The high turbine inlet temperature of modern gas turbines poses a challenge to the material used in the turbine blading of the primary stages. Mechanical failure mechanisms are more pronounced at these high temperatures, setting the lifetime of the blade. It is therefore crucial to obtain accurate local metal temperature predictions of the turbine blade. Accurately predicting the external heat transfer coefficient (HTC) distribution of the blade is therefore of uttermost importance. At present time, Siemens Energy uses the boundary layer code TEXSTAN for this purpose. The limitations coupled to such codes however make them less applicable for the complex flow physics involved in the hot gas path of turbine blading. The thesis therefore aims at introducing CFD for calculating the external HTC. This includes conducting an extensive literature study to find and validate a suitable methodology. The literature study was centered around RANS modeling, reviewing how the calculation of the HTC has evolved and the performance of some common turbulence and transition models. From the literature study, the SST k − ω model in conjunction with the γ − Reθ transition model, the v2 − f model and the Lag EB k − ε model were chosen for the investigation of a suitable methodology. The validation of the methodology was based on the extensively studied LS89 vane linear cascade of the von Karman Institute. In total 13 test cases of the cascade were chosen to represent a wide range of flow conditions. Both a periodic model and a model of the entire LS89 cascade were tested but there were great uncertainties whether or not the correct flow conditions were achieved with the model of the entire cascade. It was therefore abandoned and a periodic model was used instead. The decay of turbulence intensity is not known in the LS89 cascade. This made the case difficult to model since the turbulence boundary conditions then were incomplete. Two approaches were attempted to handle this deficiency, where one was ultimately found invalid. It was recognized that the Steelant-Dick postulation could be used in order to find a turbulent length scale which when specified at the inlet, lead to fairly good agreement with data of the HTC. The validation showed that the SST γ − Reθ model performs relatively well on the suction side and in transition onset predictions but worse on the pressure side for certain flow conditions. The v2 − f model performed better on the pressure side and on a small portion of the suction side. Literature emphasized the importance of obtaining proper turbulence characteristics around the vane for accurate HTC-predictions. It was found that the results of the validation step could be closely coupled to this statement and that further work is needed regarding this. Further research must also be done on the Steelant-Dick postulation to validate it as a reliable method in prescribing the inlet length scale.