An analytical permeability model is proposed for incompressible flow in porous media. Based on a general non-equilibrium thermodynamic stability theory, the model is derived from maximizing the entropy production rate to achieve a stable system. The resulting formula is in a form similar to previous empirical equations, but with calculable coefficients. Both three-dimensional lid-driven cavity and cubicle natural convection problems have been computed, via a modern computational fluid dynamics (CFD) solver, for numerical investigations of its performance. (C) 2016 Elsevier Ltd. All rights reserved.