This paper considers a system that involves the attack of water vapor on a graphite cylinder such as occurs in gas-cooled nuclear reactors. Its purpose is to describe such a system, develop a mathematical model for it, and provide a means of solving the model. This is accomplished by first discussing the transport and rate mechanisms of the system: convective transport of reactants by an inert flowing stream, solid-state diffusion into a porous conduit, and chemical reaction with the conduit material. Based on these mechanisms, mass balance equations are written which give a mathematical description of the system. This mathematical model is then solved by two essentially different numerical techniques.