use quasi-steady state analysis to find the time for the rod to disappear

A cylindrical graphite (pure carbon) rod of length L and initial radius of r1 (in cm ) is inserted into a flowing air stream at T and total pressure P. The flowing gas creates a stagnant gas bolundary layer of 0.5cm thickness around the external surface of the rod. At this high temperature, the solid carbon oxidizes to carbon dioxide (CO2) gas C(s)+O2(g)CO2(g) The oxidation reaction is limited by the molecular diffusion of the O2 (species A) through the stagnant gas film surrounding the surface of the rod. Outside of the gas film, the bulk composition of the air stream (the mole fraction of O2 is yA1 ) prevails. The density of solid graphite is C and the molecular weight is Mc. The mass diffusivity of oxygen in the gas mixture is DAB. The rate of the reaction between carbon and oxygen at this temperature is so high that the concentration of oxygen at the rod is essentially zero. Use a quasi-steady state analysis to find the time for the rod to disappear. In the unsteady state portion, you do not need to do the final integration on r for full credit; however, clearly show the integral and the limits of integration