CHEMICAL ENGINEERING

MASS TRANSFER 245

Then:

∂CN^0

∂t

D

∫ 1

0

ept

∂C^0

∂t

dt (equation 10.102)

D[eptC^0 ]^10 Cp

∫ 1

0

eptC^0 dtDpCN^0 (equation 10.103)

Since the Laplace transform operation is independent ofy,

∂^2 C^0

∂y^2

D

∂^2 C^0

∂y^2

(equation 10.104)

Taking Laplace transforms of both sides of equation 10.100:

pCN^0 DD

∂^2 CN^0

∂y^2

∂^2 CN^0

∂y^2



p

D

CN^0 D 0

From which: CN^0 DAe

p

p/D

yCBe

p

p/D

y (equation 10.105)

When yD1, CN^0 D0andAD 0

When yD 0 , CN^0 DC^0 i/p and BDC^0 i/p

∴ CN^0 D

C^0 i

p

e

p

p/D

y

dCN^0

dy

D

C^0 i

p

pD

e

p

p/D

y

Inverting:

∂C^0

∂y

D

C^0 i

p

D

ð

1

p

t

ey

(^2) / 4 Dt
(See Volume 1, Appendix Table 12)
The mass transfer rate at the surface,NA (^) tDD

(

∂C^0

∂y

)

yD 0

DC^0 i

√

D

t

at timet

The average rate of mass transfer in timet:

1

t

∫t

0

C^0 i

√

D

t

dtD 2 C^0 i

√

D

t

Taking 1 m^2 of surface, the area disrupted by the bubbles per second is:

120 ð 15 / 10000 D 0. 18 /s

∴Average surface age durationD 1 / 0. 18
D 5 .55 s

C^0 iD 0. 16  0. 03
/ 100 D 0 .0013 kg O 2 /kg steelD 0. 0013 / 32
ð 7100
D 0 .2885 kmol/m^3