Answer:
Explanation:
SO; If we assume that:
P should be the diffusion of oxygen towards the surface ; &
Q should be the diffusion of carbondioxide away from the surface.
Then the total molar flux of oxygen is illustrated by
:
where;
r is the radial distance from the center of the carbon particle.
Since ;
; we have:
The system is not steady state and the molar flux is not independent of r because the area of mass transfer is not a constant term.
Therefore, using quasi steady state assumption, the mass transfer rate is assumed to be independent of r at any instant of time.
= constant
The oxygen concentration at the surface of the coal particle will be calculated from the reaction at the surface.
The mole fraction of oxygen at a location far from pellet is 1.
Thus, separating the variables and integrating result into the following:
The mole of oxygen arrived at the carbon surface is equal to the mole of oxygen consumed by the chemical reaction.
Obtaining the total gas concentration from the ideal gas law; we have the following:
where;
R=
The steady state molar consumption rate is: