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)