Question 10.24: A large deep bath contains molten steel, the surface of whic...
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 m² of surface per second, each bubble disrupts and mixes about 15 cm² 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 steel = 1.2 × 10^{-8} m²/s. Density of molten steel = 7100 kg/m³ .
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