In this paper, the dimensionless reaction rate density of a two-dimensional channel with catalyst on its boundary was maximized by optimizing its aspect ratio H/L. Order of magnitude expressions in the limit of small H/L and in the limit of large H/L were developed and then intersected to predict the optimal aspect ratio and maximum reaction rate. Numerical simulations were performed and the results corroborated very well with the scale analysis. The results showed that the optimal design of microreactors depends on the Schmidt number (Sc), the Bejan number (Be) and the Catalyst number (Ct). Correlations based on those numbers are proposed. The analysis was performed for steady-state laminar flows, using the dilute species assumption and a first order kinetic expression. (C) 2012 Elsevier Ltd. All rights reserved.