The convection-diffusion equations with wall reaction are solved for the case of fully developed laminar flow in monoliths having smooth (circular or flat plate) as well as geometries with sharp corners (triangular, rectangular, square, or sinusoidal). The circumferentially averaged Nusselt/Sherwood numbers along the channel length are calculated and their dependency on the local Damkohler number (phi(s)(2)), solid to fluid conductivity ratio (kappa = k(s)/k(f)), and monolith aspect ratio (d(h)/L) is studied. As these parameters are varied, the asymptotic Sherwood/Nusselt numbers are bounded by the constant flux (Sh(H2)/Nu(H2)), the axially constant flux (Sh(H1)/Nu(H1)), and the constant wall temperature (Sh(T)/Nu(T)) asymptotes. For asymmetric geometries, the difference between Nu(H2) and Nu(H1) is a measure of the nonuniformity of ignition in the circumferential direction for kappa = 0. When wall conduction. is significant (K ! 10), ignition can be predicted accurately by using Nu(H1) value in a one-dimensional model, whereas conversion in the mass transfer controlled regime is determined by Sh(T). (C) 2004 American Institute of Chemical Engineers.