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What is Mass Transfer?

“Mass transfer specifically refers to therelative motion of species in a mixture dueto concentration gradients.”

Since the principles of mass transfer are very similar to those of heat transfer, the analogy between heatand mass transfer will be used throughout this

module.

Analogy between Heat and Mass Transfer

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Mass transfer through DiffusionConduction Mass Diffusion

sm J

dydT k q

2

(Fourier’s law)

smkg

dyd D j A

AB A 2

(Fick’s law)

is the density of the gas mixture

DAB is the diffusion coefficientis the mass concentration of component A / A A

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Mass transfer through DiffusionA B

A j

B j

The sum of all diffusion fluxes must be zero: 0i j

1 B A

B A dyd

dyd

DBA = D AB = D

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Heat and Mass Diffusion: Analogy

• Consider unsteady diffusive transfer through a layer

Heat conduction, unsteady, semi-infinite plate

2

2

2

2

xT

xT

ck

t T

x

T k

xt

T c

02*

2

2

d d

dyd

t x

4Similarity transformation:PDE → ODE

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Heat and Mass Diffusion: Analogy

Solution:

t x

erf T T T T

u 410

Temperature field

Heat flux T T t kc

T T t k

dxdT

k q uu x x

000

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Heat and Mass Diffusion: Analogy

Diffusion of a gas component, which is brought in contact with another gas layer at time t=0

Transient diffusion2

2

2

2

x D

t

x D

t ii

ii

Differential equation:

Initial and boundary

conditions:

oii

uii

oii

xt

xt

xt

,

,

,

,0

0,0

,0

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Heat and Mass Diffusion: Analogy

Solution:

Concentration field

Diffusive mass flux

Dt xerf

oiu

oii

41

,

,

oiPhi xi Dt D

j ,,0

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Diffusive mass transfer on a surface(Mass convection)

Fick's

Law, diffusive mass flow rate:

Dimensionless mass transfer

number, the Sherwood number Sh

0*

*

0*

y

w

y A y L D

y D j

mass transfer coefficientsm

kghmass 2

wmass A h j

)Sc(Re,Sh0

*

*

* f y D

Lh y

mass

nm ScC Sh Re

Note: Compare with energy eqn. and Nusselt

No.: The constants C and the

exponents m and n of both relationships must be equal for comparable boundaryconditions.

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Diffusive mass transfer on a surface..

Dimensionless number to representthe relative magnitudes of heat andmass diffusion in the thermal andconcentration boundary layers

Comparing the correlation for theheat and mass transfer

Lewis No.

ydiffusivitMassydiffusivitThermal

Pr Sc

Le D

Analogy between heat and mass transfern

Sc NuSh

Pr

1

Pr /

n

p

mass Scch

hHence,

For gases, Pr ≈

Sc, hence: 1

/ p

mass

chh Lewis relation