CHEMICAL ENGINEERING

252 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

CAxatyD0 is now a variable

yD1,CAD 0

Hence: AD0andCNADCNAxe

p

p/D

y

and:

dCNA

dy

D

√

p

D

CNAxe

p

p/D

y

and:

(

dCN 1

dy

)

yD 0

D

√

p

D

CNAx

To maintain mass balance at the film boundary:

D

L

CAiCAx DD

(

∂CA

∂y

)

yD 0

Taking Laplace transforms:

D

L

(

CAi

p

CNAx

)

DD

(

∂CNA

∂y

)

yD 0

D

√

pDCNAx

So:

D

L

CAi

p

D

(

D

L

C

√

pD

)

CNAx

and: CNAxD

D

L

CAi

p

D

L

C

p

pD

Hence:

dCNAx

dy

D

√

p

D

D

L

CAi

p

1

D

L

C

p

pD

e

p

p/D

y

DCAi

1

p

p

1 /L

p

D

L

C

p

p

e

p

p/D

y

Inverting:

∂CA

∂y

D

CAi

L

ey/LeDt/L

2

erfc

(p

Dt

L

C

y

2

p

Dt

)

NA (^) yD 0 DD

(

∂CA

∂y

)

yD 0

DCAi

D

L

eDt/L

2

erfc

(p

Dt

L

)

CAi

D

L

eDt/L

2

erfc

(p

Dt

L

)

√

D

t

CAi

D 0. 16