Flow Through Star-Shaped Cracks Filled with a Porous Medium

The important problem of the flow through a star-shaped crack is studied. Both clear and porous medium-filled ducts are solved for the first time. An accurate modified Ritz method is used to accommodate concave sharp corners. Flow rates and Poiseuille numbers are determined for star ducts with 2–6 pointy branches. Asymptotic approximations and corner singularities are discussed.