MASS TRANSFER 247
When tD 0 , L<y< 0 CADCA 0
When tD 0 , 0 <y<L CAD 0
When t> 0 yDLCADCA 0
When t> 0 yDCLCAD 0
For gasB:
∂CB
∂t
DD
∂^2 CB
∂y^2
When tD 0 L<y< 0 CBD 0
When tD 00 <y<L CBDCB 0
When t> 0 yDLCBD 0
When t> 0 yDCLCBDCB 0
and for all values ofy:
∂CA
∂y
C
∂CB
∂y
D 0
As in previous problems, these equations may be solved by the use of Laplace transforms.
Fory>0:
CNADAe
p
p/D
yCBe
p
p/D
y
and fory<0:
CNADA^0 e
p
p/D
yCB (^0) e
p
p/D
yCC
A 0 /p
The boundary conditions may now be used to evaluate the constants thus:
AD
CA 0 /p
Pe^2
p
p/D
L
2 1 e^2
p
p/D
L
BD
CA 0 /p
2 1 e^2
p
p/D
L
A^0 DB^0 e^2
p
p/D
L
B^0 D
Be^2
p
p/D
LC 1
e^2
p
p/D
LC 1
Substituting these values:
CAD
CA 0
2
n∑D1
nD 0
[
erfc
2 nLCy
2
p
Dt
erfc
2 nC 1
Ly
2
p
Dt
]
This relation can be checked as follows:
(a) WhenyD0:CAD
CA 0
2
∑^1
0
[
erfc
nL
p
Dt
erfc
nC 1
L
p
Dt
]
D
CA 0
2
(b) WhenyDL:CAD 0