The present study deals with the effects of wall geometry on the fluid flow and heat transfer in an annulus. Rectangular-rib structural wall roughness on the inner wall is considered. This roughness is characterized by rib height, width and pitch. A detailed parametric investigation of the effect of rib width-to-height ratio on the friction coefficient is performed for different rib pitches. This ratio varies from 0.125 to 6.0. Various rib pitches are considered, from those corresponding to a smooth wall, and up to the pitch-to-rib-height ratio of 16. Examples of various rib heights are also shown. The hydraulic diameter and the flow Reynolds number serve as additional parameters. Numerical simulations are performed using a modified k-ε turbulence model, which makes possible the prediction of flow separation, reattachment and adverse pressure gradients. The model is validated by comparing its results with experimental and numerical results for overall and local flow parameters reported in the literature. The results of the present study indicate that for the given hydraulic diameter of the annulus and flow Reynolds number, the pitch that corresponds to maximal flow resistance depends on the rib width-to-height ratio. It appears that when the width-to-height ratio decreases, this optimal pitch approaches an asymptotic value. On the other hand, the optimum rib distance-to-height ratio remains almost constant. These findings are discussed in context of the available literature. Generalization of the results is attempted through the use of dimensionless groups based on the flow and geometrical parameters of the systems. A correlation for the friction factor is suggested.