Existence of multiple solutions for the laminar flow in a porous channel with suction at both slowly expanding and contracting walls

The asymptotic behavior of solutions of a similarity equation for the laminar flow in a porous channel with suction at both expanding and contracting walls has been obtained by using a singular perturbation method. However, in the matching process, this solution neglects exponentially small terms. To take into account these exponentially small terms, a method involving the inclusion of exponentially small terms in a perturbation series was used to find two of the solutions analytically. The series involving the exponentially small terms and expansion ratio predicts dual solutions. Furthermore, the result indicates that the expansion ratio has much important influence on the solutions.