The existence of multiple solutions for the laminar flow in a uniformly porous channel with suction at both walls

Summary

A numerical investigation is made to establish whether multiple solutions exist for laminar, incompressible, steady flow in a parallel plate porous channel with uniform suction at both walls. For values of the wall suction Reynolds number,R, greater than 12.165 three numerical solutions are observed for eachR, while forR less than 12.165 only one solution for eachR can be found. A method involving the inclusion of exponentially small terms in a perturbation series is used to find two of the solutions analytically, while an appeal to the numerical results gives an indication of how the third solution can be obtained. The series involving the exponentially small terms, as well as predicting dual solutions, gives more accurate analytic results for the skin friction at the channel walls.