Viscous flow in a curved tube filled with a porous medium

Viscous flow in a tube is basic in fluid mechanics. However, there are cases where the tube is filled with a porous medium, such as those in filters, catalytic reactors or matrix-filled biological pores. The boundary condition is that the velocity is zero on the tube wall. The number of terms N taken contains the highest homogeneous powers. Typically 12 terms guarantees a three-figure accuracy. The method adopted would not compute directly the flow in a straight tube, but the straight tube can be approached in the limit of very small tube dimension to curvature radius. Due to curvature, the velocity is not concentric as in a straight tube. The maximum velocity moves from the center towards the curvature axis. An increase in the porous media parameter k decreases the velocity magnitude and further moves the maximum off center. Numerical methods such as finite differences or finite elements can also be used, but they require much more computational effort.