Increasing the turbine inlet temperature of gas turbine engines significantly increases their power output and efficiency, but it also increases the likelihood of thermal failure. Internal passages with tiny ribs are typically cast into turbine blades to cool them, and the ability to accurately predict the flow and heat transfer within these channels leads to higher design reliability and prevention of blade failure resulting from local thermal loading. Prediction of the flow through these channels is challenging, however, because the flow is highly turbulent and anisotropic, and the presence of rotational body forces further complicates the flow. Large Eddy Simulations are used to study these flows because of their ability to predict the unsteady flow effects and anisotropic turbulence more reliably than traditional RANS closure models. Calculations in a stationary duct are validated with experiments in the developing flow, fully developed, and 180° bend regions to establish the accuracy and prediction capability of the LES calculations and to aid in understanding the major flow structures encountered in a ribbed duct. It is found that most flow and heat transfer calculations come to within 10-15% of the measurements, typically showing excellent agreement in all comparisons. In the developing flow region, Coriolis effects are found to destabilize turbulence and increase heat transfer along the trailing wall (pressure side), while decreasing leading wall heat transfer by stabilizing turbulence. Coriolis forces improve flow turning in the 180° bend by shifting the shape of the separated recirculation zone at the tip of the dividing wall and increasing the mainstream flow area. In addition, turbulence is attenuated near the leading wall throughout the bend, while Coriolis forces have little effect on trailing wall turbulence in the bend. Introducing and increasing centrifugal buoyancy in the developing flow region increases trailing wall heat transfer monotonically. Along the leading wall, buoyancy increases the size of the recirculation zones, shifting the peak heat transfer to a region upstream of the rib, which decreases heat transfer at low buoyancy parameters but increases it as the buoyancy parameter is increased beyond a value of 0.3. Centrifugal buoyancy in the 180° bend initially decreases the size of the recirculation zone at the tip of the dividing wall, increasing flow area and decreasing flow impingement. At high buoyancy, however, the recirculation zone shifts to the middle of the bend, increasing flow resistance and causing strong flow impingement on the back wall. The Boussinesq approximation is used in the buoyancy calculations, but the accuracy of the approximation comes into question in the presence of large temperature differences. A variable property algorithm is developed to calculate unsteady low speed flows with large density variations resulting from large temperature differences. The algorithm is validated against two test cases: Rayleigh-Bénard convection and Poiseuille-Bénard flow. Finally, design issues in rotating ribbed ducts are considered. The fully developed assumption is discussed with regard to the developing flow region, and controlling the recirculation zone in the 180° bend is considered as a way to determine the blade tip heat transfer and pressure drop across the bend. / Ph. D.