In this thesis, the effects of computational domain size and radius ratio on fully developed turbulent flow and heat transfer in a concentric annular pipe are investigated using direct numerical simulation (DNS). To perform DNS, a new parallel computer code based on the pseudo-spectral method was developed using the FORTRAN 90/95 programing languages and the message passing interface (MPI) libraries. In order to study the effects of computational domain size on the turbulence statistics, twelve test cases of different domain sizes are compared. The effects of radius ratio are investigated through a systematic study based on four radius ratios of a concentric pipe. The characteristics of the velocity and temperature fields are examined at two Reynolds number of Re_(D_h ) =8900$ and 17700. The radius ratio affects the interaction of two boundary layers of the concentric annular pipe and has a significant impact on the turbulent flow structures and dynamics. The characteristics of the flow and temperature fields are investigated in both physical and spectral spaces, which include the analyses of the first- and second-order statistical moments, budget balance of the transport equation of Reynolds stresses, two-point correlation coefficients, and premultiplied spectra of velocity, vorticity, and temperature fluctuations. It is observed that the scales and dynamics of turbulence structures vary with the radius ratio as well as the surface curvature of the concave and convex walls. The characteristic length scales of the turbulence structures are identified through a spectral analysis.