CHEMICAL ENGINEERING

224 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

D

2 C^0 i

L^2

∫L

0

ysinny/L

dy

2 C^0 i

L

∫L

0

sinny/L

dy

D

2 C^0 i

L^2

∫L

0

^1

2 C^0 i

L

∫L

0

^2

∫L

0

D 1

[



Ly

n

cos

ny

L

]L

0

C

∫L

0

L

n

cos

ny

L

dy

PuttinguDy,duDdy

and: dvDsinny/L
dy, vD

L

n

cos

ny

L

∴

∫L

0

D 1

(



Ly

n

cos

ny

L

)L

0

C

(

L^2

n^2 ^2

sin

ny

L

)L

0

D

L^2

n

cosnC

L^2

n^2 ^2

sinnD

L^2

n

 1

 n

∫L

0

D 2

(



L

n

cos

ny

L

)L

0

D

L

n

cosnC

L

n

D

L

n

cosnC

L

n

D

L

n

 1

 nC

L

n

AnD

2 C^0 i

L^2

 1

2 C^0 i

L

D 2

2 C^0 i

L^2

(



L^2

n

 1

 n

)



2 C^0 i

L

(



L

n

 1

 nC

L

n

)

D 2 C^0 i/n

PROBLEM 10.8

Show that under the conditions specified in Problem 10.7 and assuming the Higbie model
of surface renewal, the average mass flux at the interface is given by:

NA (^) tDCAiCAo
D/L

{

1 C 2 L^2 /^2 Dt

n∑D1

nD 1

[

^2

6



1

n^2

expn^2 ^2 Dt/L^2

]}

Use the relation

∑^1

nD 1

1

n^2

D^2 /6.

Solution

The rate of transference across the phase boundary is given by:

NADD∂CA/∂y

yD 0