CHEMICAL ENGINEERING

MASS TRANSFER 257

(b) For an age range of surface from 0 to 2/s, application of equation (ii) gives:

1 DK

∫ 2 /s

0

estdtDK

[

est

s

] 2 /s

0

D

K

s

 1 e^2

or: KD

s

1 e^2

and: ft
D

s

1 e^2

est

ThusNAfrom equation (ii) is multiplied by factor 1/ 1 e^2 or:

NAD

1

1 e^2

p

DsCAD 1 .16 times the value in equation 3.

The mass transfer rate per unit total area of surface is:

NAD

∫ 2 /s

0

(√

D

t

CA

)

 1. 16 sestdt

D

√

D



1. 16 sCA

∫ 2 /s

0

t^1 /^2 estdt

Putting: stDˇ^2

then: t^1 /^2 D

p

s

ˇ

and: sdtD 2 ˇdˇ

Integrating:

∫p 2

0

p

s

ˇ

eˇ

22 ˇ

s

dˇD

2

p

s

∫p 2

0

eˇ

2

dˇ

D

2

p

s

p



2

erf

p

2

D

√



s

erf

p

2

NAD

√

D



1. 16 s

√



s

CAerf

p

2 D 1. 16 ð 0. 954

p

DsCA

D 1. 107

p

DsCA

The mass transfer coefficient,hDD 1. 107

p

Ds, an increase of 10.7%

(c) For probability of surface renewal being linearly related to age,sDkt(wherekis a
constant)
Equation (i) becomes:
f^0 t
Cktft
D 0.

The integrating factor is: e

∫

ktdtDekt^2 / 2

ekt

(^2) / 2
ft
DK
and: ft
DKekt
(^2) / 2