Variational treatment of chemical reaction and diffusion in a catalytic tubular reactor

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The boundary method of Galerkin is used to approximate the solution of the elliptic boundary value problem associated with a two-dimensional laminar flow tubular reactor with axial and radial diffusion, a first-order homogeneous reaction, and a first-order heterogeneous reaction at the wall. It is shown that this method yields asymptotic solutions (for the concentration of the species of interest) directly. Furthermore, it is shown that a one-dimensional treatment of this problem yields an asymptotic solution that is several orders of magnitude at variance with the more rigorous two-dimensional treatment.