CHEMICAL ENGINEERING

MASS TRANSFER 263

Thus:

CAs

p

DB. 1

and: CNAD

CAs

p

e

p

p/Dy.

Inverting:

CA

CAs

Derfc

y

2

p

Dt

See Table in Volume 1, Appendix

Differentiating with respect toy:

1

CAs

∂CA

∂y

D

∂

∂y

{

2

p



∫ 1

y/ 2

p

Dt

ey

(^2) / 4 Dt
d

(

y

2

p

Dt

)

D

2

p



Ð

1

2

p

Dt

ey

(^2) / 4 Dt
D

1

p

Dt

ey

(^2) / 4 Dt
The mass transfer rate att,y,NDD

{

 1

p

Dt

ey

(^2) / 4 Dt

}

CAs

when:t>0, then:

(

D

∂CA

∂y

)

yDy

DCAs

√

D

Dt

ey

(^2) / 4 Dt
i
Att>0andyD0, then: N 0 DCAs

√

D

t

ii

For a concentrated 1% of surface value atyD1 mm,CA/CAsD 0 .01 and:

0. 01 Derfc

{

10 ^3

2

p

1. 5 ð 10 ^9 t

}

Writing erfxD 1 erfcx, then:

0. 99 Derf 12. 91 t^1 /^2

From tables 1. 82 D 12. 91 t^1 /^2

tD 50 .3s

The mass transfer rate at the interface attD 50 .3sisgivenbyequation(ii)as:

N 0 DCAs

√

D

t

DCAs

√

1. 5 ð 10 ^9

ð 50. 3

D 3. 08 ð 10 ^6 CAskmol/m^2 s

The mass transfer rate atyD1mm.andtD 50 .3sisgivenbyequation(i)as:

NDN 0 ey

(^2) / 4 Dt
D 3. 08 ð 10 ^6 e^10
 (^6) / 4 ð 1. 5 ð 10  (^9) ð 50. 3

CAs
D 1. 121 ð 10 ^7 CAswhereCAsis in kmol/m^3.