Fully turbulent channel flow is a very common and effective way to investigate the boundary layer flow over the flat plates. Mean flow characteristics of the channel flow can be predicted using steady Reynolds Averaged Navier-Stokes (RANS) simulations although the turbulent flow has an unsteady nature. The objective of the present study is to evaluate the predictive capability of the turbulence models, which are based on RANS decomposition, in channel flow involving smooth surfaces. The study covers the application of the Reynolds-stress based second-moment turbulence closure model and the most preferred linear eddy viscosity models to determine the mean flow characteristics. The turbulence properties were compared with the DNS data obtained from the open literature. Also, an iterative study was performed for the fine-tuning of the coefficients appearing in the Reynolds-stress turbulence model. A tuned version of the Reynolds-stress model for two different frictional Reynolds numbers (Reτ) of 180 and 590 is presented. These studies will form a basis for further computations on the channel flow with a higher Reynolds number range and different channel sections. They will also serve as the initial steps for the future experimental and computational studies that will focus on the understanding of the flow mechanism over the dimpled surfaces at Reynolds numbers (based on half channel height and mean bulk velocity) up to 2.105.