On the nonunique solutions of laminar flow through a porous tube or channel

The equations describing similarity solutions for flow through a uniformly porous tube and channel with equal rates of injection or suction at the walls are analyzed. The number and character of the solutions possible for various values of suction and injection are found. For the channel problem it is shown there is exactly one solution possible for injection and exactly three solutions possible for suction. For the tube problem it is found there are two types of solutions for injection and small suction and at most four possible solutions for large suction under the assumption that the solutions are analytic at zero. It is also shown that for one value of suction no solutions are possible under these assumptions. Numerical integration is then applied to obtain those solutions which have not been completely reported previously.