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