QuaLiKiz, a model based on a local gyrokinetic eigenvalue solver (Bourdelle et al 2002 Nucl. Fusion 42 892-902) is expanded to include momentum flux modeling in addition to heat and particle fluxes (Bourdelle et al 2007 Phys. Plasmas 14 112501, Casati et al 2009 Nucl. Fusion 49 085012). Essential for accurate momentum flux predictions, the parallel asymmetrization of the eigenfunctions is successfully recovered by an analytical fluid model. This is tested against self-consistent gyrokinetic calculations and allows for a correct prediction of the E * B shear impact on the saturated potential amplitude by means of a mixing length rule. Hence, the effect of the E * B shear is recovered on all the transport channels including the induced residu...