7/31/2019 m 10 Teacher Slides
http://slidepdf.com/reader/full/m-10-teacher-slides 1/10
7/31/2019 m 10 Teacher Slides
http://slidepdf.com/reader/full/m-10-teacher-slides 2/10
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
7/31/2019 m 10 Teacher Slides
http://slidepdf.com/reader/full/m-10-teacher-slides 3/10
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
7/31/2019 m 10 Teacher Slides
http://slidepdf.com/reader/full/m-10-teacher-slides 4/10
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
7/31/2019 m 10 Teacher Slides
http://slidepdf.com/reader/full/m-10-teacher-slides 5/10
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
7/31/2019 m 10 Teacher Slides
http://slidepdf.com/reader/full/m-10-teacher-slides 6/10
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
7/31/2019 m 10 Teacher Slides
http://slidepdf.com/reader/full/m-10-teacher-slides 7/10
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
7/31/2019 m 10 Teacher Slides
http://slidepdf.com/reader/full/m-10-teacher-slides 8/10
Heat and Mass Diffusion: Analogy
Solution:
Concentration field
Diffusive mass flux
Dt xerf
oiu
oii
41
,
,
oiPhi xi Dt D
j ,,0
7/31/2019 m 10 Teacher Slides
http://slidepdf.com/reader/full/m-10-teacher-slides 9/10
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.
7/31/2019 m 10 Teacher Slides
http://slidepdf.com/reader/full/m-10-teacher-slides 10/10
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