In a tank with molten raw iron, pure oxygen bubbles up$,$ which can be assumed to be spheres with a radius of $1\mathrm{.}5$ cm$.$ Iron contains $5$ mol$\%$ carbon constant at a distance of $4$ times the radius of a bubble, and diffuses to react with oxygen to form CO$2.$ It is considered that both gases, O$2$ and COz, do not interact with the diffusion of carbon in iron, so n$=0$ despite the stoichiometry of the reaction. The flux of carbon over the surface of a spherical oxygen bubble is given by:

NA$|$s $=-$krsC

Where krS$=1\mathrm{.}0$x$10-6$ m$/$s$,$ the diffusion coefficient of C in iron is Das $=7\mathrm{.}5$x$10-9$ ms$.$ The density of cast iron is p $=7874$ kg$/$m$3$ and its molecular weight is $55\mathrm{.}85$ kg$/$kmol$.$

a$)$ Specify the diffusion and reaction model $($heterogeneous or homogeneous$)$ and why it applies to this case.

b$)$ Determine the flux NA if the fraction on the surface of the bubble is Y$\_$As $=0\mathrm{.}0215$

c$)$ Determine the flow again if we assume that the reaction is immediate.