This study presents a numerical procedure to optimize shape of streamwise periodic ribs mounted on both of the principal walls to enhance turbulent heat transfer in a rectangular channel flow. The response surface method is used as an optimization technique. The optimization is based on Navier-Stokes analysis of flow and heat transfer with $k-{varepsilon}$ turbulence model. The width-to-height ratio of a rib, rib height-to-channel height ratio and rib pitch to rib height ratio are chosen as design variables. The object function is defined as a function of heat transfer coefficient and friction drag coefficient with weighting factor. Optimum shapes of the rib have been obtained for the range of 0.02 to 0.1 of weighting factor.