This work presents a numerical procedure to optimize the shape of two-dimensional channel with periodic ribs mounted on both of the walls to enhance turbulent heat transfer. The response surface method is used as an optimization technique with Reynolds-averaged Navier-Stokes analysis of flow and heat transfer. Standard k-epsilon. turbulence model is used as a turbulence closure. Computational results for overall heat transfer rate show good agreements with experimental data. The width-to-height ratio of the rib, rib height-to-channel height ratio, pitch-to-rib height ratio and distance between opposite ribs to rib pitch ratio are chosen as design variables. The objective function is defined as a linear combination of heat-transfer and friction-loss related terms with weighting factor. D-optimal design is used to reduce the data points, and, with only 36 points, reliable response surface is obtained. Optimum shapes of the channel have been obtained in the range from 0.0 to 0.1 of weighting factor. In the weighting factor range where designer's goal is shifted to reduction of pressure loss, both of pitch-to-rib height ratio and distance between opposite ribs to rib pitch ratio reach almost constant values. (C) 2004 Elsevier Ltd. All rights reserved.