturearerelatedtoeachotherby
❑Mole Basis

8. 07 Version: 1, KEC KatiharDEPARTMENT OF MECHANICAL ENGINEERING
❖Fick’s Law of Diffusion:
▪StationaryMediumConsistingofTwoSpecies

9. 08 Version: 1, KEC KatiharDEPARTMENT OF MECHANICAL ENGINEERING
▪Herej
diff,Aisthe(diffusive)massfluxofspeciesA(masstransferbydiffusionper
unittimeandperunitareanormaltothedirectionofmasstransfer,inkg/s·m
2
)and
¯j
diff,Aisthe(diffusive)molarflux(inkmol/s·m
2
).
▪RememberthattheconstantofproportionalityinFourier’slawwasdefinedasthetransport
propertythermalconductivity.Similarly,theconstantofproportionality
inFick’slawisdefinedasanothertransportpropertycalledthebinarydiffusion
coefficientormassdiffusivity,D
AB.Theunitofmassdiffusivityism
2
/s,whichisthesameasthe
unitsofthermaldiffusivityormomentumdiffusivity(alsocalledkinematicviscosity)

10. ▪Thediffusioncoefficients,ingeneral,arehighestingasesandlowestinsolids.The
diffusioncoefficientsofgasesareseveralordersofmagnitudegreaterthanthose
ofliquids.
▪Diffusioncoefficientsincreasewithtemperature.Thediffusioncoefficient(andthus
themassdiffusionrate)ofcarbonthroughironduringahardeningprocess,for
example,increasesby6000timesasthetemperatureisraisedfrom500°Cto1000°C.
DEPARTMENT OF MECHANICAL ENGINEERING Version: 1, KEC Katihar09