In the present study, the second order response surface method (RSM) is carried out to get optimum thermal design for enhancing heat transfer in a square channel with bleed flow. The RSM is used as an optimization technique. To calculate the heat transfer, RNG k-epsilon model and enhanced wall function are used. To design optimum rib turbulators, two design variables such as attack angle of rib $({alpha})$ and rib pitch-to-rib height ratio (p/e) are optimized. In these analyses, the channel inlet Reynolds number was fixed at 10,000 in both non-bleeding and bleeding cases. The response surfaces of two design variables are constructed in cases with and without bleed flow. As a result, the optimum (or highest) heat transfer values are almost the same in ranges of two cases with and without bleed flow. However, the friction losses in the case with bleed flow are lower than those without bleed flow.