CHEMICAL ENGINEERING

MASS TRANSFER 225

According to the Higbie model, if the element is exposed for a timete, the average
rate of transfer is given by:

NAD

1

te

∫te

0

D∂C/∂z

zD 0 dt

From Problem 10.7, the concentrationCis:

CDCAoCCAiCAo

[

1 

y

L



2



∑^1

nD 0

1

n

expn^2 ^2 Dte/L^2 sinny/L

]

∂C

∂y

DCAiCAo

[



1

L



2



∑^1

nD 0



L

expn^2 ^2 Dte/L^2 cosny/L

]

(

∂C

∂y

)

yD 0

DCAiCAo

[



1

L



2



∑^1

0



L

expn^2 ^2 Dte/L^2

]

NAD

DCAiCAo

te

∫te

0

[



1

L



2



∑^1

0



L

expn^2 ^2 Dte/L^2

]

dt

D

DCAiCAo

te

[



te

L



2



∑^1

0



L

(



L^2

n^2 ^2 D

)

expn^2 ^2 Dte/L^2

]te

0

D

DCAiCAo

te

[



te

L



2



∑^1

0

(



L

n^2 D

)

expn^2 ^2 Dte/L^2 C

2



∑^1

0



L

(



L^2

n^2 ^2 D

)]

NAD

D

L

CAiCAo

{

1 C

2 L^2

^2 Dte

[ 1

∑

0

 1

n^2

expn^2 ^2 Dte/L^2 C

∑^1

0

1

n^2

]}

∑^1

0

 1

n^2

expn^2 ^2 Dte/L^2 C

∑^1

0

1

n^2

D

∑^1

0

 1

n^2

expn^2 ^2 Dte/L^2 C

∑^1

1

 1

n^2

expn^2 ^2 Dte/L^2 C

∑^1

0

1

n^2

C

∑^1

1

1

n^2

Dexp^2 Dte/L^2 C

∑^1

1

 1

n^2

expn^2 ^2 Dte/L^2 C 1 C^2 / 6

D

∑^1

1

[

^2

6



1

n^2

expn^2 ^2 Dte/L^2 C 1 exp^2 Dte/L^2

]

Considering the terms 1exp^2 Dte/L^2 and Dte/L^2 to be very small so that
^2 Dte/L^2 is small and exp^2 Dte/L^2 !1. Therefore, 1exp^2 Dte/L^2 is