An analytical method for flow calculations in an annular porous media bounded by a solid outer wall and subject to a countercurrent flow in its inner boundary is presented. The analysis is rigorous and makes it possible to evaluate the effect of the boundaries in the transport capacity of porous channels. The mathematical model is applicable to wicks, such as those found in heat pipes. The paper explores the conditions, that is. the value of critical parameters, under which boundary effects are not negligible and should be taken into account in wick design.