This study attempts to understand one of the most fundamental and challenging problems in fluid flow and heat transfer for rotating machines. The study focuses on gas turbines and electric generators for high temperature and high energy density applications, respectively, both which employ rotating cooling channels so that materials do not fail under high temperature and high stress environment. Prediction of fluid flow and heat transfer inside internal cooling channels that rotate at high rotation number and high density ratio similar to those that are existing in turbine blades and generator rotors is the main focus of this study. Both smooth-wall and rib-roughened channels are considered here. Rotation, buoyancy, bends, ribs and boundary conditions affect the flow inside theses channels. Ribs are introduced inside internal cooling channel in order to enhance the heat transfer rate. The use of ribs causes rapid increase in the supply pressure, which is already limited in a turbine or a generator and requires high cost for manufacturing. Hence careful optimization is needed to justify the use of ribs. Increasing rotation number (Ro) is another approach to increase heat transfer rate to values that are comparable to those achieved by introduction of ribs. One objective of this research is to study and compare theses two approaches in order to decide the optimum range of application and a possible replacement of the high-cost and complex ribs by increasing Ro. A fully computational approach is employed in this study. On the basis of comparison between two-equation (k-[epsilon] and k-[omega]) and RSM turbulence models, against limited available experimental data, it is concluded that the two-equation turbulence models cannot predict the anisotropic turbulent flow field and heat transfer correctly, while RSM showed improved prediction. For the near wall region, two approaches with standard wall functions and enhanced near wall treatment were investigated. The enhanced near wall approach showed superior results to the standard wall functions approach. Thus RSM with enhanced near wall treatment is validated against available experimental data (which are primarily at low rotation and buoyancy numbers). The model was then used for cases with high Ro (as much as 1.29) and high-density ratios (DR) (up to 0.4). Particular attention is given to how turbulence intensity, Reynolds stresses and transport are affected by Coriolis and buoyancy/centrifugal forces caused by high levels of Ro and DR. Variations of flow total pressure along the rotating channel are also predicted. The results obtained are explained in view of physical interpretation of Coriolis and centrifugal forces. Investigation of channels with smooth and with rib-roughened walls that are rotating about an orthogonal axis showed that increasing Ro always enhances turbulence and the heat transfer rate, while at high Ro, increasing DR although causes higher turbulence activity but does not necessarily increase Nu and in some locations even decreases Nu. The increasing thermal boundary layer thickness near walls is the possible reason for this behavior of Nu. The heat transfer enhancement for smooth-wall cases correlates linearly with Ro (with other parameters are kept constant) and hence it is possible to derive linear correlation for the increase in Nu as a function of Ro. Investigation of channels with rib-roughened walls that rotate about orthogonal axis showed that 4-side-average Nur correlates with Ro linearly, where a linear correlation for Nur/Nus as a function of Ro is derived. It is also observed that the heat transfer rate on smooth-wall channel can be enhanced rapidly by increasing Ro to values that are comparable to the enhancement due to the introduction of ribs inside internal cooling channels. This observation suggests that ribs may be unnecessary in high-speed machines, and has tremendous implications for possible cost savings in these machines. In square channels that rotate about parallel axis, the heat transfer rate enhances with Ro on three surfaces of the square channel and decreases on the inner surface (that is the one closest to the axis of rotation). However, the four-sides average Nu increases with Ro. Increasing wall heat flux at high Ro does not necessarily increase Nu on walls although higher turbulence activity is observed. This study examines the rich interplay of physics under the simultaneous actions of Coriolis and centrifugal/buoyancy forces in one of the most challenging internal flow configurations. Several important conclusions are reached from this computational study that may have far-reaching implications on how turbine blades and generator rotors are currently designed. Since the computation study in not validated for high Ro cases, these important results call for a experimental investigation.