Chapter 14
Mass Transfer
Steady Mass Diffusion Through a Wall
1442C
The relations for steady onedimensional heat conduction and mass diffusion through a plane wall
are expressed as follows:
Heat conduction
:
Q
k A
T
T
L
cond
= 

1
2
Mass diffusion
:
m
D
A
w
w
L
D
A
L
diff,A,wall
AB
A,1
A,2
AB
A,1
A,2
=

=

ρ
where
A
is the normal area and
L
is the thickness of the wall, and the other variables correspond to each
other as follows:
rate of heat conduction
Q
cond
←→
m
diff,A,wall
rate of mass diffusion
thermal conductivity
k
←→
D
AB
mass diffusivity
temperature
T
←→
A
density of
A
1443C
(
a
) T,
(
b
) F,
(
c
) T,
(
d
) F
1444C
During onedimensional mass diffusion of species
A
through a plane wall of thickness
L,
the
concentration profile of species
A
in the wall will be a straight line when (1) steady operating conditions are
established, (2) the concentrations of the species
A
at both sides are maintained constant, and (3) the
diffusion coefficient is constant.
1445C
During onedimensional mass diffusion of species
A
through a plane wall, the species
A
content of
the wall will remain constant during steady mass diffusion, but will change during transient mass diffusion.
1419
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View Full DocumentChapter 14
Mass Transfer
1446
Pressurized helium gas is stored in a spherical container. The diffusion rate of helium
through the
container is to be determined.
Assumptions
1
Mass diffusion is
steady
and
onedimensional
since the helium concentration in the tank
and thus at the inner surface of the container is practically constant, and the helium concentration in the
atmosphere and thus at the outer surface is practically zero. Also, there is symmetry about the center of the
container.
2
There are no chemical reactions in the pyrex shell that results in the generation or depletion of
helium.
Properties
The binary diffusion coefficient of helium in the pyrex at the specified temperature is 4.5
×
10
15
m
2
/s (Table 143b). The molar mass of helium is
M
= 4 kg/kmol (Table A1).
Analysis
We can consider the total molar concentration
to be constant (
C
=
C
A
+
C
B
2245
C
B
= constant), and the
container to be a
stationary
medium since there is no
diffusion of pyrex molecules (
N
B
=
0 ) and the
concentration of the helium in the container is extremely
low (
C
A
<< 1). Then the molar flow rate of helium
through the shell by diffusion can readily be determined
from Eq. 1428 to be
( .
)( .
.
N
r r D
C
C
r
r
diff
AB
A,1
A,2
2
3
m
m)(4.5
10
m
/ s)
(0.00073
0) kmol / m
1.50
1.45
kmol / s
=


=
×


=
×


4
4
145
150
180
10
1 2
2
1
15
15
π
The mass flow rate is determined by multiplying the molar flow rate by the molar mass of helium,
(
m
MN
diff
diff
kg / kmol)(1.80
kmol / s)
=
=
×
=
×


4
10
15
7.2
10
kg / s
15
Therefore, helium will leak out of the container through the shell by diffusion at a rate of 7.2
×
10
15
kg/s or
0.00023 g/year.
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 Spring '06
 Rajadas

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