Fractional flow reserve (FFR) has proved its efficiency in improving patients diagnosis. In this paper, we consider a 2D reconstructed left coronary tree with two artificial lesions of different degrees. We use a generalized fluid model with a Carreau law and implement the Windkessel boundary conditions at the outlets. We introduce our methodology to quantify the FFR, and lead several numerical experiments. For two different finite element meshes, we compare the FFR results for Navier Stokes versus generalized flow models, and for Windkessel versus free outlets boundary conditions. We also used mixed boundary conditions. Our results highlight the fact that free outlets boundary conditions are sensitive to the FFR sensor position. The computational FFR results show that the degree of stenosis is not enough to classify a lesion, while there is a good agreement between Navier Stokes and generalized flow model in classifying the lesions.