Steady-state simulations of convection, diffusion and first-order irreversible heterogeneous chemical reaction are presented for catalytic channels with rectangular cross section and nonuniform catalyst activity. Finite difference results from the microscopic three-dimensional mass transfer equation also satisfy the cross-section-averaged one-dimensional form of the same equation. Comparisons between viscous flow and plug flow in square cross-section channels suggest how previous inferences of surface-averaged reaction velocity constants from plug flow simulations should be modified when convective diffusion in the mass transfer boundary layer adjacent to the catalytic surface is modeled correctly. Over the following range of Damkohler numbers (i.e., 20 to 10(3) ), viscous flow in rectangular ducts with aspect ratios between two and three can be approximated by the corresponding problem in tubes with the same effective diameter. For Damkohler numbers between 0.5 and 10(3) , aspect ratios greater than 20 are required to simulate viscous flow between two parallel plates with catalyst coated on both walls. At low Damkohler numbers where reactant diffusion toward the catalytic surface is not the rate-limiting step, nonuniform activity profiles suggest that most of the catalyst should be deposited in regions that are easily accessible to the reactants. However, this strategy for converting reactants to products is not more effective than uniform deposition in the diffusion-limited regime.