We conducted an optimization using the second-order response surface method to determine the transverse rib geometry required to achieve the highest cooling performance in a circular channel. The best rib geometry was based on three design variables; rib height, rib width, and rib pitch. The turbulent heat transfer coefficients and friction losses were first calculated and then used to determine the thermal performance. We constructed the response surfaces of the three design variables as functions of the average Nusselt number ratio, friction loss, and thermal performance. These functions led to the optimum design point at the highest heat transfer rate in the special case of an actual turbine cooling passage with a constant friction loss. (C) 2010 Elsevier Ltd. All rights reserved.