Gas turbines (GT) play a crucial role in the transition to fully sustainable energy. Conversely, the expected growth of the GT market is met with more stringent regulatory requirements. Clearly, an increasing turbine inlet temperature (TIT) is beneficial for the efficiency of GT cycles. With increasing TIT, however, the magnitude of the thermal loads becomes unbearable, causing thermal fatigue of the component in a transient setting such as GT start-up or shut-down. Therefore, it is crucial that the thermal loads are well managed, which is typically achievable only by adequate external and internal cooling. Generally, such cooling systems are modeled in the industry using an uncoupled heat transfer (HT) approach, assuming that the heat coefficients (HTCs) are only influenced by the aerodynamics of the flow field: HTCs are obtained in a separate computational fluid dynamics (CFD) simulation and are extracted and mapped on the solid domain of the component. Firstly, the report presents a comparison between the uncoupled approach and the increasingly popular conjugate heat transfer (CHT) approach, in which the fluid and solid domains are solved in a single simulation. To do so, the commercial code (STAR-CCM+) is first validated for both laminar flat plate and turbulent offset jet in a steady-state setting. The latter is done by comparing three Reynolds-Averaged Navier-Stokes (RANS) models. The popular wall treatment methods: blended and high-y+ wall functions (WFs) are also compared. The comparison between the two HT methodologies is done by a parameter sensitivity study, involving the thermal conductivity of the solid (for both laminar and turbulent cases), Turbulent Prandtl number, and turbulence intensity. It was concluded that the realizable k-epsilon model is the most accurate for this flow. Conjugation played a marginal role for all parameters. with only a considerable difference in the stagnation regions, when the solid conductivity is low. The results using a high-y+ WF displayed high numerical dissipation due to the coarse mesh size and hence the difference between the HT methodologies was artificially low. It is therefore advised that the study of the high-y+ WF is repeated on a different flow arrangement/setting (e.g. increased inlet velocity). Secondly, the thesis details a study around the internal cooling of Siemens GT transition piece (TP), using CHT. An introduction of perpendicular ribs into a fully developed turbulent channel flow can theoretically significantly increase the heat transfer coefficient through the introduction of large-scale vortices downstream. An optimization routine was run with a hybrid algorithm to study the effect of different rib configurations in a steady RANS simulation, aiming to minimize both mass flow and transition bond coat temperature. The performance is compared to the baseline smooth channels used in the Siemens TP. No better results were achieved for both objective functions in comparison to the baseline case mostly due to the length of the channels. However, a considerable decrease in the coolant consumption was present with a limited increase in the BC temperature. The study showed that the optimization of such ribs can minimize the effect of skin friction (which influences the amount of coolant), and presents a possible further improvement of the TP cooling, without relying solely on the experience of the designer.