A two-dimensional (2-D) injection model is used with a 2-D low Reynold's number k-ε model boundary layer code. The three-dimensional effects of the discrete hole injection process is introduced in the 2-D prediction scheme through an "entrainment fraction" (T). An established correlation between T and the injection parameters obtained in a previous paper is used to predict the film cooling effectiveness (η¯) and heat transfer coefficients for multirow injection, injection into a laminar boundary layer and finally injection on convex curved surfaces. Predictions of η¯are in good agreement with experimental data for most of the cases tested. Predictions of Stanton numbers defined by St(0) and St(1) are good for low injection ratios (M) but as M increases the values are underpredicted. In spite of some shortcomings, in the authors' opinion the present 2-D prediction scheme is one of the most comprehensive developed so far. It is seen that the entrainment fraction T is quite universal in its application to 2-D predictions of the discrete hole film cooling process.