CHEMICAL ENGINEERING

244 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

At a pressurePkN/m^2 :

nDPA/ 101. 3 

 1 / 22. 4 

 273 / 293

 D 4. 11 ð 10 ^4 PAkmol/m^3

and: dn/dtD 4. 11 ð 10 ^4 dPA/dt

∴ 4. 11 ð 10 ^4

dPA

dt

D 3. 81 ð 10 ^7  4. 3 PA

∴

∫ 2. 3

0. 8

dPA

 4. 3 PA

D 9. 27 ð 10 ^4 dt

from whichtD604 s10 min

PROBLEM 10.24

A large deep bath contains molten steel, the surface of which is in contact with air. The
oxygen concentration in the bulk of the molten steel is 0.03% by mass and the rate of
transfer of oxygen from the air is sufficiently high to maintain the surface layers saturated
at a concentration of 0.16% by weight. The surface of the liquid is disrupted by gas
bubbles rising to the surface at a frequency of 120 bubbles per m^2 of surface per second,
each bubble disrupts and mixes about 15 cm^2 of the surface layer into the bulk.
On the assumption that the oxygen transfer can be represented by a surface renewal
model, obtain the appropriate equation for mass transfer by starting with Fick’s second
law of diffusion and calculate:

(a) The mass transfer coefficient

(b) The mean mass flux of oxygen at the surface

(c) The corresponding film thickness for a film model, giving the same mass transfer

rate.

Diffusivity of oxygen in steelD 1. 2 ð 10 ^8 m^2 /s. Density of molten steelD7100 kg/m^3.

Solution

IfC^0 is defined as the concentration above a uniform datum value:

∂C^0

∂t

DD

∂^2 C^0

∂y^2

(equation 10.100)

The boundary conditions are:

when tD 0 , 0 <y< 1 C^0 D 0
t> 0 yD 0 C^0 DC^0 i
t> 0 yD1 C^0 D 0
The equation is most conveniently solved using Laplace transforms. The Laplace trans-
formCN^0 ofC^0 is:

CN^0 D

∫ 1

0

eptC^0 dt (equation 10.101)