Fluid flow and effective permeability of an infinite matrix containing disc-shaped cracks

► Analytical and semi-analytical solutions for flow around elliptical disc-shaped cracks obeying to Poiseuille's law are given ► Differences between Poiseuille's cracks and the limit of flattened ellipsoidal inclusions obeying to Darcy's law are shown. ► Mori-Tanaka and self-consistent estimates for the effective permeability of micro-cracked porous materials are given.