A transient model based on the finite element method (CFD Comsol) to simulate numerically the flow (momentum equation) and the concentration (diffusion-convection equation) in an ultrafiltration unit is presented. The CFD model was developed by solving the 2D Navier-Stokes equation and the mass conservation equation for transient conditions. A resistance model was used to link the retained protein concentration, the feed and permeate velocity and the pressure at the membrane surface. The ultrafiltration unit consists of a hollow fiber module, a feed tank and a feed pump. In the hollow fiber module, the variable transmembrane pressure, a variable viscosity of the retentate and a polarization layer and a time variable cake occurring on the membrane are considered. Under laminar flow regime, the model allows for the predictions of the velocity fields, the pressure and the concentration along the membrane fiber. The model predictions for the transient permeate flux and the pressure profile in the fiber are compared to experimental data during the concentration of soy protein extracts in a hollow fiber module where total retention of the soy protein is achieved. The comparison shows that the proposed model fits well with the experiments and shows the interest to take into account the variation of resistance and the concentration dependant viscosity flux. The model shows that the transmembrane pressure is an important element on the polarization concentration profile and that a constant transmembrane pressure yields erroneous conclusion on the concentration polarization. The model alleviates some limitations on the polarization modeling avoiding the need to estimate the polarization thickness in the computation of the polarization resistance. The flexibility of the current model is only limited by the ability of the user to accurately define the variations of the properties of the system for industrial applications. (C) 2009 Elsevier B.V. All rights reserved.