The present study aims to support the designer in the task of maximizing film cooling effectiveness of turbine blades; this is accomplished by predicting the temperature field in the blade wall as influenced by heat convection to and from the blade wall and conduction of heat within the blade wall. This study provides a general overview and some insight. It should also be useful for preliminary design studies and can serve as a starting point to a more extensive analysis. The temperature variation along a thin blade wall is described by a one-dimensional heat conduction equation with the solution presenting the dimensionless wall temperature field as a function of a Biot number, provided that the local variation of the convective heat transfer coefficient is prescribed. The thus determined wall temperature distribution exhibits two-dimensional ridges. It is of special interest to find to what degree these ridges are reduced by heat conduction in the wall. The answer to this is presented by simple expressions provided that the shapes of the ridges are approximated by sine curves for groups of ridges (as occurs in film cooling downstream of the cooling hole) or by Gaussian functions for single ridges (as occurs at the leading edge of the blade or at the streamwise location of boundary layer transition).
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