In this thesis a numerical study has been undertaken to investigate turbulent flow and heat transfer in a number of flow problems, representing the gas-cooled reactor core flows. The first part of the research consisted of a meticulous assessment of various advanced RANS models of fluid turbulence against experimental and numerical data for buoyancy-modified mixed convection flows, such flows being representative of low-flow-rate flows in the cores of nuclear reactors, both presently-operating Advanced Gas-cooled Reactors (AGRs) and proposed 'Generation IV' designs. For this part of the project, an in-house code ('CONVERT'), a commercial CFD package ('STAR-CD') and an industrial code ('Code_Saturne') were used to generate results. Wide variations in turbulence model performance were identified. Comparison with the DNS data showed that the Launder-Sharma model best captures the phenomenon of heat transfer impairment that occurs in the ascending flow case; v^2-f formulations also performed well. The k-omega-SST model was found to be in the poorest agreement with the data. Cross-code comparison was also carried out and satisfactory agreement was found between the results.The research described above concerned flow in smooth passages; a second distinct contribution made in this thesis concerned the thermal-hydraulic performance of rib-roughened surfaces, these being representative of the fuel elements employed in the UK fleet of AGRs. All computations in this part of the study were undertaken using STAR-CD. This part of the research took four continuous and four discrete design factors into consideration including the effects of rib profile, rib height-to-channel height ratio, rib width-to-height ratio, rib pitch-to-height ratio, and Reynolds number. For each design factor, the optimum configuration was identified using the 'efficiency index'. Through comparison with experimental data, the performance of different RANS turbulence models was also assessed. Of the four models, the v^2-f was found to be in the best agreement with the experimental data as, to a somewhat lesser degree were the results of the k-omega-SST model. The k-epsilon and Suga models, however, performed poorly. Structured and unstructured meshes were also compared, where some discrepancies were found, especially in the heat transfer results. The final stage of the study involved a simulation of a simplified 3-dimensional representation of an AGR fuel element using a 30 degree sector configuration. The v^2-f model was employed and comparison was made against the results of a 2D rib-roughened channel in order to assess the validity and relevance of the precursor 2D simulations of rib-roughened channels. It was shown that although a 2D approach is extremely useful and economical for 'parametric studies', it does not provide an accurate representation of a 3D fuel element configuration, especially for the velocity and pressure coefficient distributions, where large discrepancies were found between the results of the 2D channel and azimuthal planes of the 3D configuration.