$2.$ A cylindrical geometry has component A and B$.$ A and B react to give C in the geometry. By the end of the cylinder, the reaction $($A$+$B $$C$)$ is catalyzed further and completely converts to C$.$ Assuming no radial change in concentration of A and B$,$ derive the concentration of A and B in the cylinder under steady state. At the entrance of the cylinder, the concentration of A and B are equal. Solve $($i$)$ neglecting convective flux; $($ii$)$ not neglecting convective flux.