CHEMICAL ENGINEERING

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